Need help with full trigonometry class

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Chapter 7 Review Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Question 4 0/10 pts 5 99

Rewrite in terms of and

Next Question

cos(x + ) π

3 sin(x) cos(x)

Question Help: Video

Solve for the smallest positive solution.

x =  

Give your answer accurate to two decimal places.

Next Question

sin(5x)cos(9x) − cos(5x)sin(9x) = − 0.45

Question Help: Video

Rewrite as

A =  

=  

Note: should be in the interval

Next Question

−5 sin(x) + 1 cos(x) A sin(x + ϕ)

ϕ

ϕ −π < ϕ < π

Write the product as a sum:

 18 cos(41w)cos(15w) =

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Question 5 0/10 pts 5 99

Question 6 0/10 pts 5 99

Question 7 0/10 pts 5 99

Question 8 0/10 pts 5 99

Next Question

Question Help: Video

Write the sum as a product:

Next Question

cos(23.6s) − cos(8.6s) =

Question Help: Video

Find all solutions to on

=  

Give your answers as a list separated by commas

Next Question

cos(7x) − cos(x) = sin(4x) 0 ≤ x < 2π

3

x

Question Help: Video

Simplify to an expression involving a single trigonometric function.

Next Question

sin(6w) − sin(4w)

cos(6w) + cos(4w)

Question Help: Video

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Question 9 0/10 pts 5 99

Question 10 0/10 pts 5 99

Question 11 0/10 pts 5 99

Solve for the four smallest positive solutions

=  

Give your answers accurate to at least two decimal places, as a list separated by commas

Next Question

sec(4x) − 6 = 0

x

Solve for all solutions

=  

Give your answers accurate to 2 decimal places, as a list separated by commas

Next Question

4 sin2(x) − 10 sin(x) + 4 = 0 0 ≤ x < 2π

x

Question Help: Video

Solve for all solutions

=  

Give your answers accurate to 2 decimal places, as a list separated by commas

Next Question

8 sin2(t) − 2 cos(t) − 5 = 0 0 ≤ t < 2π

t

Question Help: Video

If , x in quadrant I, then �nd (without �nding x)

sin x = 2

5

sin(2x) =

cos(2x) =

tan(2x) =

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Question 12 0/10 pts 5 99

Question 13 0/10 pts 5 99

Question 14 0/10 pts 5 99

Question 15 0/10 pts 5 99

Next Question

Solve for all solutions

=  

Give your answers accurate to at least 2 decimal places, as a list separated by commas

Next Question

4 sin(2ϕ) + 2 cos(ϕ) = 0 0 ≤ ϕ < 2π

ϕ

Question Help: Video

Solve for all solutions

=  

Give your answers accurate to at least 2 decimal places, as a list separated by commas

Next Question

6 cos(2β) = 6 cos2(β) − 1 0 ≤ β < 2π

β

Question Help: Video Video

If for then

Next Question

csc(x) = 4, 90 ∘ < x < 180 ∘ ,

sin( ) = x

2

cos( ) = x

2

tan( ) = x

2

Question Help: Video

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Question 16 0/10 pts 5 99

Question 17 0/10 pts 5 99

A population of rabbits oscillates 33 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 750 rabbits and increases by 120 each year. Find an equation for the population, P, in terms of the months since January, t.

=  

Next Question

P(t)

Question Help: Video

-  

-  

-  

-   a.

b.

c.

d.

Match each graph with it's equation type:

Next Question

(mx + b)sin(5x)

ab x + sin(5x)

sin(5x) + mx + b

(abx)sin(5x)

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Question 18 0/10 pts 5 99

Question 19 0/10 pts 5 99

Find an equation of the form that �ts the data below

x 0 1 2 3 y 6 34 150 746

To �t the data:

a =  

b =  

c =  

Next Question

y = abx + c sin( x)π 2

Find all solutions of the equation The answer is and where is any integer, ,

  ,   ,

  ,   .

Next Question

2 cos x − 1 = 0. A + Bkπ C + Dkπ k 0 < A < C < 2π

A = B =

C = D =

For use a double-angle or half-angle formula to simplify the equation and then �nd all solutions of the equation in the interval The answers are

  ,

  ,

  and

with .

Next Question

sin 2x + cos x = 0, [0, 2π).

x1 =

x2 =

x3 =

x4 =

x1 < x2 < x3 < x4

Question Help: Worked Example 1

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Question 20 0/10 pts 5 99

Question 21 0/10 pts 5 99

Question 22 0/10 pts 5 99

Question 23 0/10 pts 5 99

Find all solutions of the equation The answer is and where is any integer, ,

  ,   ,

  ,   .

Next Question

2 sin x + √3 = 0. A + Bkπ C + Dkπ k 0 < A < C < 2π

A = B =

C = D =

Find all solutions of the equation in the interval

The answer is   ,   and

  with .

Next Question

2 sin2 x − cos x = 1 [0, 2π).

x1 = x2 = x3 =

x1 < x2 < x3

Find all solutions of the equation in the interval

The answer is   ,   and

  with .

Next Question

2 cos 3x = 1 [0, π).

x1 = x2 = x3 =

x1 < x2 < x3

Convert the polar coordinate to Cartesian coordinates.

Enter exact values.

x =  

y =  

(8, ) π

6

Question Help: Worked Example 1

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Question 24 0/10 pts 5 99

Question 25 0/10 pts 5 99

Question 26 0/10 pts 5 99

Question 27 0/10 pts 5 99

Next Question

Convert the Cartesian coordinate (2, 5) to polar coordinates, .

r =  

Enter an exact value.

=  

Next Question

0 ≤ θ < 2π

θ

Question Help: Worked Example 1

Simplify to a single trig function.

Next Question

1 + sin(t)

1 + csc(t)

Simplify to an expression involving a single trig function with no fractions.

Next Question

sin2(t) + cos2(t)

sin2(t)

Simplify to a single trig function.

Next Question

sin(t)

sec(t) − cos(t)

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Question 28 0/10 pts 5 99

Simplify and write the trigonometric expression in terms of sine and cosine:

  . = 1 + cos y

1 + sec y

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Assignment 8.3-8.4: Polar Coordinates and Graphs Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

(20, 393°)

(-20, 213°)

(-20, -147°)

(20,-327°)

(-20, -393°)

(20, 213°)

Which points are the same as (20, 33°)?

. Check all that apply.

Next Question

Convert the polar coordinate to Cartesian coordinates.

Enter exact values.

x =  

y =  

Next Question

(6, ) 3π

4

Question Help: Worked Example 1

Convert the polar coordinate to Cartesian coordinates.

x =  

y =  

Next Question

(7, ) 11π

6

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Question 4 0/10 pts 5 99

Question 5 0/10 pts 5 99

Question 6 0/10 pts 5 99

Question 7 0/10 pts 5 99

Convert the Cartesian coordinate (3, 1) to polar coordinates, .

r =  

Enter an exact value.

=  

Next Question

0 ≤ θ < 2π

θ

Question Help: Worked Example 1

Convert the Cartesian coordinate (5, 4) to polar coordinates,

r =  

Enter exact value.

=  

Next Question

0 ≤ θ < 2π

θ

Question Help: Worked Example 1

Convert the Cartesian coordinate (6, -3) to polar coordinates,

r =  

Enter exact value.

=  

Next Question

0 ≤ θ < 2π

θ

Question Help: Worked Example 1

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Question 8 0/10 pts 5 99

Question 9 0/10 pts 5 99

Question 10 0/10 pts 5 99

Rewrite the Cartesian equation as a polar equation.

=  

Enter theta for if needed.

Next Question

x = − 1

r(θ)

θ

Question Help: Video

Rewrite the polar equation as a Cartesian equation.

Next Question

r = 4 cos(θ)

Question Help: Video

Rewrite the Cartesian equation y = 5x2 as a polar equation.

r(θ) =  

Enter theta for θ if needed.

Next Question

Question Help: Video

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Question 11 0/10 pts 5 99

Question 12 0/10 pts 5 99

Write a polar equation for the graph below. Enter theta for `theta` if needed.

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

`r(theta)` =  

Next Question

Question Help: Video

A curve with polar equation `r=\frac(36 )(9 \sin theta+37 \cos theta)`

represents a line. This line has a Cartesian equation of the form `y = mx + b` ,where `m` and `b` are constants. Give the formula for `y` in terms of `x`. For example, if the line had equation `y = 2x+3` then the answer would be `2*x + 3`.

y =  

Next Question

Question Help: Video

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-  

-  

-  

-  

a. `r=5+4 cos(theta)`

b. `r=9+4 cos(theta)`

c. `r=1+4 cos(theta)`

d. `r=4+4 cos(theta)`

e. `r=4 cos(theta)`

Match each graph with its equation

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Question 13 0/10 pts 5 99

-  

Next Question

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-  

-  

-  

-  

a. `r=cos(2 theta)`

b. `r=cos(5 theta)`

c. `r=sin(6 theta)`

d. `r=cos(6 theta)`

e. `r=cos(7 theta)`

Match each graph with its equation

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Question 14 0/10 pts 5 99

Question 15 0/10 pts 5 99

-  

Next Question

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

Which of the following is the equation for the graph shown above?

`r=1+2 sin(theta)`

`r=3 cos(3 theta)`

`r=3 cos(2 theta)`

`r=1+2 cos(theta)`

`r=3 sin(2 theta)`

Next Question

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-  

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

-  

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

-  

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

-  

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

a. `r=3 sin(2 theta)`

b. `r=1+2 sin(theta)`

c. `r=3 cos(2 theta)`

d. `r=1+2 cos(theta)`

e. `r=3 cos(3 theta)`

Match each graph with its equation

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Question 16 0/10 pts 5 99

-  

1 2 3 4-1-2-3-4

1 2 3 4

-1 -2 -3 -4

Next Question

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-  `r=theta sin(theta)`

-  `r= 5/sqrt(theta)`

-  `r=5 sin(theta/2)`

-  `r = 1+3 cos(3 theta)`

a.

b.

c.

d.

Match each equation with its graph

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Section 8.4 Courtney Garrity

Question 1 0/1 pt 2 99

Question 2 0/1 pt 2 99

Write the vector shown above in component form.

Vector =

Note: In the graph, each box is 1 unit by 1 unit in size

Next Question

Question Help: Video

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Question 3 0/1 pt 2 99

Vector

-  

-  

-  

-  

-  

Vector Combination

a.

b.

c.

d.

e.

u v

q r

s

t p

Match the vectors with one of the combinations of the and vectors from the graph.

Next Question

→p, →q , →r, →s, and →t →u →v

→r

→t

→p

→s

→q

3→u − →v

3→u

→v − 2→u

−→v

→u + →v

Question Help: Video

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Question 4 0/1 pt 2 99

u v

Write the vector shown below as a combination of vectors and shown above

Vector = +

Note: In both graphs, each box is 1 unit by 1 unit in size

Next Question

→u →v

→u →v

Question Help: Video

A vector with magnitude 3 points in a direction 310 degrees counterclockwise from the positive x axis.

Write the vector in component form.

Vector =  

Give each value accurate to at least 1 decimal place

Question Help: Video

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Question 5 0/1 pt 2 99

Question 6 0/1 pt 2 99

Question 7 0/1 pt 2 99

Next Question

Given the vector , �nd the magnitude and angle in which the vector points (measured counterclockwise from the positive x-axis, )

=  

=  

Next Question

→u = ⟨ − 4, − 1⟩

0 ≤ θ < 2π

||→u||

θ

Question Help: Video Video Video Video

A person leaves home and walks 5 miles west, then 2 miles southwest.

How far from home is she?

  miles

In what direction must she walk to head directly home?

  degrees North of East

Next Question

Question Help: Video

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Question 8 0/1 pt 2 99

Question 9 0/1 pt 2 99

A person starts walking from home and walks: 3 miles East 6 miles Southeast 4 miles South 5 miles Southwest 2 miles East

This person has walked a total of   miles

Find the total displacement vector for this walk:  

If this person walked straight home, they'd have to walk   miles

Next Question

Question Help: Video

Three di�erent forces act on an object. They are:

Find the net force on the object (the sum of the forces)

Find what fourth force, would need to be added so the object feels no force, that is, so

=  

Next Question

→F 1 = < − 4, 3 >

→F 2 = < − 6, − 2 >

→F 3 = < 1, − 5 >

Fnet

Fnet =

F4

Fnet = 0

F4

Question Help: Video

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Question 10 0/1 pt 2 99

Question 11 0/1 pt 2 99

Question 12 0/1 pt 2 99

An airplane is heading north at an airspeed of 800 km/hr, but there is a wind blowing from the northeast at 50 km/hr.

The plane will end up �ying   degrees o� course

The plane's speed relative to the ground will be   km/hr

Next Question

Question Help: Video Video

An airplane needs to head due north, but there is a wind blowing from the southwest at 60 km/hr. The plane �ies at an airspeed of 500 km/hr,

To end up due north, the pilot will need to �y the plane   degrees

west of north

Next Question

Question Help: Video Video

As part of video game, the point (6,1) is rotated counterclockwise about the origin through an angle of 20 degrees.

Find the new coordinates of this point

x =  

y =  

Next Question

Question Help: Video

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Two children are throwing a ball back-and-forth straight across the back seat of a car. The ball is being thrown 7 mph relative to the car, and the car is travelling 25 mph down the road.

If one child doesn't catch the ball and it �ies out the window, in what direction does the ball �y (ignoring wind resistance)?

  degrees, measured relative to the car's forward direction

Question Help: Video

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Section 8.3 Courtney Garrity

Question 1 0/1 pt 2 99

Question 2 0/1 pt 2 99

Question 3 0/1 pt 2 99

Question 4 0/1 pt 2 99

Question 5 0/1 pt 2 99

Evaluate the expression and write the result in the form .

Next Question

√−9 a + bi

Question Help: Video

Evaluate the expression and write the result in the form .

Next Question

√−3√−27 a + bi

Question Help: Video

Evaluate the expression and write the result in the form .

Next Question

(1 + 7i) + (4 − 5i) a + bi

Question Help: Video

Evaluate the expression and write the result in the form .

Next Question

( − 6 − 8i) − ( − 3 − i) a + bi

Question Help: Video

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Question 6 0/1 pt 2 99

Question 7 0/1 pt 2 99

Question 8 0/1 pt 2 99

Question 9 0/1 pt 2 99

Evaluate the expression and write the result in the form .

Next Question

( − 1 − 3i)(4 − 2i) a + bi

Question Help: Video

Evaluate the expression and write the result in the form .

Next Question

1 + 2i

7i a + bi

Question Help: Video

Divide: 5 - 5i 3 + 6i

. Write your answer in a + bi form

Next Question

Question Help: Video

Rewrite the complex number `2 e^(1.5 i)` in `a + b i` form

Next Question

Question Help: Video

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Question 10 0/1 pt 2 99

Question 11 0/1 pt 2 99

Write the following numbers in the polar form `re^(i theta)`, `0 \le theta < 2\pi `: (a) ` \frac(1)(6)`

` r = `   , ` theta = `   ,

(b) ` 3\ +\ 3 i`

` r = `   , ` theta = `   ,

(c) ` - 7 + 7 i`

` r = `   , ` theta = `   .

Next Question

Question Help: Video

Calculate `(-2+i)^6`. Give your answer in `a + b i` form

Next Question

Question Help: Video Video

Calculate `sqrt(-4+4i)`. Give your answer in `a + b i` form. Give the solution with smallest positive angle.

Question Help: Video

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Section 8.6 Courtney Garrity

Question 1 0/1 pt 2 99

Question 2 0/1 pt 2 99

Question 3 0/1 pt 2 99

Eliminate the parameter to �nd a simpli�ed Cartesian equation of the form for

The Cartesian equation is =  

Next Question

t y = mx + b

{ x(t) = 8 − t

y(t) = − 3 − 4t

y

Question Help: Video

Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x

=  

Next Question

{ x(t) = 3√t

y(t) = 8t + 4

y(x)

Question Help: Video

Eliminate the parameter t to �nd a Cartesian equation in the form for:

The resulting equation can be written as =  

Next Question

x = f(y)

{ x(t) = − 4t2

y(t) = − 7 + 1t

x

Question Help: Video

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Question 4 0/1 pt 2 99

Question 5 0/1 pt 2 99

Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x

=  

Next Question

{ x(t) = e4t

y(t) = e7t

y(x)

Question Help: Video

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-  

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5

-1 -2 -3 -4 -5

-  

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5

-1 -2 -3 -4 -5

-  

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5

-1 -2 -3 -4 -5

-  

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5

-1 -2 -3 -4 -5

a.

b.

c.

d.

e.

Match equation graph with its parametric equation. Not all equations will be used. All graphs shown for −5 ≤ t ≤ 5

{ x(t) = t + cos(t)

y(t) = t + sin(t)

{ x(t) = t cos(t)

y(t) = t sin(t)

{ x(t) = t3

y(t) = t2

{ x(t) = t3 − t

y(t) = t2

{ x(t) = t2

y(t) = t3

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Question 6 0/1 pt 2 99

Question 7 0/1 pt 2 99

Question 8 0/1 pt 2 99

Next Question

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5

-1 -2 -3 -4 -5

The graph below can be represented by parametric equations of the form

Where a = and b =

Next Question

{ x(t) = a cos(t)

y(t) = b sin(t)

Question Help: Video

The ellipse can be drawn with parametric equations where is written in the

form

with r =

and y(t) =  

Next Question

+ = 1 x2

22 y2

32 x(t)

x(t) = r cos(t)

Question Help: Video

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Question 9 0/1 pt 2 99

Suppose parametric equations for the line segment between and have the form:

If the parametric curve starts at when and ends at at , then �nd , , , and .

Next Question

(6, − 10) (9, 3)

{ x(t) = a + bt

y(t) = c + dt

(6, − 10) t = 0 (9, 3) t = 1 a

b c d

a =

b =

c =

d =

Question Help: Video

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Question 10 0/1 pt 2 99

1 2 3 4 5 6-1-2-3-4-5-6

1 2 3 4 5 6

-1 -2 -3 -4 -5 -6

The plot above is created with the parametric equations

x(t) = a cos(bt) y(t) = c sin(dt)

To acheive this graph,

a =

b =

c =

d =

Hint: b and d are both whole numbers from 1 to 3

Next Question

{

Question Help: Video Video Video Video

A bicycle wheel has radius `R`. Let P be a point on the spoke of a wheel at a distance `d` from the center of the wheel. The wheel begins to roll to the right along the the x-axis. The curve traced out by `P` is given by the following parametric equations:

` {( x(theta) = 25 theta - 15 sin(theta)), (y(theta) = 25 - 15 cos(theta) ) :} `

What must we have for `R` and `d`?

`R` =  

`d` =  

Question Help: Video

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Section 9.4 Courtney Garrity

Question 1 0/1 pt 2 99

Question 2 0/1 pt 2 99

Question 3 0/1 pt 2 99

-  

-  

-  

-  

Determine the shape of each polar curve.

Next Question

r = 8

1 + 3 sin(θ)

r = 8

3 + sin(θ)

r = 8

r = 8

1 + sin(θ)

Question Help: Video

Given the polar equation ,

The eccentricity is  

The equation of the directrix is:  

The shape of the curve is: Select an answer

Next Question

r = 8

6 − 3 cos(θ)

e =

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Question 4 0/1 pt 2 99

Question 5 0/1 pt 2 99

Write a polar equation for a conic having focus at the origin, directrix , and eccentricity .

Type theta for .

Next Question

x = − 2 e = 5

r =

θ

Sketch a graph of . Use the graph to write a Cartesian equation for the conic.

Next Question

r = 40

4 − 6 cos(θ)

Sketch a graph of . Use the graph to write a Cartesian equation for the conic.

r = 16

5 − 3 sin(θ)

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Assignment 7.5: Solving Trigonometric Equations Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Question 4 0/10 pts 5 99

Find all solutions to on the interval .

=  

Give your answers as exact values in a list separated by commas.

Next Question

2 sin(θ) = 1 0 ≤ θ < 2π

θ

Question Help: Video Video

Find all solutions to on the interval .

=  

Give your answers as exact values in a list separated by commas.

Next Question

2 cos(θ) = − √3 0 ≤ θ < 2π

θ

Question Help: Video Video

Solve for , .

=  

Give your answers as values rounded to at least two decimal places in a list separated by commas.

Next Question

t 0 ≤ t < 2π

18 sin(t)cos(t) = 12 cos(t)

t

Question Help: Video

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Question 5 0/10 pts 5 99

Question 6 0/10 pts 5 99

Question 7 0/10 pts 5 99

Solve for all solutions .

=  

Give your answers as exact values in a list separated by commas.

Next Question

2 cos2(x) + 3 cos(x) + 1 = 0 0 ≤ x < 2π

x

Question Help: Video

Solve for all solutions .

=  

Give your answers as values accurate to at least two decimal places in a list separated by commas.

Next Question

12 sin2(w) − 7 sin(w) + 1 = 0 0 ≤ w < 2π

w

Question Help: Video

Solve for all solutions .

=  

Give your answers as values accurate to at least two decimal places in a list separated by commas.

Next Question

4 sin2(x) − 13 sin(x) − 12 = 0 0 ≤ x < 2π

x

Question Help: Video

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Question 8 0/10 pts 5 99

Question 9 0/10 pts 5 99

Solve for all solutions .

=  

Give your answers as values accurate to at least two decimal places in a list separated by commas.

Next Question

cos2(w) = − 4 sin(w) 0 ≤ w < 2π

w

Question Help: Video Video

Solve on .

There are two solutions, A and B, with A < B.

A =  

B =  

Give your answers accurate to 3 decimal places.

Next Question

sin(x) = 0.34 0 ≤ x < 2π

Question Help: Video

Solve on .

There are two solutions, A and B, with A < B.

A =  

B =  

Give your answers accurate to 3 decimal places.

Next Question

cos(x) = − 0.87 0 ≤ x < 2π

Question Help: Video

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Question 10 0/10 pts 5 99

Question 11 0/10 pts 5 99

Question 12 0/10 pts 5 99

Question 13 0/10 pts 5 99

Solve for the smallest three positive solutions.

Give your answers accurate to at least two decimal places, as a list separated by commas.

Next Question

8 cos(5x) = 5

Question Help: Video

Solve for the four smallest positive solutions.

=  

Give your answers accurate to at least two decimal places, as a list separated by commas.

Next Question

3 sin( x) = 2π 3

x

Question Help: Video

Solve for all solutions .

=  

Give your answers accurate to at least 2 decimal places and in a list separated by commas.

Next Question

2 sin(2α) − 3 sin(α) = 0 0 ≤ α < 2π

α

Question Help: Video

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Question 14 0/10 pts 5 99

Question 15 0/10 pts 5 99

Question 16 0/10 pts 5 99

Solve for all solutions .

=  

Give your answers accurate to at least 2 decimal places and in a list separated by commas.

Next Question

6 cos(2w) = 6 cos2(w) − 4 0 ≤ w < 2π

w

Question Help: Video

Solve 2sin2(x) + sin(x) - 1 = 0 for all solutions.

x = +2kπ ; Select an answer  

Give your answers as exact values in a list separated by commas.

Next Question

Question Help: Video

Solve `2cos^2(w)+5cos(w)+3 = 0` for all solutions.

`w` = where Select an answer  

Give your answer as an exact value.

Next Question

Question Help: Video

Solve `2cos^2(x)-cos(x)-3 = 0` for all solutions.

`x` = where `k \in \ZZ`  

Question Help: Video

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Chapter 10 Review Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Find the standard form for the equation of a circle

with a diameter that has endpoints and .

Next Question

(x − h) 2

+ (y − k) 2

= r2

( − 1, 1) (7, 5)

h =

k =

r =

Question Help: Video

Recall the equation for a circle with center and radius . At what point in the �rst quadrant does the line with equation intersect the circle with radius 4 and center (0, 5)?

=

=

Enter your answer correct to 3 decimal places .

Next Question

(h, k) r

y = 0.5x + 5

x

y

Question Help: Video

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Question 4 0/10 pts 5 99

Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola:

The focus is  

The directrix is  

The focal diameter is  

The vertex is  

The axis of symmetry is  

Be sure to enter each answer in the appropriate format. Hint: What is the appropriate notation for a line or a point?

Next Question

18.8y = x 2

Question Help: Video

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Question 5 0/10 pts 5 99

Draw a sketch graph of from the following information:

1.

2. the range of the function is

3. the roots of di�er by 8.

Draw in the symmetry line and indicate all the axis intercepts with a dot.

Next Question

p(x) = ax2 + bx + c

= − 2 b

2a

y ≥ − 3

p(x) = 0

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

6

-1

-2

-3

-4

-5

-6

Question Help: Video

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-  

-  

-  

-  

a.

1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

1

2

3

4

-1

-2

-3

-4

b.

1 2 3 4 5 6-1-2-3-4-5-6

1

2

-1

-2

Match each graph with its equation.

− + = 1 x

2

6 2

y 2

2 2

− + = 1 x

6

y 2

2 2

+ = 1 x

2

6 2

y 2

2 2

− = 1 x

2

6 2

y

2

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Question 6 0/10 pts 5 99

c.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

-1

-2

d.

2 4 6-2-4-6

2

-2

Next Question

Question Help: Video

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Question 7 0/10 pts 5 99

Question 8 0/10 pts 5 99

Write the equation of the hyperbola in standard form

,

Where: h =

k =

a =

b =

Next Question

16x2 − 9y2 − 64x + 90y − 305 = 0

− = 1 (x − h)

2

a2

(y − k) 2

b2

Question Help: Video

2 4 6 8 10-2-4-6-8-10

4

8

12

16

20

-4

-8

-12

-16

-20

x

y

Identify a and b for the hyperbola with equation .

a =

b =

Next Question

− = 1 x2

a2

y2

b2

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Question 9 0/10 pts 5 99

Question 10 0/10 pts 5 99

Find the equation for the parabola that has its focus at the and has directrix at

.

equation is  

Next Question

( − , 6) 45

4

x = 21

4

Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola

Focus =  

Directrix =  

Focal diameter =  

Vertex =  

Axis of symmetry =  

Be sure to enter each answer in the appropriate format. Hint: What is the appropriate notation for a line or a point?

Next Question

−72(y − 1) = (x − 4)2

Question Help: Video Video

is the equation of a circle with center and radius for:

and

and

x2 + y2 − 16x + 6y + 69 = 0 (h, k) r

h =

k =

r =

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Question 11 0/10 pts 5 99

Question 12 0/10 pts 5 99

Question 13 0/10 pts 5 99

Next Question

Question Help: Video

Draw a circle with an equation of .

Next Question

x 2 + y2 − 2y = 8

1 2 3 4 5-1-2-3-4-5

1

2

3

4

5

-1

-2

-3

-4

-5

Question Help: Video Video

Find the equation for the parabola that has its focus at and has directrix .

The equation is:  

Next Question

( , − 5) 5

4 x =

59

4

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-  

-  

-  

a.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

b.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

c.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Match the graphs to their equations

Next Question

= + 1 (y + 3)2

9

(x − 2)2

4

− = 1 (y − 3)2

9

(x − 2)2

4

− = 1 (x − 2)2

9

(y − 3)2

4

Question Help: Video

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Question 14 0/10 pts 5 99

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-  

-  

-  

-  

a.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

b.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

c.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Match the graphs to their equations.

+ = 1 (x + 3)2

9

(y + 2)2

16

+ = 1 (x − 3)2

16

(y + 2)2

9

+ = 1 (x + 3)2

16

(y − 2)2

9

+ = 1 (x − 3)2

9

(y − 2)2

16

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Question 15 0/10 pts 5 99

d.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Next Question

Question Help: Video

Given the ellipse ,

Find the center point:

List the vertices (separated by a comma):

+ = 1 (x − 6)2

4

(y − 4)2

25

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Section 10.4: General Form: Identifying Conics Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Identify the conic with equation .

hyperbola

ellipse

circle

parabola

Next Question

+ (y + 1)2 = 1 (x + 5)

2

14

Question Help: Video

Identify the conic with equation .

parabola

ellipse

hyperbola

circle

Next Question

3x2 + 3y2 − 2x − 6y − 4 = 0

Question Help: Video

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-  

-  

-  

-  

a.

1 2 3 4 5 6-1-2-3-4-5-6

1

2

3

4

-1

b.

1 2 3 4 5-1-2-3-4-5

1

2

3

4

-1

-2

-3

-4

Match each graph with its equation.

+ = 1 x

2

5 2

y

4

+ = 1 x

2

5 2

y 2

5 2

+ = 1 x2

5 2

y 2

4 2

− + = 1 x

2

5 2

y2

4 2

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Question 4 0/10 pts 5 99

c.

1 2 3 4 5-1-2-3-4-5

1

2

3

4

5

-1

-2

-3

-4

-5

d.

1 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

1

2

3

4

5

6

7

8

9

-1

-2

-3

-4

-5

-6

-7

-8

-9

Next Question

Question Help: Video

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Question 5 0/10 pts 5 99

-  

-  

-  

a. black

b. orange

c. green

Match each graph with its equation.

2 4 6 8 10-2-4-6-810

2

4

6

8

10

-2

-4

-6

-8

-10

Next Question

− + = 1 x

2

2 2

y2

6 2

+ = 1 x

2

y 2

6 2

+ = 1 x2

2 2

y2

6 2

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-  

-  

-  

-  

a.

1 2 3 4 5-1-2-3-4-5

1 2 3 4 5 6

-1 -2 -3 -4 -5 -6

b.

1 2 3 4 5-1-2-3-4-5

1

2

3

4

5

-1

-2

-3

-4

-5

Match each graph with its equation.

+ = 1 x

2

5 2

y2

6 2

− = 1 x2

5 2

y 2

6 2

− = 1 x2

5 2

y

6

+ = 1 x

2

5 2

y2

5 2

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Question 6 0/10 pts 5 99

c.

1 2 3 4 5 6-1-2-3-4-5-6

1

2

-1

-2

-3

-4

-5

-6

d.

2 4 6 8 10-2-4-6-810

2 4 6 8 10

-2 -4 -6 -8 -10

Next Question

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Question 7 0/10 pts 5 99

Question 8 0/10 pts 5 99

Identify the type of conic section given by the following equation:

Parabola

Ellipse

Hyperbola

Degenerate Conic

Next Question

x 2

+ 4x + 8y − 28 = 0

Identify the type of conic section given by the following equation:

Parabola

Ellipse

Hyperbola

Degenerate Conic

Next Question

16x 2

+ 4y 2

+ 320x + 24y + 1572 = 0

Identify the type of conic section given by the following equation:

Parabola

Ellipse

Hyperbola

Degenerate Conic

4x 2

− 9y 2

− 16x + 126y − 461 = 0

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Assignment 10.3: The Parabola Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola:

The focus is  

The directrix is  

The focal diameter is  

The vertex is  

The axis of symmetry is  

Be sure to enter each answer in the appropriate format. Hint: What is the appropriate notation for a line or a point?

Next Question

10.4y = x2

Question Help: Video

Find an equation for the parabola that has its vertex at the origin and has its focus at the point: .

Enter your answer as an equation. Note: Answer should be exact...no rounding.

Next Question

(0, − 4.4)

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Question 4 0/10 pts 5 99

Question 5 0/10 pts 5 99

Find the equation for the parabola that has its vertex at the origin and has directrix at .

The equation is:  

Next Question

y = 1

24

Find the equation for the parabola that has its focus at and has directrix

.

The equation is:  

Next Question

( − , 5) 39

4

x = − 25

4

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Question 6 0/10 pts 5 99

Find the focus, directrix, vertex and axis of symmetry for the parabola

Focus =  

Directrix =  

Vertex =  

Be sure to enter each answer in the appropriate format. Hint: What is the appropriate notation for a line or a point?

Graph the parabola. Include the directrix and focus with your graph.

Next Question

12(y − 1) = (x + 1)2

1 2 3 4 5 6-1-2-3-4-5-6

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Question Help: Video

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Find the vertex, focus, and directrix for the following parabolas.

(a)

vertex : 

focus : 

directrix:   

(b)  

vertex : 

focus : 

directrix"   

(c)  

vertex : 

focus : 

directrix"   

(d)  

vertex : 

focus : 

directrix"   

(y − 6) 2

= 20(x − 2)

y 2 − 4y = 4x − 22

(x − 3)2 = 4(y − 5)

x 2 + 40x = 4y − 24

Question Help: Video Video Video Video

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Question 7 0/10 pts 5 99

Question 8 0/10 pts 5 99

Question 9 0/10 pts 5 99

Question 10 0/10 pts 5 99

Next Question

Write the equation of a parabola whose directrix is y = - 10.25 and has a focus at (3, - 5.75).

Next Question

Write the equation of a parabola whose directrix is `x=-2.25` and has a focus at `(-11.75,-4)`.

Next Question

Find the coordinates of the vertex and the focus for the parabola given by the following equation:

`x^2-2x-12y+109 = 0`

Round all answers to 2 places after the decimal point, if necessary.

Coordinates of the vertex: ( , )

Coordinates of the focus: ( , )

Next Question

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Question 11 0/10 pts 5 99

Question 12 0/10 pts 5 99

An arch is in the shape of a parabola. It has a span of 256 meters and a maximum height of 16 meters.

Find the equation of the parabola (assuming the origin is halfway between the arch's feet).

Determine the height of the arch 103 meters from the center. Select an answer

Next Question

An arch is in the shape of a parabola. It has a span of 252 feet and a maximum height of 21 feet.

Find the equation of the parabola.  

Determine the distance from the center at which the height is 11 feet.

Select an answer

Next Question

A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 96 feet across at its opening and 6 feet deep at its center, where should the receiver be placed?

nasa.gov

Find the equation of the parabola.  

How far above the vertex should the receiver be placed? Select an answer

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Assignment 10.2: The Hyperbola Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Write the equation of the hyperbola in standard form

,

Where:

h =

k =

a =

b =

Next Question

36x2 − 25y2 + 72x − 200y − 1264 = 0

− = 1 (x − h)2

a2

(y − k)2

b2

Question Help: Video

3 6 9-3-6-9

1

2

3

-1

-2

-3

x

y

Identify a and b for the hyperbola with equation .

a =

b =

− = 1 x2

a2

y2

b2

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Question 3 0/10 pts 5 99

Next Question

Question Help: Video

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-  

-  

-  

a.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

b.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

c.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Match the graphs to their equations

= + 1 (y + 3)2

4

(x − 2)2

9

− = 1 (x − 2)2

4

(y − 3)2

9

− = 1 (y − 3)2

4

(x − 2)2

9

Question Help: Video Video

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Section 10.1: The Ellipse Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1

2

3

4

5

-1

-2

-3

-4

-5

x

y

Give the equation for the ellipse graphed above.

Next Question

Question Help: Video Video

Given the ellipse ,

Find the center point:

List the vertices (separated by a comma):

Next Question

+ = 1 (x − 4)

2

36

(y − 2) 2

9

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Question 4 0/10 pts 5 99

Question 5 0/10 pts 5 99

Given the ellipse ,

Find the center point:

List the four vertices:

Next Question

+ = 1 (x − 3)2

16

(y − 6)2

25

Write the equation of the ellipse in standard form

,

where: h =

k =

a =

b =

Next Question

36x2 + 25y2 − 72x + 200y − 464 = 0

+ = 1 (x − h)

2

a2

(y − k) 2

b2

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-  

-  

-  

-  

a.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

b.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

c.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

Match the graphs to their equations.

+ = 1 (x − 1)2

1

(y + 3)2

16

+ = 1 (x + 1)2

1

(y − 3)2

16

+ = 1 (x − 1)2

16

(y − 3)2

1

+ = 1 (x + 1)2

16

(y + 3)2

1

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d.

1 2 3 4 5 6 7-1-2-3-4-5-6-7

1 2 3 4 5 6 7

-1 -2 -3 -4 -5 -6 -7

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Assignment 10.0: Circles Courtney Garrity

Question 1 0/10 pts 5 99

Question 2 0/10 pts 5 99

Question 3 0/10 pts 5 99

Question 4 0/10 pts 5 99

Write the equation of the circle centered at with radius 1.

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(3, 7)

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Write the equation of the circle centered at with diameter 20.

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(8, − 1)

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Find the standard form for the equation of a circle

with a diameter that has endpoints and .

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(x − h)2 + (y − k)2 = r2

(0, 2) (3, − 4)

h =

k =

r =

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Question 5 0/10 pts 5 99

is the equation of a circle with center and radius for:

and

and

Graph the circle.

Next Question

x2 + y2 − 6x + 2y + 9 = 0 (h, k) r

h =

k =

r =

1 2 3 4 5 6 7 8 9 10-1-2-3

1 2 3

-1 -2 -3 -4 -5 -6 -7 -8 -9

-10

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Question 6 0/10 pts 5 99

Question 7 0/10 pts 5 99

is the equation of a circle with center and radius for:

and

and

Next Question

3x2 + 3y2 − 6x − 24y − 24 = 0 (h, k) r

h =

k =

r =

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2x2 + 2y2 + 12x + 4y + 12 = 0 is the equation of a circle with center (h, k) and radius r for:

h =  

and

k =  

and

r =  

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Question 8 0/10 pts 5 99

Question 9 0/10 pts 5 99

Recall the equation for a circle with center `(h,k)` and radius `r`. At what point in the �rst quadrant does the line with equation `y = x+3` intersect the circle with radius 3 and center (0, 3)?

`x` =

`y` =

Enter your answer correct to 3 decimal places .

Next Question

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A small radio transmitter broadcasts in a 63 mile radius. If you drive along a straight line from a city 81 miles north of the transmitter to a second city 73 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

miles  

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Draw a circle with an equation of `x^2 + 2 x + y^2 -4 y = 4`.

1 2 3 4 5-1-2-3-4-5

1

2

3

4

5

-1

-2

-3

-4

-5

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Section 8.5 Courtney Garrity

Question 1 1/1 pt 1 99

Question 2 0/1 pt 2 99

Question 3 0/1 pt 2 99

Question 4 0/1 pt 2 99

Let and . Compute the dot product.

30  

Next Question

→a = ⟨ − 3, 3⟩ →b = ⟨ − 8, 2⟩

→a ⋅ →b =

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The vector has length 20 and points at an angle of The vector has length 11 and points at an angle of

=  

Next Question

→u 30 ∘

→v 55 ∘

→u ⋅ →v

Let and .

Find the angle between the vector, in degrees.

°  

Next Question

→a = ⟨ − 2, − 5⟩ →b = ⟨ − 5, 4⟩

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Let and .

Find k so that and will be orthogonal (form a 90 degree angle).

k =  

→a = ⟨1, 4⟩ →b = ⟨ − 1, k⟩

→a →b

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Question 5 0/1 pt 2 99

Question 6 0/1 pt 2 99

Question 7 0/1 pt 2 99

Next Question

Find the magnitude of the projection of onto the vector

Next Question

⟨ − 7, − 7⟩ ⟨ − 5, − 6⟩

Let and .

Find the projection of onto .

< , >

Next Question

→a = ⟨ − 3, 2⟩ →b = ⟨2, − 5⟩

→b →a

proj →a  →b =

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An object is pulled along the ground by exerting a force of 60 pounds a rope that makes a 25° angle with the ground. How much work is done dragging the object 28 feet?

  foot-pounds

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Math25Exam2.pptx

Math25 Unit 2 Take Home Midterm

Due 03/16/2020

All problems worth 1 point except problem 32.

(4 bonus points possible)

6.

28.

Suppose a 13-foot ladder is leaning against a building, reaching to the bottom of a second-floor window 12 feet above the ground. What angle, in radians, does the ladder make with the building?

29.

Suppose you drive 0.6 miles on a road so that the vertical distance changes from 0 to 150 feet. What is the angle of elevation of the road?

30.

A truss for the roof of a house is constructed from two identical right triangles. Each has a base of 12 feet and height of 4 feet. Find the measure of the acute angle adjacent to the 4-foot side.

31..

32. (2 points)

Math25HW14_040120.pptx

HW 14 Law of Sines / Cosines

Math 25

1.

2.

3.

4.

5.

6.

7.

Midterm3Written.doc

Chapter 8 Exam Review

1)

÷

ø

ö

ç

è

æ

=

3

2

,

5

)

,

(

p

q

r

Find the unknown sides and angles of these triangles:

2) You happen to know the radio tower on the top of a building is 30 feet tall. To find how far you are from the building, you measure the angle of elevation to the bottom of the tower to be 20 degrees, and the angle of elevation to the top of the tower to be 23 degrees. How far from the building are you.

3) Convert the polar coordinate

to a Cartesian coordinate

4) Convert the Cartesian coordinate

)

7

,

4

(

)

,

(

-

-

=

y

x

to a polar coordinate

5) Rewrite the equation

9

2

2

=

+

y

x

as a polar equation

6) Rewrite the equation

2

=

x

as a polar equation

7) Rewrite the equation

)

sin(

2

q

=

r

as a Cartesian equation

8) Rewrite the equation

)

2

sin(

q

=

r

as a Cartesian equation (hint: use an identity)

9) Sketch a graph of

)

3

sin(

q

=

r

. For what values of θ is the graph at the origin? The furthest from the origin?

10) Multiply:

(34)(2)

ii

+-

11) Divide:

32

4

i

i

-

+

12) Rewrite in polar form:

512

i

+

13) Rewrite in Cartesian form:

6

7

i

e

p

14) Calculate

4

512

i

+

. Give your answer in a+bi form.

15) Given the vectors shown, sketch

34

uv

-

rr

16) A man walks 5 miles north, 3 miles at 30o north of east, 4 miles southeast, and 2 miles west.

a. Draw a picture showing the man’s path as set of vectors

b. Resolve each vector into components

c. Find the vector showing the man’s total displacement (the vector from where he started to where he ended up)

d. How far is the man from where he started at the end of his walk?

e. In what direction should he walk to get back to his starting position?

17) Parameterize the curve:

2

3

xy

=-

18) Rewrite as a Cartesian equation:

3

1

sin()

xt

ytt

ì

=+

í

=-

î

19) Rewrite as a Cartesian equation:

2cos()

3sin()

xt

yt

=

ì

í

=

î

20) Find a possible equation of the form

sin()

cos()

xat

ybt

=

ì

í

=

î

for:

6

5

3

130o

12

20o

_1178044385.unknown

_1289806091.unknown

_1367394725.unknown

_1367394810.unknown

_1367394916.unknown

_1368973910.unknown

_1367394766.unknown

_1289806464.unknown

_1289806494.unknown

_1360838207.unknown

_1289806274.unknown

_1289806039.unknown

_1289806068.unknown

_1178044502.unknown

_1178043976.unknown

_1178044241.unknown

_1178043849.unknown

parametriceqn_0 (3).pdf

Parametric Equations 8.5 NAME____________________

Parametric equations are a general method for describing any curve.

There are three variables for each “point”, the x direction, the y direction and t, the time it takes

to get to that point.

1. Given the equations tx  4y t  

a. Fill in the following table and graph the points. Indicate the direction of the

curve/line with respect to time by using arrows.

b. Using the two original equations, eliminate the parameter, t, to obtain an equation for

y as a function of x. Does the equation you found match the function you’ve drawn?

2. Find the parametric equations x(t) & y(t) for the line that passes through the point (3,6) ,

when t=0 and (-4, 9), when t = 2. *hint substitute in t & x, t & y for point 1& 2 then solve for a, b, c, d

x(t) = a +bt

y(t) = c + dt

T x y

0

1

2

3

4

Y

X

3. Sketch a graph of sin( )

cos(2 )

x t

y t



 and write it as a Cartesian equation

4. Sketch a graph of sin(2 )

cos( )

x t

y t



 and write it as a Cartesian equation

Classwork82polar.pdf

Math 142 – Polar Coordinates Worksheet Name: ________________________

8.2 Lippman/Rasmussen – W11

1) On the polar grid provided, plot the

following polar points:

A)  

  



6 ,3 

B)  

  



4

5 ,2 

C)  

  

 

3 ,4 

D)  

  

 

6 ,3 

E)  2,4

2) Find the Cartesian coordinates of the polar point  

  



6 ,3 

3) Find the polar coordinates of the Cartesian point (-2, -5)

4) Rewrite the equation 2xy  as a polar equation

5) Rewrite the equation )cos(2 r as a Cartesian equation

6) For each of the equations below, complete a table of values, plot the points, then connect the

points with a smooth curve.

a) )sin(4 r

θ 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6

r

θ π 7π/6 5π/4 4π/3 3π/2 5π/3 7π/4 11π/6

r

b) 1)cos(3  r

θ 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6

r

θ π 7π/6 5π/4 4π/3 3π/2 5π/3 7π/4 11π/6

r

c) )2sin(4 r

θ 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6

r

θ π 7π/6 5π/4 4π/3 3π/2 5π/3 7π/4 11π/6

r

HW02_Math25_012720.pdf

HW02 1.

2.Draw each angle

3. Convert from radians to degrees or degrees to radians. Round solutions to 2 decimals where appropriate

0.75 rad 3 rad 50 rad

rad

radrad

rad

rad

rad

4. If s is the arc length, r is the radius and A is the area, fill in the blanks:

Find s and A – round two 2 decimal places. 5.

Extra Credit

Extra Credit