due by 11pm
Heynay8888
math_4.rtfWA 4, p. 3
Name:
College ID:
Thomas Edison State College
College Algebra (MAT-121-GS)
Section no.:
Semester and year:
Written Assignment 4
Answer all assigned exercises, and show all work.
Dimensions of a garden (see section 1. 5 , Example 1 ) — An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m 2 . Find the dimensions of the garden. [ 4 points]
Width of flower border (see section 1. 5 , Example 1 ) — A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 ft 2 for the border, how wide can the border be? [ 4 points]
Height of a kite (see section 1. 5 , Example 2 ) — Grady is flying a kite on 50 ft of string. Its vertical distance from his hand is 10 ft more than the horizontal distance from his hand. Assuming that the string is being held 5 ft above ground level, find the distance from Grady and its vertical distance from the ground. [ 4 points]
Height of a projectile (see section 1.5, Examples 3 and 4) —A projectile is launched from ground level with an initial velocity of v 0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by
2
0
16.
stvt
=-+
Find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v 0 . Round answers to the nearest hundredth if necessary. [ 4 points]
0
16
v
=
Solve each equation. (See section 1 . 6 , Example s 4–6 .) [ 16 points]
41321
xx
+=-
240
xx
-+=
23122
xx
=+-
2522
xx
-=+-
Solve the equation. (See section 1 . 6 , Example s 8 and 9 .) [ 4 points]
42
310250
xx
+-=
S olve the equation for the indicated variable. Assume all denominators are nonzero. [ 4 points]
2/32/32/3
,
xya
+=
for y
Match the following inequality with its equivalent interval notations ( a–d ). [4 points]
(,6]
-¥-
(,6)
-¥-
[6,)
-¥
(,6]
-¥
The three-part inequality a < x < b means “ a is less than x and x is less than b .” Which one of the following inequalities is not satisfied by some real number x ? [ 4 points]
310
x
-<<
06
x
<<
31
x
-<<-
810
x
-<<-
Solve each inequality. Write each solution set in interval notation. (See section 1 . 7 , Example s 1 and 2 .) [ 8 points]
432
xx
-+³-+
25
1
8
x
x
-
£-
-
Break-even interval—Find all intervals where the product will at least break even. (See section 1 . 7 , Example 3 .) [ 4 points]
The cost to produce x units of baseball caps is
1006000,
Cx
=+
while the revenue is500.
Rx
=
Which of the following inequalities has solution set
?
Æ
[ 4 points]
2
(3)0
x
-³
2
(56)0
x
-£
2
(64)0
x
+>
2
(87)0
x
+<
Solve the following rational inequality. Write the solution set in interval notation. (See section 1 . 7 , Example s 8 and 9 .) [ 4 points]
6
2
35
x
-
£
-
Solve each equation. (See section 1 . 8 , Example 1 .) [ 8 points]
733
x
-=
23
1
34
x
x
+
=
-
The equation
563
xx
-=
cannot have a negative solution. Why? [ 4 points]
Determine the solution set of each equation by inspection. [ 8 points]
xx
-=
xx
-=
2
xx
=
9
x
-=
Solve the inequality. Give the solution set using interval notation. (See section 1 . 8 , Example 2 .) [ 8 points]
3
1
5
x
+<
734
x
->
Write the statement as an absolute value equation or inequality. (See section 1 . 8 , Example 5 .) [ 4 points]
z is no less than 5 units from 4.
