1 MATH 108 Quiz 3 This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work. Questions 5 – 8 are each worth 6 points; show your work to earn full credit. Write...

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MATH 108 Quiz 3
This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work.
Questions 5 – 8 are each worth 6 points; show your work to earn full credit.
Write answers on the answer sheet that is provided with this quiz.
Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in
lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using
positive exponents except when using scientific notation. Simplify all radicals and rationalize the
denominators. Write complex numbers in the form a + bi. Applied problems must have the variables
identified (Let x =) and an equation for full credit.
Reminder: When asked for component form, it will be rectangular (x, y), polar (r, θ), or vector .
Select the letter of the one alternative that best completes the statement or answers the question. Check
that the answers are all letters (A, B, C, D, or E) and not a value.
1.) Find the rectangular coordinates of (10,
?
3
).
A) (5, −5√3) B) (
√3
2
, XXXXXXXXXXC) (
√3
2
, 5) D) (5√3, 5) E) None of these
2.) The letters r and θ represent polar coordinates. Write the equation r – 9cos θ = 7sin θ using
ectangular coordinates (x, y).
A) ?2 + 9? + ?2 = 2? XXXXXXXXXXB) ?2−9? + ?2 − 7? = XXXXXXXXXXC) √?2 + ?2 = 16 + ??
D) ?2 + 9? + ?2 + 7? = XXXXXXXXXXE) None of these

3.) Find ||3w - v|| if v = -4i + 7j and w = -i - 3j.

A) √410 B) √397 C) √257 D XXXXXXXXXXE) None of these

4.) Find the angle in degrees between �⃗� = ⟨ 2, −5⟩ and ? = ⟨1, 4⟩.

A XXXXXXXXXX° B) -18° C XXXXXXXXXX° D XXXXXXXXXX° E) None of these

The following questions are each worth 6 points. Show your work.
5.) Find the exact polar coordinates of the points of intersection of these two polar equations:
= 1 – 2 sin θ and r = 2.

6.) Find the vector projection of ? onto �⃗⃗� given that ? = 〈2, −3〉 and �⃗⃗� = 〈5, 7〉.

7.) A 350 pound block is hanging on two cables which are attached to
the ceiling. The left hand cable makes a 55° angle with the ceiling
while the right hand cable makes a 37° angle with the ceiling.
What is the tension on each of the cables?

8) Use the polar grid function of the Desmos Graphing Calculator or any
other graphing calculator to copy and paste the graph of the polar equation: r = 4 cos 5θ on the
interval (-2π, 2π). (3 points)
Also include any one point on the graph of the equation. Label the point. (3 points)
Hint: select any θ, calculate r, and then, determine (x, y). Next, use the label function to identify
the point. (The label should be values, not the letters x and y.)
Use the software, do not post a hand-drawn graph and do not label point by hand.

MATH 108 Quiz 4
This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work. Questions
5 – 8 are each worth 6 points; show your work to earn full credit.
Write answers on the answer sheet that is provided with this quiz.
Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in
lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using
positive exponents except when using scientific notation. Simplify all radicals and rationalize the
denominators. Write complex numbers in the form a + bi. Applied problems must have the variables
identified (Let x =) and an equation for full credit.
Select the letter of the one alternative that best completes the statement or answers the question.
Check that the answers are all letters (A, B, C, D, or E) and not a value.
1.) Find the equation in standard form for the hype
ola that has center (4, -1), focus (7, -1), and
vertex (6, -1).
A)
(?−1)2
4
−
(?+4)2
5
= 1 B)
(?−4)2
5
−
(?+1)2
4
= 1 C)
(?−4)2
4
+
(?+1)2
5
= 1
D)
(?−4)2
4
−
(?+1)2
5
= 1 E) None of these
2.) Graph the equation:
(?+1)2
9
+
(?+2)2
4
= 1.
A) XXXXXXXXXXB)
C) XXXXXXXXXXD)
E) None of these
3.) Find the asymptotes of 4?2 − ?2 = 16.

A) ? = ±
1
2
? B) ? = ± 2? C) ? = ±4 ? D) ? = ±
1
4
? E) None of these
4.) Fill in the blank: ______________________
A sealed-beam spotlight is in the shape of a paraboloid of revolution. The bulb, which is placed at
the focus, is 12 centimeters from the vertex. If the depth is to be 20 centimeters, what is the
approximate diameter of the headlight at its opening?
The following questions are each worth 6 points. Show your work.
5.) An (half) elliptical tunnel arch is constructed which is 20 feet wide at the base and 20 feet tall in
the middle. Find the approximate height of the arch exactly 1 foot in from the base of the arch.

6.) Find the equation in standard form for the parabola that has focus (10, 1) directrix is x = 5.
7.) a. Write the equation in standard form of the conic 4?2 + ?2 − 8? − 2? + 1 = XXXXXXXXXXpoints)
. Using the Desmos Graphing Calculator or any other graphing calculator, plot one graph that
has the conic in Part a and the center of that graph. Label the point by giving the x and y
coordinates. Use appropriate domain and range to include the graph of the conic.
Use the software, do not post a hand-drawn graph and do not label point by hand. (3 points)
8.) a. Write the equation in standard form of the conic ?2 − 4? − 2? = XXXXXXXXXXpoints)
. Using the Desmos Graphing Calculator or any other graphing calculator, plot one graph that
has the conic in Part a and the vertex and focus of that graph. Label the points by giving the x
and y coordinates. Use appropriate domain and range to include the graph of the conic.
Use the software, do not post a hand-drawn graph and do not label point by hand. (3 points)

MATH 108 Quiz 5
This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work. Questions
5 – 8 are each worth 6 points; show your work to earn full credit. Write answers on the appropriate
numbered blank. You can insert additional lines if needed.
Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in
lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using
positive exponents except when using scientific notation. Simplify all radicals and rationalize the
denominators. Write complex numbers in the form a + bi. Applied problems must have the variables
identified (Let x =) and an equation for full credit.
Select the letter of the one alternative that best completes the statement or answers the question.
Check that the answers are all letters (A, B, C, D, or E) and not a value.
1.) Write the system of equations associated with the augmented matrix. Do not solve.
[
5 5 5 8
3 7 0 −9
4 0 6 8
]
A) {
5? + 5? + 5? = 8
3? + 7? = −9
4? + 6? = 8
XXXXXXXXXXB) {
5? + 5? + 5? = 8
3? XXXXXXXXXX? = −9
4? + 6? = 8
XXXXXXXXXXC) {
5? + 5? + 5? = 8
3? + 7? = −9
4? XXXXXXXXXX? =

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Answered 4 days After Sep 16, 2021

Solution

Itika answered on Sep 21 2021

141 Votes

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SOLUTION.PDF

1 MATH 108 Quiz 3 This quiz is worth 40 points. Questions 1 - 4 are each worth 4 points; do not show your work. Questions 5 – 8 are each worth 6 points; show your work to earn full credit. Write...

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