Sequences & Series Questions and Answers

Fill in the blanks For the line 2x 3y 6 the x intercept is and the y intercept is For the line 2x 3y 6 the x intercept is and the y intercept is Type integers or fractions

In studios and on stages cardiold microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone Suppose one such cardioid pattern is given by the equation x y 8y 64x 64Y a Find the intercepts of the graph of the equation b Test for symmetry with respect to the x axis y axis and origin Select the correct choice below and if necessary fill in the answer box to complete your choice OA The intercept s is are Type an ordered pair Use a comma to separate answers as needed Type each answer only once

Complete the sentence below The lines y 3x 1 and y ax 2 are perpendicular if a The lines y 3x 1 and y ax 2 are perpendicular if a Simplify your answer

Sketch the functionfx 2x2 5x 3x2 7x 12 Using intercept s hole s asymptote s end behaviours and behaviours approaching asymptotes Show all of your supporting work algebraically and label the graph clearly 8 Function f x 2x2 5x 3x2 7x 12 x intercept s 1 y intercept 0 5 Hole s 1 Vertical Asymptote s 1 Horizontal Asymptote s 0 5 End Behaviours 1 Behaviours approaching vertical asymptotor 1

4 Suppose the rabbit population r and the wolf population w are governed by the differential equations dr dt dw dt 4r 2w r w a Suppose the initial populations are r 300 and w 200 Solve the system of equations to give equations for r t and w t b What will the proportion of rabbits to wolves be as too

Suppose that M is an mx m matrix with entries Mij 0 such that EM 1 for each of the columns j 1 m Show that 1 is an eigenvalue of Mk for any k E N

X9 For each rational equation determine the least common denominator 10 5 7 R x 4 6 R b C d 12 32 1 1 2m 5m 4k 1 k 4 5 10k 2 f g 5 3R P 2 R 2 p 4 10 2x 1 8 5 P

6 Multiply each expr 9 k In which expressions does the entire denominator cancel a b C d 7 9k 2k 9 k 4 k 2 5 k noteer

1 In each expression what cancels if anything 8 4 5 8 4 5 a b C d 4 5 8 4 S 8 4 5 4 5

Let S be the solid obtained by rotating the region bounded by y 6 sin 2x 2 and y 0 around the y axis

1 Sketch by hand slope fields for the following DE s Sketch sample solution curve y 3 y For this DE also explain what happens to solutions as x co dx Exercise a b dx x y dy dx

Wendell is looking over some data regarding the strength measured in Pascals Pa of some building materials and how the strength relates to the length The data are represented by the exponential function f x 2 where x is the length Explain how he can convert this equation to a logarithmic function when strength is 8 Pascals

The given function is not one to one h x x 5 10 5 10 5 5 10 5 Restrict its domain so that the resulting function is one to one O 4 O 6 O 6 O 5 0 10

The functions f and g are defined as f x 4x 1 and g x 9x a Find the domain of f g f g f g fg ff and b Find f g x f g x fg x ff x a The domain of fis Type your answer in interval notation 4 00 and 7 04 ICC

length of the fireplace C 0 00 0 07 A B 43 44 13 16 44 Speed 1x 44 Paused 45

An Internet bookstore charges 20 shipping for orders under 100 but provides free shipping for orders of 100 or more The cost C of an order is a function of the total price x of the bool purchased given by x 20 C x 2x if x 100 if x 100 Find C 65 C 90 C 100 and C 110 C 65 C 90 C 100 C 110

Find an equation of the line parallel to z 4 that passes through the point 2 6 If possible write the equation in slope intercept form The equation is

The graph of the invertible function f is shown on the grid below y f x 11111 9 8 7 6 5 4 3 2 Y of 987654 8 7 6 5 4 3 27 2 1 2 3 23456789 5 6 7 8 9 3 What is the value of f 0 C 1111 1 2 3 4 5 6 7 8 9

The conjugate of 4 10 is Select one O a 4 10 O b O c 4 10 1 4 10 O d 4 10

Consider the equation ax bx c mx d where a b c m and d are all constants g x nrx d a b e t x a p C 8 g h b g c d j k m n Given the graph above what values of x make the statement ax bx c mx d true p q Question 4 20 points 3 xq xD x

An exponential function f x ab passes through the points 0 3000 and 2 480 What are the values of a and b a b

Use the rational zeros theorem to list all possible zeros of the function f x 3 4x 2x 7 Enter the possible zeros separated by commas You do not need to factor the polynomial

x 3 x 7x 12 1 f x 2 f x 2 x 5x 6 3 f x x 8x 16 x 4 1 HA Holes VA 2 HA Holes VA 3 HA Holes VA

Graph the solutions of the linear inequality y2x 1 4 3 2 1 4 5432 1 1 2 3 54 3 2 1 621 1 1

Question 7 of 10 What is the explicit formula for this sequence 7 3 1 5 OA an 7 n 1 4 OB an 7 n 1 4 OC an 4 n 1 7 O D an 9 n 1 4

5 Connor claims that y is the inverse of y x Anna disagrees Who is correct Justify your answer

A 20 foot long footbridge has two diagonal supports that meet in the center of the bridge Each support makes a 65 angle with a short vertical support 65 X x 20 ft What is the length x of a diagonal support to the nearest tenth of a foot feet The solution is 65

Leandra is renting a car for one week The total cost to rent the car includes a weekly rate plus an additional charge per mile driven Which graph shows the correct labels for the axes to describe the total cost Leandra will pay to rent the car for one week

you calculate In 7 you would be finding the value of which of the following expressions O log10 7 O log 10 O log e O log 7 When

Investing 5 000 in a savings account at 2 annual interest compounded quarterly will result in approximately how much money after 10 years mt P 1 m Use the formula A P 1 O 6 103 97 O 6 000 00 5 361 61 Ing zero depending on your

A square is increased by 3 on one side and decreased by 2 on the other Let x be the length of a side Write the function that represents how much the AREA changed after the transformation Ox x 1 Ax x 6 f x x 6 x x 1 A Original Square Transformed Shape X 3

Consider the graphs of the functions f x and g x 54 3 2 1 f x 0 0 7 1 3 L 2 A 3 2 2 3 What is the value of g f 2 g x

13 For a particular geometric sequence a 2 and S 4 8 13a Solve for r the common ratio of the series Enter your next step here x X Jo af

et A 1 1 1 1 2 2 3 1 4 2 3 6 1 51 1 and b 1 3 2 i Find a lower unitriangular matrix L an upper triangular matrix U and a permutation matrix P such that PA LU ii Solve the system Ax b using the factorization obtained in i

The count in a bacteria culture was 100 after 10 minutes and 1300 after 40 minutes Assuming the count grows exponentially What was the initial size of the culture 42 53 Find the doubling period 8 11 Find the population after 80 minutes OF S 0 When will the population reach 15000 68 60 You may enter the exact value or round to 2 decimal places Or

What is the domain of the function graphed below 6 33 3 8765432 O x 7 O x 7 O 2 x 3 1 1 G 3 15 at t 5 6 7 8 x LA

Order Lorzepam 1mg every 6 hours How many tablet s should the nurse order Round to the nearest half tablet

A cabinet maker is required to make at least 4 large cabinets each week He is not required to make any small cabinets It takes 5 hours to build a large cabinet and 4 hours to build a small cabinet The cabinet maker has no more than 40 hours to build cabinets each week Let x represent the number of large cabinet and y represent the number of small cabinets Write a system of constraints to represent this situation 0 24 y20 5x 4y 40 0 20 y24 5x 4y 40 x24

10 points The side opposite the 60 angle in at 30 60 90 triangle is 7 Find the exact lengths of the other 2 sides Rationalize denominators as needed bollet yng In

Which of the following could below could be classified as a POLYNOMIAL Oat set 5x 2x 3 2g 3 022 x

Pg 329 3 14 all 3 45x 41 6 24x 2x 9 8 3 243 10 216 6x 10 64 26 243 35 49 7 4 7 4 78 7 2 64 9 3 9 7 5 49 11 64 x 4 165x 16 4 5 3 x 64 4 37x 8 12 27 9x

The graph of a function f x passes through the following points 0 2 1 0 1 0 Which of the following could be f x O f x 2x 2 f x 2 x 2 f x 2x 2 f x 2x 2

Kelly invested 5 000 in a CD at Charter Bank The annual rate is 4 9 compounded monthly How much is her investment at the end of 8 years 2 393 78 O 5 000 49 7 393 78 8 2114 22 Certificate of Deposit Question 4 18 points The equation for compound interest is A P ert where P is the initial amount invested r is the interest rate as a decimal and t is the number of years Determine the value of the account if the initial investment is 2500 compounded continuously at a rate of 4 after 15 years O 1500 4000 4555 30

vet a V Match each equation with a graph above In x 9 d log x 10 a blue b red c black d green

Exponential Function FX Parent Function Y 2x x h General Form Y a b n h Domain Range Extrema Parent Function X 1 0 1 9 Increasing Decreasing End Behavior 1 2 x f x x f x y 2 Transformed Equation Transformed Function Y X O Domain Range Extrema Increasing Decreasing End Behavior x f x x f x

Find the domain and range of y log4 1 6x 1 1 00 The domain is The range is P OFT

Write the equation in logarithmic form Assume that all constants are positive and not equal to 1 10 V

Evaluate In 0 332 Give your answer to 4 decimal places In 0 332 question below Question Help Video

Draw the graph of f z 4 MODE 10 9 8 7 63 43 21 6 KKY WHILE 7 KO ARTY MEH MOCK 65 1 LADIES MATEI TIME 77 177

A car was valued at 37 000 in the year 1993 The value depreciated to 12 000 by the year 2002 A What was the annual rate of change between 1993 and 2002 T Round the rate of decrease to 4 decimal places B What is the correct answer to part A written in percentage form T C Assume that the car value continues to drop by the same percentage What will the value be in the year 2006 value Question Help Round to the nearest 50 dollars Video