Sequences & Series Questions and Answers

The height of a cone h varies directly with its volume V and inversely with the square of its radius r If le is the constant of proportionality which of the following equations represents the correct relationship between height volume and radius 0 h kVr Oh Vk 72 0 h k 0 h k Vr

If f x x 5x O 48 O 48 0 6 O 0 12 and g x 3x what is g f 1

number of gallons g in a circular swimming pool varies jointly with the square of the radius r and the depth d If g 800 when r 2 and d 4 find the radius of the pool if the depth is 1 25 and the pool is holding 1000 gallons of water 07 05

Angela paid 18 000 for her car and kept a record of its value Number Value of Years in dollars y x 0 18 000 1 14 580 2 11 810 3 9566 4 7748 5 6276 Assuming the relationship is exponential which equation best models the curve of best fit for the data O y O 22222 0 81 18000 0 81 y y 14580 1 23

Complete the sentence about the sequence using the drop down options The sequence 0 5 2 8 32 128 is a n of sequence because the sequence has a common

Part 1 Predict the next 2 terms in the sequence State whether the sequence is arithmetic geometric or neither Justify your answer by giving the common difference or common ratio 1 64 48 36 27 2 1 11 111 1111 3 40 10 5 2 5 8 74 4 3 9 27 81 5 Create a predictable sequence of at least 4 numbers that is NOT arithmetic or geometric

Camille dilates a digital photograph by a factor of 1 25 to create a new digital photograph similar to her original photograph Select from the drop menus to correctly complete the statement times larger than the perimeter of her original photograph and the area The perimeter of Camille s new photograph is Choose of her new photograph is Choose times larger than the area of her original photograph

If the expression b and c 6x is written in the form axby then what is the product of a 16x5y4

For the function f x 2 9 8 find f x 4 O f x 4 x 8 9 x 4 x 8 9 f x 4 x 8 9 O f x 4 x 9 8 7 A

Simplify the rational expression Use positive exponent 3x y 5x O 3x 51 5 O 253 6 0 25y

Simplify the rational expression O O 0 1 2wr 2 317 1 2w p 3w p7

10 Professor Pietro has just developed a new super ball and you have been asked to test its rebound capabilities From your experiments you have learned that if you drop the ball from a height of 250 centimeters the first bounce will be 210 cm on average a What is the rebound ratio of Professor Pietro s ball

Factor each monomial completely 13 10a 15 28pq2 19 30 48 Find the GCF of each set of monomials 17 12 18 21 20 36 64 23 16c 2162d 14 27x y 25 32xyz 48xy 16 44m ns3 18 20 27 20 24 81 22 42 60 78 24 18a 48a4 26 12m n 44mn

and state its degree type and leading coefficient See Example 1 In Exercises 1 6 determine whether the function is a polynomial function If so write it in standard form 1 f x 3x 5 61 2 3 f x 9x 8r 6r 2x 2 p x x 3x 4x 6x 1 4 g x 3 12x 13x on in standar 2 5 Write o Combin 6x 4 on in sta

Solve the system by substitution y 3x 6 y 4x 12

M Determine the change in length of a 20 m railroad track made of steel if the temperature is changed from 10 C to 40 C OSTEEL 1 3 05 C For credit show your work below

O omain 3 5 4 6 5 7 3 9 Function YES Range or

5 Domain 2 6 7 11 4 8 7 15 Function YES or es ice 0 01 2 8 Range NO

Function Domain Range 2 YES or NO X rodi

1 Domain Range 0 2 Function YES 3 or 3 5 11 21 NO 1001 iniemod

11 Rosie was watching a YouTube video that was 6 minutes long When she glanced at the progress bar she could see that she had watched 2 3 of the video How many minutes of the video had Rosie watched

m 9 4start fraction 9 divided by m end fraction plus 4 when m 3m 3m equals 3

3 If f x x and g x x 8 simplify the expressions fog 2 f of 25 gof x and fog x fog 2

A pre paid cell phone company charges 11 05 as a monthly access fee and 0 19 per minute of calling time T Express the monthly cost C in terms of minutes of call time What will the monthly cost be if you make 165 minutes of calls this month S

6 n K P n Part C Both of the products continue to work well Does it make more sense to model the values of the products as arithmetic linear sequences or as geometric exponential sequences Provide evidence to support your answer

A rental car company charges 35 plus 35 cents per each mile driven Part1 Which of the following could be used to model the total cost of the rental where m represents th miles driven 0 35m 35 OC 35m 35 OC 3 5m 35 S OC S Part 2 The total cost of driving 150 miles is

A rectangular room is 4 meters longer than it is wide and its perimeter is 20 meters Find the dimension of the room The length is meters and the width is meters

Question 10 Which would be 3m 4n 12 solved for 1 A n m 3 B n 3mm 3 C n m 3 3 D n m 3

Which property justifies the following statement If 5x 7 10 then 5x 3 A Subtraction property of equality B Multiplication property of equality C Substitution property of equality

D Which of the following graphs shows the solution set to the inequality given below 3 2y 5 3y 12 2 2 2 1 1 1 0 0 0 1 1 1 2 2 2 3 3 3 4 4

Write an equation for a line parallel to y 5x 3 and passing through the point 3 20 y

Give the equation for each graph 5 4 3 2 1 5 4 3 2 1 4 234 54 5 4 3 2 1 5 4 3 2 1 1 2 3 5 1 2 3 4 5 1 2345

Solve the equation 6x 3 3x 6 algebraically x

Write an equation for a line perpendicular to y 2z 4 and passing through the point 4 7 y

Sketch a graph of y 2x 2 2 2 1 Clear AlL Draw 3 2 NO 7 1 2 m 5 1 2 on 3 uit

For the equation x 5y 5 a Complete the table X 0 y b Plot the two points you found in the table 6 5 6 5 4 3 2 1 4 3 2 1 My IR 2 0 4 1 2 3 4 5 6

Find the x and y intercepts of the equation 5x 2y 30 The intercepts are intercept y intercept 0 0

Question 7 Consider two sequences an and bn 1 Suppose that for all n an 0 and bn 0 Further suppose an lim c 0 n bn a Show that there exists an integer N such that for all n N bn an n 5 3c 2 bn b Show that 1 an and 1 bn either both converge or both diverge 1 c State whether or not 2m n converges

E A self serve frozen yogurt store sells servings up to 12 ounces It charges 0 50 per ounce for a serving between 0 and 8 ounces and 4 for any serving greater than 8 ounces and up to 12 ounces Find the cost of a frozen yogurt that weighs 6 ounces

The graph of a polynomial function is shown 6 2 The polynomial has and x The polynomial has two x intercepts x y 6 4 2 f 2 x degree and a leading coefficient turning points The graph has with a multiplicity of with a multiplicity of The degree of the polynomial is

3 5 7 8 1 6 4 2 Given m 4 100 1 m 2 2 m 5 3 m 4 00 4 m4

Write an equation for a rational function vertically stretched by 5 has a horizontal shift at x 3 and a vertical shift at y 7 O O O y y y 5 x 3 5 x 7 5 x 7 5 x 3 7 3 3 7

For f x x 2x 2 what value of g x gives f g 3 11 a 2 Ob 11 Oc 11 d 2

For any function f x what would be the result of f x O a not enough information to determine O b f x O co S

Which of the following functions must be subtracted from f x 3x 2x 1 for the resulting function to be an odd function a g x 3x 1 b g x 3x c g x 3x d g x 2x 1

fg x and gf a are the same function This statement is a false for most functions f x and g x b always true c true for most functions f x and g x d always false

Perform the indicated operation f a 2a 1 g a a 5 Find fog x O 2a 11 O a 3a 3a 3 O 2a 11

Perform the indicated operation g n 2n 4 Find g g n O n O 4n 4 O 4n 4 An

Solve each radical equation x 3 5

3 Solve 5 x 2 4 40 O x 18 O x 36 O x 6 O x 12