Question 1

Give two parametric representations for the equation of the parabola.
-$$y = x ^ { 2 } - 6 x + 13$$

Accepted Answer

A)  $x = t , y = t ^ { 2 } - 6 t - 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$ 
B)  $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$ 
C)  $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$ 
D)  $x = t , y = t ^ { 2 } - 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$ 
A)  $x = t , y = t ^ { 2 } - 6 t - 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$ 
B)  $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 4$ for $t$ in $( \infty , \infty )$ 
C)  $x = t , y = t ^ { 2 } + 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$ 
D)  $x = t , y = t ^ { 2 } - 6 t + 13$ for $t$ in $( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 4$ for $t$ in $( \infty , \infty )$

Question 2

Find sum of the pair of complex numbers.
--3, 9

Accepted Answer

A)  6 
B)  9 - 3i 
C)  -3 + 9i 
D)  6i 
A)  6 
B)  9 - 3i 
C)  -3 + 9i 
D)  6i

Question 3

Solve the problem.
-A projectile is fired with an initial velocity of 600 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the
Nearest tenth of a second.)

Accepted Answer

A)  39.3 sec 
B)  38 sec 
C)  31.8 sec 
D)  35.2 sec 
A)  39.3 sec 
B)  38 sec 
C)  31.8 sec 
D)  35.2 sec

Question 4

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in $$\left[ 0,360 ^ { \circ } \right]$$
-$\langle 10 \sqrt { 3 } , 10 \rangle$

Accepted Answer

A)  $20 ; 30 ^ { \circ }$ 
B)  $20 \sqrt { 2 } ; 60 ^ { \circ }$ 
C)  $40 ; 30 ^ { \circ }$ 
D)  $20 ; 150 ^ { \circ }$ 
A)  $20 ; 30 ^ { \circ }$ 
B)  $20 \sqrt { 2 } ; 60 ^ { \circ }$ 
C)  $40 ; 30 ^ { \circ }$ 
D)  $20 ; 150 ^ { \circ }$

Question 5

Find sum of the pair of complex numbers.
--8 - 11i, 12 + 8i

Accepted Answer

A)  4 + 3i 
B)  4 - 3i 
C)  -1 + 3i 
D)  3 - 4i 
A)  4 + 3i 
B)  4 - 3i 
C)  -1 + 3i 
D)  3 - 4i

Question 6

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 0 , - \sqrt { 5 } )$

Accepted Answer

A)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 0 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$ 
C)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 5 } , 0 ^ { \circ } \right) , \left( - \sqrt { 5 } , 180 ^ { \circ } \right)$ 
A)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 0 ^ { \circ } \right)$ 
B)  $\left( \sqrt { 5 } , 270 ^ { \circ } \right) , \left( - \sqrt { 5 } , 90 ^ { \circ } \right)$ 
C)  $\left( \sqrt { 5 } , 90 ^ { \circ } \right) , \left( - \sqrt { 5 } , 270 ^ { \circ } \right)$ 
D)  $\left( \sqrt { 5 } , 0 ^ { \circ } \right) , \left( - \sqrt { 5 } , 180 ^ { \circ } \right)$

Question 7

Find sum of the pair of complex numbers.
--4 - 9i, -6 - 6i

Accepted Answer

A)  -10 - 15i 
B)  -10 + 3i 
C)  -10 - 3i 
D)  15 + 10i 
A)  -10 - 15i 
B)  -10 + 3i 
C)  -10 - 3i 
D)  15 + 10i

Question 8

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant.
-$$| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }$$

Accepted Answer

A) 
  
B) 
  
A) 
  
B)

Question 9

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-Two people are carrying a box. One person exerts a force of 138 pounds at an angle of $49.2 ^ { \circ }$ with the horizontal. The other person exerts a force of 93 pounds at an angle of $59.5 ^ { \circ }$. Find the weight of the box.

Accepted Answer

A)  $285 \mathrm { lb }$ 
B)  $231 \mathrm { lb }$ 
C)  $190 \mathrm { lb }$ 
D)  $121 \mathrm { lb }$ 
A)  $285 \mathrm { lb }$ 
B)  $231 \mathrm { lb }$ 
C)  $190 \mathrm { lb }$ 
D)  $121 \mathrm { lb }$

Question 10

Determine two pairs of polar coordinates for the point with $$0 ^ { \circ } \leq \theta < 360 ^ { \circ }$$
-$( 5,5 )$

Accepted Answer

A)  $\left( 5 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
B)  $\left( 5 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
C)  $\left( 5 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 5 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 225 ^ { \circ } \right)$ 
A)  $\left( 5 \sqrt { 2 } , 135 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 315 ^ { \circ } \right)$ 
B)  $\left( 5 \sqrt { 2 } , 225 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 45 ^ { \circ } \right)$ 
C)  $\left( 5 \sqrt { 2 } , 315 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 135 ^ { \circ } \right)$ 
D)  $\left( 5 \sqrt { 2 } , 45 ^ { \circ } \right) , \left( - 5 \sqrt { 2 } , 225 ^ { \circ } \right)$

Question 11

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-A plane is heading due south with an airspeed of $232 \mathrm { mph }$. A wind from a direction of $55 ^ { \circ }$ is blowing at $8 \mathrm { mph }$. Find the bearing of the plane.

Accepted Answer

A)  $182 ^ { \circ }$ 
B)  $177 ^ { \circ }$ 
C)  $93 ^ { \circ }$ 
D)  $88 ^ { \circ }$ 
A)  $182 ^ { \circ }$ 
B)  $177 ^ { \circ }$ 
C)  $93 ^ { \circ }$ 
D)  $88 ^ { \circ }$

Question 12

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
-a, b, and c

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 13

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
\mathrm { B } = 63 ^ { \circ } 30 ^ { \prime } \
\mathrm { a } = 12.2 \mathrm { ft } \
\mathrm { c } = 7.8 \mathrm { ft }
\end{array}$$

Accepted Answer

A)  $b = 11.2 \mathrm { ft } , \mathrm { A } = 77 ^ { \circ } 49 ^ { \prime } , \mathrm { C } = 38 ^ { \circ } 41 ^ { \prime }$ 
B)  No triangle satisfies the given conditions. 
C)  $\mathrm { b } = 12.2 \mathrm { ft } , \mathrm { A } = 75 ^ { \circ } 07 ^ { \prime } , \mathrm { C } = 41 ^ { \circ } 23 ^ { \prime }$ 
D)  $b = 13.2 \mathrm { ft } , \mathrm { A } = 73 ^ { \circ } 07 ^ { \prime } , \mathrm { C } = 37 ^ { \circ } 23 ^ { \prime }$ 
A)  $b = 11.2 \mathrm { ft } , \mathrm { A } = 77 ^ { \circ } 49 ^ { \prime } , \mathrm { C } = 38 ^ { \circ } 41 ^ { \prime }$ 
B)  No triangle satisfies the given conditions. 
C)  $\mathrm { b } = 12.2 \mathrm { ft } , \mathrm { A } = 75 ^ { \circ } 07 ^ { \prime } , \mathrm { C } = 41 ^ { \circ } 23 ^ { \prime }$ 
D)  $b = 13.2 \mathrm { ft } , \mathrm { A } = 73 ^ { \circ } 07 ^ { \prime } , \mathrm { C } = 37 ^ { \circ } 23 ^ { \prime }$

Question 14

Find the indicated vector.
-Let $\mathbf { u } = \langle 8,7 \rangle , \mathbf { v } = \langle 8 , - 4 \rangle$. Find $\mathbf { u } - \mathbf { v }$.

Accepted Answer

A)  $\langle 1,12 \rangle$ 
B)  $\langle 16,3 \rangle$ 
C)  $\langle 0,11 \rangle$ 
D)  $\langle 12 , - 1 \rangle$ 
A)  $\langle 1,12 \rangle$ 
B)  $\langle 16,3 \rangle$ 
C)  $\langle 0,11 \rangle$ 
D)  $\langle 12 , - 1 \rangle$

Question 15

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\left[ 2 \operatorname { cis } \frac { 5 \pi } { 9 } \right] ^ { 2 }$

Accepted Answer

A)  $- 1.3681 - 3.7588 \mathrm { i }$ 
B)  $- 0.6946 + 3.9392 \mathrm { i }$ 
C)  $- 1.8794 - 0.6840 \mathrm { i }$ 
D)  $- 3.7588 - 1.3681 \mathrm { i }$ 
A)  $- 1.3681 - 3.7588 \mathrm { i }$ 
B)  $- 0.6946 + 3.9392 \mathrm { i }$ 
C)  $- 1.8794 - 0.6840 \mathrm { i }$ 
D)  $- 3.7588 - 1.3681 \mathrm { i }$

Question 16

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-$$\begin{array} { l } 
a = 47 \mathrm { ft } \
\mathrm { b } = 59 \mathrm { ft } \
\mathrm { c } = 65 \mathrm { ft }
\end{array}$$

Accepted Answer

A)  $1337 \mathrm { ft } ^ { 2 }$ 
B)  $1671 \mathrm { ft } ^ { 2 }$ 
C)  $145 \mathrm { ft } ^ { 2 }$ 
D)  $2006 \mathrm { ft } ^ { 2 }$ 
A)  $1337 \mathrm { ft } ^ { 2 }$ 
B)  $1671 \mathrm { ft } ^ { 2 }$ 
C)  $145 \mathrm { ft } ^ { 2 }$ 
D)  $2006 \mathrm { ft } ^ { 2 }$

Question 17

Find the component form of the indicated vector.
-Let $\mathbf { u } = \langle 2,7 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangle$. Find $\mathbf { v } - \mathbf { u }$.

Accepted Answer

A)  $\langle - 11 , - 13 \rangle$ 
B)  $\langle - 8 , - 16 \rangle$ 
C)  $\langle - 7,1 \rangle$ 
D)  $\langle 5,3 \rangle$ 
A)  $\langle - 11 , - 13 \rangle$ 
B)  $\langle - 8 , - 16 \rangle$ 
C)  $\langle - 7,1 \rangle$ 
D)  $\langle 5,3 \rangle$

Question 18

Solve the problem.
-A projectile is fired with an initial velocity of 550 feet per second at an angle of 70° with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

Accepted Answer

A)  6320 ft 
B)  6190 ft 
C)  5940 ft 
D)  6080 ft 
A)  6320 ft 
B)  6190 ft 
C)  5940 ft 
D)  6080 ft

Question 19

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
a = 20 \mathrm { ft } \
b = 38 \mathrm { ft } \
c = 42 \mathrm { ft }
\end{array}$$

Accepted Answer

A)  $\mathrm { A } = 28.4 ^ { \circ } , \mathrm { B } = 32.3 ^ { \circ } , \mathrm { C } = 119.3 ^ { \circ }$ 
B)  No triangle satisfies the given conditions. 
C)  $A = 64.6 ^ { \circ } , B = 28.4 ^ { \circ } , C = 87 ^ { \circ }$ 
D)  $\mathrm { A } = 28.4 ^ { \circ } , \mathrm { B } = 64.6 ^ { \circ } , \mathrm { C } = 87 ^ { \circ }$ 
A)  $\mathrm { A } = 28.4 ^ { \circ } , \mathrm { B } = 32.3 ^ { \circ } , \mathrm { C } = 119.3 ^ { \circ }$ 
B)  No triangle satisfies the given conditions. 
C)  $A = 64.6 ^ { \circ } , B = 28.4 ^ { \circ } , C = 87 ^ { \circ }$ 
D)  $\mathrm { A } = 28.4 ^ { \circ } , \mathrm { B } = 64.6 ^ { \circ } , \mathrm { C } = 87 ^ { \circ }$

Question 20

Find the indicated angle or side. Give an exact answer.
-Find the exact length of side a.

Accepted Answer

A)  9 
B)  $\sqrt { 109 }$ 
C)  $\sqrt { 47 }$ 
D)  7 
A)  9 
B)  $\sqrt { 109 }$ 
C)  $\sqrt { 47 }$ 
D)  7

Give two parametric representations for the equation of the parabola. - $y = x ^ { 2 } - 6 x + 13$

Find sum of the pair of complex numbers. --3, 9

Solve the problem. -A projectile is fired with an initial velocity of 600 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the Nearest tenth of a second.)

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle 10 \sqrt { 3 } , 10 \rangle$

Find sum of the pair of complex numbers. --8 - 11i, 12 + 8i

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 0 , - \sqrt { 5 } )$

Find sum of the pair of complex numbers. --4 - 9i, -6 - 6i

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 10 , | \mathbf { w } | = 4 , \theta = 40 ^ { \circ }$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 5,5 )$

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -a, b, and c

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - =63 =12.2 =7.8

Find the indicated vector. -Let $\mathbf { u } = \langle 8,7 \rangle , \mathbf { v } = \langle 8 , - 4 \rangle$ . Find $\mathbf { u } - \mathbf { v }$ .

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 2 \operatorname { cis } \frac { 5 \pi } { 9 } \right] ^ { 2 }$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. - a=47 =59 =65

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 2,7 \rangle , \mathbf { v } = \langle - 9 , - 6 \rangle$ . Find $\mathbf { v } - \mathbf { u }$ .

Solve the problem. -A projectile is fired with an initial velocity of 550 feet per second at an angle of 70° with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - a=20 b=38 c=42

Find the indicated angle or side. Give an exact answer. -Find the exact length of side a.

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 9: Applications of Trigonometry

Give two parametric representations for the equation of the parabola. - y=x2−6x+13y = x ^ { 2 } - 6 x + 13y=x2−6x+13