MTH 220T Wk 5 – Final Exam

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MTH 220T Wk 5 – Final Exam
MTH 220T Wk 5 – Final Exam
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MTH 220T Wk 5 – Final Exam

Complete the final exam. You have one attempt at the exam. So, be sure to review all previous course materials before attempting the exam.

Question 1

10 Points

How many four-character passwords can be formed using the characters A, B, C, 1, 2 if the characters can be repeated?

 

 

256

 

 

625

 

 

120

 

 

1024

 

 

Question 2

10 Points

Find the radius of the circle 5 x squared plus 5 y squared plus 10 x minus 20 y equals 55 .

 

 

r equals 16

 

 

r equals 4

 

 

r equals 35

 

 

r equals 6

 

 

Question 3

10 Points

Find the sum of the first six terms in the sequence {1, 5, 9, 13, …}.

 

 

66

 

 

21

 

 

60

 

 

11

 

 

Question 4

10 Points

Find the sum of the following infinite series:

 

begin inline style sum from i equals 1 to infinity of end style 5 times 0.2 to the power of i minus 1 end exponent

 

 

7.8

 

 

25

 

 

6.25

 

 

5

 

 

Question 5

10 Points

Find the equation of a horizontal parabola that has vertex (-3, -4) and distance to the focus p equals 1 half .

 

 

x equals 1 half left parenthesis y minus 3 right parenthesis squared plus 4

 

 

x equals negative 1 half left parenthesis y minus 4 right parenthesis squared minus 3

 

 

x equals 1 half left parenthesis y plus 4 right parenthesis squared minus 3

 

 

x equals negative 1 half left parenthesis y plus 3 right parenthesis squared minus 4

 

 

Question 6

10 Points

Find the sum of the following series:

 

begin inline style sum from n equals 1 to 30 of end style 2 n

 

 

435

 

 

900

 

 

465

 

 

930

 

 

Question 7

10 Points

Find the sum of the first five terms using the geometric series formula for the sequence left curly bracket 1 half comma space minus 1 comma 2 comma negative 4 comma… right curly bracket .

 

 

11 over 2

 

 

11 over 32

 

 

fraction numerator negative 31 over denominator 6 end fraction

 

 

33 over 2

 

 

Question 8

10 Points

Convert the equation 6 x squared minus 3 y squared plus 12 x minus 18 y minus 3 equals 0 to the standard form of a hyperbola.

 

 

fraction numerator 2 left parenthesis x plus 1 right parenthesis squared over denominator 1 end fraction plus fraction numerator left parenthesis y plus 3 right parenthesis squared over denominator 1 end fraction equals 1

 

fraction numerator left parenthesis x minus 1 right parenthesis squared over denominator 3 end fraction minus fraction numerator left parenthesis y minus 3 right parenthesis squared over denominator 6 end fraction equals 1

 

 

fraction numerator left parenthesis y plus 3 right parenthesis squared over denominator 6 end fraction minus fraction numerator left parenthesis x plus 1 right parenthesis squared over denominator 3 end fraction equals 1

 

 

fraction numerator 3 left parenthesis y plus 3 right parenthesis squared over denominator 13 end fraction minus fraction numerator 6 left parenthesis x plus 1 right parenthesis squared over denominator 13 end fraction equals 1

 

 

Question 9

10 Points

Find the equations of the asymptotes of the hyperbola x squared over 25 minus y squared over 16 equals 1 .

 

 

y equals 4 over 5 x space a n d space y equals negative 4 over 5 x

 

 

y equals 5 over 4 x space a n d space y equals negative 5 over 4 x

 

 

y equals 5 over 4 x minus 1 space a n d space y equals negative 5 over 4 x minus 1

 

 

y equals 4 over 5 x plus 1 space a n d space y equals negative 4 over 5 x plus 1

 

 

Question 10

10 Points

Evaluate begin inline style sum from n equals 3 to 7 of end style left parenthesis n squared plus 2 n right parenthesis .

 

 

78

 

 

63

 

 

185

 

 

196

 

 

Question 11

10 Points

Evaluate P left parenthesis 8 comma space 2 right parenthesis .

 

 

64

 

 

360

 

 

16

 

 

56

 

 

Question 12

10 Points

Find the 9th term using the general term a subscript n equals 4 left parenthesis n minus 5 right parenthesis .

 

 

13

 

 

16

 

 

20

 

 

36

 

 

Question 13

10 Points

Find the length of the semi-major axis of the ellipse x squared over 49 plus y squared over 36 equals 1 .

 

 

36

 

 

6

 

 

7

 

 

49

 

 

Question 14

10 Points

Find the foci of the ellipse fraction numerator left parenthesis x plus 1 right parenthesis squared over denominator 28 end fraction plus fraction numerator left parenthesis y plus 5 right parenthesis squared over denominator 23 end fraction equals 1 .

 

 

left parenthesis negative 1 comma negative 5 plus square root of 5 right parenthesis space a n d space left parenthesis negative 1 comma negative 5 minus square root of 5 right parenthesis

 

 

left parenthesis negative 5 plus square root of 5 comma negative 1 right parenthesis space a n d space left parenthesis negative 5 minus square root of 5 comma negative 1 right parenthesis

 

 

left parenthesis negative 1 plus square root of 5 comma negative 5 right parenthesis space a n d space left parenthesis negative 1 minus square root of 5 comma negative 5 right parenthesis

 

 

left parenthesis negative 5 comma negative 1 plus square root of 5 right parenthesis space a n d space left parenthesis negative 5 comma negative 1 minus square root of 5 right parenthesis

 

 

Question 15

10 Points

Graph the nonlinear system to identify the number of solutions.

 

x squared plus y squared equals 16 space a n d space y equals x squared minus 4

 

 

No solutions

 

 

Three solutions

 

 

Two solutions

 

 

One solution

 

 

Question 16

10 Points

How many committees of four can be formed from a group of nine members?

 

 

126

 

 

756

 

 

36

 

 

3024

 

 

Question 17

10 Points

What are the solutions to the following nonlinear system of equations?

 

table row cell space space space space space space space space space space space space y equals negative 2 x end cell row cell y squared plus 4 x squared equals 128 end cell end table

 

 

left parenthesis 4 comma negative 8 right parenthesis space a n d space left parenthesis negative 4 comma 8 right parenthesis

 

 

left parenthesis 8 comma 16 right parenthesis space a n d space left parenthesis negative 8 comma negative 16 right parenthesis

 

 

left parenthesis 4 comma 8 right parenthesis space a n d space left parenthesis negative 4 comma negative 8 right parenthesis

 

 

left parenthesis negative 16 comma 32 right parenthesis space a n d space left parenthesis 16 comma negative 32 right parenthesis

 

 

Question 18

10 Points

Evaluate C left parenthesis 7 comma 4 right parenthesis .

 

 

35

 

 

28

 

 

210

 

 

840

 

 

Question 19

10 Points

Convert the equation 3 x squared plus 3 y squared plus 6 x plus 24 y equals 9 to the standard form of a circle.

 

 

left parenthesis x squared plus 2 x right parenthesis plus left parenthesis y squared plus 8 y right parenthesis equals 3

 

 

left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 4 right parenthesis squared equals 20

 

 

left parenthesis x minus 1 right parenthesis squared plus left parenthesis y minus 4 right parenthesis squared equals 16

 

 

left parenthesis x plus 1 right parenthesis squared plus left parenthesis y plus 4 right parenthesis squared equals 9

 

 

Question 20

10 Points

Find the radius of the circle 2 x squared plus 2 y squared equals 50 .

square root of 50

 

 

50

 

 

5

 

 

25