math

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Spring 2020 Name: _________________________ MATH 175 – Final Exam (Show Your Work )

1. Graph quadratic function ( ) 2 1 2 19

5 5 5 f x x x= − + + . Give the (a) vertex, (b) axis, (c) domain, and

(d) range. Then determine (e) the largest open interval of the domain over which the function is increasing,

(f) the largest open interval over which the function is decreasing.

2. Solve 𝟐𝟕𝟑𝒙+𝟐 = 𝟗𝟓𝒙−𝟖. Give the solution to the nearest ten thousandth.

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3. Find EXACT values of the six trigonometric functions for Angle 𝜃 = −1470𝑜 . Rationalize denominators when applicable.

4. (a) Find the approximate value of s, to four decimal places in the interval 0, 2

     

that makes 𝑐𝑜𝑡 𝑠 = 0.3760 a true

statement.

(b) Find the EXACT value of s in the interval [ 3𝜋

2 , 2𝜋] that makes 𝑐𝑜𝑠 𝑠 =

√3

2 a true statement.

Do not use a calculator.

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5. Given 𝑡𝑎𝑛 𝛼 = 15

8 and 𝑡𝑎𝑛 𝛽 =

4

3 ,  and  in quadrant III, find (a) ( )sin  + , (b) ( )tan  + ,

(c) the quadrant of the angle ( ) + .

6. Solve Triangle ABC, given that 𝐴 = 37𝑜 38′, 𝑏 = 12.03 m, 𝑐 = 10.14 m. Give angles in degrees and minutes.

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7. Find the partial fraction decomposition for

5 4 3 2

3 2

3 16 13 7 50 30

5 6

x x x x x

x x x

− − + − −

− −

8. Let 𝐵 = [ −3 9 4 11 7 −6

] and 𝑐 = [ 5 6 −8

−2 4 6 ]. Find BC .

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9. Solve 3 7 20

5 3 84

x y

x y

+ = −  − + = −

by using the inverse of the coefficient matrix

10. Solve {

2𝑥 − 3𝑦 + 2𝑧 = 3 4𝑥 + 8𝑦 + 𝑧 = 2

−𝑥 − 7𝑦 + 3𝑧 = 14 by using the inverse of the coefficient matrix

Given: [ 2 −3 2 4 8 1

−1 −7 3 ]

−1

= 1

61 [

31 −5 −19 −13 8 6 −20 17 28

]