Sequences & Series Questions and Answers

If the mean of five observations x x 2 x 4 x 6 and x 8 is 11 then the mean of the last three observations is 1 2 13 17 3 15

Fill in the blank with an appropriate inequality sign a If x 4 then x 3 3 1 b If x 4 then 3x 12 c If x 2 then 3x 6 d If x 2 then x 2

Solve the following inequality and graph the solution 8 x 6 0 Choose test values and indicate whether the inequality is true or false in each region Enter the test values from smallest to largest Test Value Inequality 12 11 True 0 10 9 8 False 7 6 5 Draw the solution above Write the solution as a compound inequality True Clear All Draw E 3

Solve the inequality 3 10s2 11s Give your answer in interval notation Enter DNE if there is no solution

Solve the rational inequality I 2 I 3 State your answer using interval notation Use U for union and oo for co 0

Solve the inequality b 96 18 Give your answer in interval notation Enter DNE if there is no solution

Simplify the compound fractional expression Y X X y 1 3x 3y 1

3 Use a number line to solve How many stuffed animals can be made from 3 yards of material if each animal requires of a yard

Find the sum of the infinite geometric series if possible 2 1 O 2 3 7 2 3 1 co the series is divergent

Each dot in the following dot plot represents the number of goals Luis scored in one lacrosse season H 43 44 3 5 45 46 Number of goals goals 47 Find the interquartile range IQR of the data in the dot plot 48

8 Construction plans for a bomb shelter call for a rectangular metal structure measuring 5m long by 4m wide by 3m high The metal structure is to be surrounded on all six sides with a layer of concrete of uniform thickness a Determine an expression for the volume of the concrete as a function of its thickness 2 b Find the thickness of the concrete shield if the volume of the concrete is 444 m 4

4 Let u v 3 3 and u v 1 1 a Find u and v b Draw the vectors u v u v u v u v u v in a single ry plan

3 Sketch the solutions to the autonomous ODE y 1 cos y that solve the initial value problems y 0 kr for k 3 2 2

Write an equation for the function graphed below 7 6 5 4 3 2 1 y 54 4 3 55 2 ist i is 4 12 Autom D a

Write an equation for a rational function with Vertical asymptotes at x 3 and x 1 x intercepts at x 2 and x 4 Horizontal asymptote at y 10

Divide 32 2 22 4 by 1 3 Fill in the table below to complete the synthetic division Only the answer is shown as correct or not Enter an integer or decimal number more R 1 Give your answer in the form Q x D T k

The polynomial of degree 3 P z has a root of multiplicity 2 at z 1 and a root of multiplicity 1 at z 5 The y intercept is y 2 5 Find a formula for P z P z

8 7 What is the least possible degree of the polynomial graphed above

Describe the long run behavior of f x x 00 f x o f x As As

The unit cost in dollars to produce bins of cat food is 16 and the fixed cost is 14112 The revenue function in dollars is R x 2x 356x Find the cost function C x Find the profit function P x At what quantity is the smallest break even point Select an answer Select an answer servings of cat food dollars bins of cat food

The function function f x on the interval 9 x 1 10 8 6 4 2 20 16 12 8 4 8 12 16 20 4 6 8 10

13 Let A 3000 0300 0020 If possible find an invertible matrix P such that 002 P AP is a diagonal matrix

Select the correct answer On a map where each unit represents one kilometer two marinas are located at P 4 2 and Q 8 12 If a boat travels in a straight line from one marina to the other how far does the boat travel A B 14 kilometers 2 29 kilometers O C 6 kilometers O D 2 5 kilometers Reset Next

di de T d P Maximum Minimum 78 Domain Range Intervals of Increase Intervals of Decrease 6 62 D 13678 4

Let ABCD be a parallelogram Triangle ABE The area is 32 square meters ED unit length 8 CF unit how many units long D E B

4a Consider the series 5 5 2 Find the common ratio r r 5 4 Enter your next step here

Geometric Sequence Consider the first six terms of this sequence 6 12 24 48 96 Which equation below explicitly defines the sequence a 6n ax 6 ax 1 a 3 2 0 A 2 ax 1

Arithmetic Sequence Consider the first six terms of this sequence 3 8 13 18 23 28 If the sequence defines a function what is the domain 1 2 3 4 5 6 O ALL REALS 3 8 13 18 23 28 ALL INTEGERS

X f x a partial set of ordered values of the function f x 3 1 1 3 0 1 Given g x is a transformation of the graph f x and the following set shows set of ordered values of g x 0 1 g x 1 Describe how f x is transformed to describe g x 26 2 9 log 26 3 log 26 x log 3 2 3 Jog 3 27 3 9 The function f x would be translated left 1 The function f x would be translated right 1 The function f x would be translated down 1 The function f x would be translated up 1 Question 9 3 6 points Rewrite the exponential equation as a logarithm 4 27

emoldo19 sallaci vprana Icoineroo 10 Complete the following table by putting in the missing values all masses are on Earth gravitational potential energy 686J 3 kg 6kg 5kg 5kg 7kg Mass kg Acceleration due to gravity m s s 9 8 m s s 9 8 m s s 9 8 m s s 9 8 m s s Height m 4m 4m 2m 4m 10m

Expand the logarithm and simplify when possible logs logs 5y 2logs xy 1 logsy 2 logs x logs z 5 logs y 2 logs xy logs 5 logsy 2 logs x logs z

OB 48 OC 72 96 OD 96 72 051 15 2 25 3 3 5 4 What is the average rate of change of the function over the interval 1 3 O A 36 46 24 4 5

Which are equivalent expressions to 4 x Select all that apply 3 4x 3 3 3 04 7x Ox 16 O x 26 Ox 64 08 x

together teammates pedro and ricky got 2667 base hits last season pedro had 277 more hits than ricky how many hits did each player have

Determine the following limit using L Hopital s Rule where appropriate Be sure to include a justification for why you can use L Hopital s Rule each time you use it 1 tan z 1 sin 2x

13 For each of the following expressions determine the numerical value and units of the resul 4 2 m 3 8 m 1 2 m a 12 4 m 2 b 8 3 ft 2 2 0 ft 4 3 ft

Match the function with its graph y 4 x 2 5 69 46 14 534 E m n T cry m 534 19 10 A ne 2 5435 10 13 4 6343 ht 7 td F 14 E A E 2 ry 1 to k 2 7 My

Function Evaluation Given the function f x x x 8 evaluate each of the following Give your answers as a simplified expressions C Evaluate f 2x f 2x D Evaluate f x 2 E Evaluate f 3x 5 f x 2 f 3x 5

A motorboat can maintain a constant speed of 36 miles per hour relative to the water The boat makes a trip upstream to a certain point in 39 minutes the return trip takes 33 minutes What is the speed of the current The speed of the current is

Betsy a recent retiree requires 5 000 per year in extra income She has 60 000 to invest and can invest in B rated bonds paying 15 per year or in a certificate of deposit CD paying 5 per year How much money should be invested in each to realize exactly 5 000 in interest per year The amount of money invested at 15 The amount of money invested at 5

A nut store normally sells cashews for 4 00 per pound and peanuts for 1 50 per pound But at the end of the month the peanuts had not sold well so in order to sell 90 pounds c peanuts the manager decided to mix the 90 pounds of peanuts with some cashews and sell the mixture for 2 50 per pound How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue The manager should mix pounds of cashews with the peanuts

Find the integral 2 1 1 1 a cos x

Find integers x that solve the following a 7x 2 17 mod 153 b 24141x 9 mod 71

Yesterday when I drove to the grocery store my gauge said that I averaged 45 miles per hour On the way home I only averaged 30 miles per hour The total time I spent driving was 50 minutes 5 6 of an hour How far is it from my house to the grocery store

17 Solve this equation x 12x 20 Type your answer as without spaces or Cannot be Factored

Perform the addition or subtraction and simplify 3 4 X X 8 7 2 x 8x

Perform the addition or subtraction and simplify u 9 U u 9

Simplify the fractional expression Expressions like this arise in calculus 1 x n x h h 1 X

Perform the addition or subtraction and simplify 5 2x 3 7 2x 3

Simplify the compound fractional expression 1 x 2 1 x 2 X X