Time and Date Stamps (logged): 17:12:20 06-10-2020 °¶Ÿ°±Ÿ±¯¯µŸ°¯Ÿ±¯±¯ Precalculus II

Precalculus II Test 3

Completely document your work and your reasoning.

You will be graded on your documentation, your reasoning, and the correctness of your conclusions.

Test should be printed using Internet Explorer.  If printed from different browser check to be sure test items have not been cut off.  If items are cut off then print in Landscape Mode (choose File, Print, click on Properties and check the box next to Landscape, etc.). 

Name and Signature of Student _____________________________

Signed by Attendant, with Current Date and Time: ______________________

If picture ID has been matched with student and name as given above, Attendant please sign here:  _________

Instructions:

Directions for Student:

Test Problems:

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Problem Number 1

Transform the equation r cos(`theta) = 8 r sin(`theta) to rectangular coordinates and graph.

 

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Problem Number 2

If P = (-3.101, -3.901) and Q = (-2.701, y) find all numbers y such that the vector with initial point P and terminal point Q has magnitude -.2240001 .

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Problem Number 3

Give the polar form of the equation y =  x^2 + y^2 = 9 x.

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Problem Number 4

Find the center, vertices and foci of the ellipse given by x^2 / 64 + y^2 / 16 = 64 .

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Problem Number 5

If the angle between v and w is 64 degrees and if || v || = 10.14 and || w ||  = 7.405, then what is the dot product of the two vectors?

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The remaining problems appear on Test 4 for distance students and these problems will not be counted on the test for distance students. These problems are required as part of Test 3 for in-class students, who will not have Test 4.

However in-class students should note that problems related to the binomial theorem, to permutations and combinations are optional on this test and will be counted only if they help your grade.

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Problem Number 6

A lecture hall has 256 rows of seats, with 35 seats in the first row.  Each row has 4 seats more than the previous.  How many seats are there?

 

 

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Problem Number 7

Express the following sequence using summation notation:

6 / 2 + 12 / 4 + 18 / 8 + ...

 

 

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Problem Number 8

Solve the following system; if the system is inconsistent say so.  Use Cramer's Rule to obtain the solution.

6 x + -10 y = -122 .

7 x + -4 y = -81 .

 

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Problem Number 9

Set up the system below as an augmented matrix and solve using row operations.

5 x + -5 y = -65 .

-7 x + -5 y = 55 .

 

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Problem Number 10

Set up the system below as a matrix multiplication of the form A B = C.   Find the inverse A^-1 of A and use it to solve the system.

5 x + -6 y + 7 z = 0 .

7 x + 7 y + 8 z = 133 .

-10 x + -10 y + -10 z = -180 .

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Problem Number 11

Solve the following system; if the system is inconsistent say so.  Use substitution.

7 x + 4 y + 15 z = -110 .

24 x + 15 y + -31 z = -80 .

             -5 x + 5 y + 8 z = 127 .

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Problem Number 12

Using the Binomial Theorem expand the expression ( x + 2 y^2 ) ^ 6.

 

 

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Problem Number 13

How many 3-letter codes can be formed from the first 16 letters of the alphabet if repeated letters are allowed?

 

 

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Problem Number 14

A ball is dropped from 16 centimeters and with every bounce its height decreases by 36%.  To bounce either up or down a distance y cm requires `sqrt(y / 490) seconds.   How long it take for the ball to stop bouncing?