Sequences & Series Questions and Answers

The glass portion of a window has a height to width ratio of 3:2. The wood trim around the glass adds an additional width and height to the window. The area of the window, including the glass and wood trim, is modeled by A(x) = 6x² +37x + 56. If the height of the window is modeled by 3x+8, find the expression to represent the width. What operation would you use to determine the width? multiplication subtraction addition

Your family is planning a trip to Australia in December. A website indicates that the weather in December has a average low temperature of 26 °C. The formula C = (F-32) gives degrees Celsius as a function of degrees Fahrenheit. Use what you know about inverse functions and determine what the average low would be in December in degrees Fahrenheit. Round to the nearest degree. 38° -3⁰ 81°

Use the following functions to determine the expression for(ƒg)(x). f(x) = 2x + 4g(x) = x² - 3h(x) = 2x² + x − 8 6x³6x²12x 2x³ + 4x² - 6x – 12 6x² - 6x - 12 2x4+4x³ - 6x² - 12x

An infinite geometric series has a sum of 12. If it has a first term of 4, calculate the common ratio. (Express your answer as a fraction)

The region enclosed by the lemniscate ² = 2 cos 20 is the base of a solid right cylinder whose top is bounded by the sphere z = √√2-2. Find the cylinder's volume.

Here are the test scores for 10 students in Mr. P's class. 59, 94, 57, 87, 75, 90, 82, 57, 65, 77 What is the percentage of these test scores that are less than 59?

Here are the fuel efficiencies (in mpg) of 12 new cars. 47. 36, 22, 18. 42. 32. 40. 55. 12. 28. 17.35 What is the percentage of these cars with a fuel efficiency less than 41 mpg?

Find the Taylor series at x = 0. 1). tan-¹(3x4)

Find the area of the region D enclosed by one loop of the four-leaved rose r = | cos(20)|. GH T Select one: O a. π/2 O b. π/4 C. π/8 O d. π/16 Oe. None of the other answers Clear my choice

The given values would be on which row of Pascal's Triangle? 1 10 45 120 210 252 210 120 45 10 1 1 45 10

Let W be a subspace of R4 spanned by the set Q = {(1,-1,3,1), (1, 1,-1, 2), (1, 1, 0, 1)}. (i) Show that Q is a basis of W. (ii) Does the vector u = (-4, 0, -7, -3) belong to space W? If that is the case, find the coordinat vector of u relative to basis Q.

17. Niki needs $5200 for university tuition when she graduates from high school in 2 years. She plans to make deposits into an account that earns 6.5% per year, compounded bi-weekly. a) Draw a time line to represent this annuity. b) How much should she deposit every 2 weeks?

(10 points) A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 80 feet/second. The height (in feet) of the ball at t seconds is given by s(t)=6+80r-16r². Include units in your answers. You may use a calculator for this problem. (a) What is the velocity of the ball at 2 seconds? (b) When will the ball reach its maximum height? (c) What is the maximum height achieved by the ball? (d) What is the acceleration of the ball at any time ?? (e) When does the ball hit the ground? Round your answer to two decimal places. (f) At what velocity does the ball strike the ground? Round your answer to two decimal places.

2. Let X be a Banach space and S,TE B(X). Show that the resolvent functions Rx(T) := (A id-T)¹ satisfy the following equations: (b) R(S)-Rx(T) = R(S)(ST)R(T) for all XE C\ (o(S) Uo(T)

Determine whether the function f(x) is one-to-one. If it is one-to-one, find a formula for the inverse. f(x) = ³√5x Is f(x) one-to-one? Yes No The inverse function is f¹(x)=[

To describe a specific geometric sequence, Jamie wrote the recursive formula: anan-1.4; a₁ = -2 Write the first five terms of this sequence.

11. Find the exact value(s) for 0 over the interval [0,27] that satisfies each expression below. (3 points each) a. cot0 = -√3 b. sin 0 = √2 c. sec 0 = -2

XX** 2 O 64 Ⓒ66 033 4 The first four elements of a pattern are shown in the diagram above. If the pattern continues, how many red boxes will there be in element 16 of the pattern?

Let W be a subspace of R4 spanned by the set Q = {(1,-1, 3, 1), (1, 1,-1,2), (1, 1, 0, 1)}. (i) Show that Q is a basis of W. (ii) Does the vector u = (-4, 0, -7, -3) belong to space W? If that is the case, find the coordinate vector of u relative to basis Q.

Write the equation of the line has the given characteristics. You may write the equation in point-slope form (y - y₁ = m(x-x₁)) or slope-intercept form (y = mx + b). Slope = -4 Goes through the point (-2, 11)

I thought the answer for the hole is 6, but the answer from the text book is (6,-22/3), How to get -22/3 ? Please help. Thanks a lot. Exer. 7-8: Identify any vertical asymptotes, horizo asymptotes, and holes. -2(x + 5)(x-6) (7) f(x) (x - 3)(x-6)

5) Find the inverse of the function f(x) = (x-3)²+2, x ≥ 2. Also write out the check. Then graph both and label each one. Also draw in the y = x line as a dashed line.

An object is fired straight up from the top of a 100-foot tower at a velocity of 40 feet per second. The height h of the object t seconds after firing is given by h(t) = -16t2 + 40t + 100. When does the object reach its maximu height? Select one: OA. 0.4 seconds OB. 2.5 seconds OC. 0.8 seconds OD. 1.25 seconds 0000

A laptop computer is purchased for $1250. After each year, the resale value decreases by 35%. What will the resale value be after 5 years? Use the calculator provided and round your answer to the nearest dollar.

Determine the transformations to the parent function y = x³ y = 1/(x+2)³-1 compressed by a factor of 1/2 Choose... + shifted 2 units to the right shifted 1 unit down reflected across the x-axis shifted 2 units up Choose... # Choose Choose... Choose... #

Use the graph of f to draw the graph of its inverse function. Choose the correct graph of the inverse function f 1 below. The graph of f is dashed in each of the choices. O A. ... O B. G D. G CON 3|||||||X HIST 201 G

The equation of a line that is perpendicular to 3x + 2y = 8 and passes through (3,61) is -2x + 3y = -9.

The new high-intensity discharge (HID) headlights containing xenon gas have an expected life of 1900 hours. Because a complete system costs $1000, it is hoped that these lights will last for the life of the car. Suppose that the actual life of the lights could be 7% longer or shorter than the advertised expected life. Write an inequality that gives the range of life of these new lights. Let x be the expected life of the headlights. What is the range of the expected life of the headlights? ≤x≤ …w hours

The function f(x) = 5x + 4 is one-to-one. Find an equation for f(x), the inverse function. f-1(x) =

The function f(x) = (x + 1)5 is one-to-one. Find an equation for f(x), the inverse function. f-¹(x) =

Determine whether the graph shows a consistent system with independent equations, a consistent system with dependent equations, or an inconsistent system with independent equations. -4 -3 -2 3- 2+ -3 2 3

Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 9% protein? How many pounds of cornmeal should be in the mixture? pounds How many pounds of soybean meal should be in the mixture? pounds

The function f(x)=-, x0, is one-to-one. Find an equation for f1(x), the inverse function. f-¹(x)=

Solve the equation for if 0 #360" (Enter your answers as a comma-separated list) 2 sin 0-sin 28-0

2x + 5 X-3 Find an equation for f1(x), the inverse function. The function f(x) = , x # 3, is one-to-one. f-¹(x)=x2 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Graph: 2<x<5 -1≤x≤3 x>4 x≥2 x < 5 Interval notation:

1. THE FIRST BUS HAS 12 MORE SEATS THAN THE SECOND BUS. THE THIRD BUS HAS 8 FEWER SEATS THAT THE SECOND BUS. IF THE TOTAL NUMBER OF SEATS IS 154, FIND THE NUMBER OF SEATS FOR EACH BUS.

2. Write the standard form of the equation of the circle having the given center and containing the given point: Center (-3, 2); point (3,-2)

The amount of a particular pollutant p from a power plant in the air above the plant depends on the wind speed s, among other things, with the relationship between p and s approximated by p= 27 -0.03s², with s in miles per hour. a. Find the value(s) of s that will make p = 0. b. What does p = 0 mean in this application? c. What solution to 0= 27-0.03s2 makes sense in the context of this application? a. The value(s) of s that will make p = 0 is/are s= 30, -30 (Simplify your answer. Use a comma to separate answers as needed.) b. Choose the correct meaning of p = 0 in this application. OA. The wind is blowing at 27 mph. OB. There are 27 units of pollution in the air. C. There is no pollution in the air. D. The wind is blowing at 0 mph. c. The solution to 0=27-0.03s² that makes sense in the context of this application is s= (Simplify your answer.)

Sketch a graph of f(x) = Solution: x³ - 2x²- 3 X - 3x 2 x + 3x + 2 Before answering this question, we need to factor f(x). Factor f(x) completely and submit your answer below.

Q) Using numerical angle values between Odegree and 360 degree (10degree increment) prove the following relationships in an EXCEL WORKSHEET. (Remember that excel only takes angles in radians) 1. sin2 0 + cos² 0 = 1

WHEN YOU SEE FRACTIONS IN THE EQUATION, YOU MUST "CLEAR" THE FRACTIONS BY MULTIPLYING BY THE COMMON DENOMINATOR. X 364 x-3x+5_5 7 4 = 14

THE SUM OF THREE CONSECUTIVE INTEGERS IS 228. FIND THE INTEGERS.

- 2. Suppose f: [0, 1] → [0, ∞) is a continuous function. Let A = Prove that √1 + A² < √√√√√₁ 1 + [ƒ (x)]² dx ≤ 1 + A. f f(x) dx. I want the proof of the left inequality only please.

4. IN 2010, THE POPULATION OF SOME COUNTRY WAS 1,200,000. FROM 2010 TO 2060, THE POPULATION IS EXPECTED TO INCREASE BY 30%. FIND THE EXPECTED POPULATION OF THE COUNTRY IN 2060.

Restaurant customers tip their server only 8 percent for poor service. If their tip was $3.70, how much was their bill? O $46.25 O $40.15 O $44.60 O $50.45

Find the average rate of change of f(x) = 2x² - 2 from 2 to 6.

Carbon-14 decays exponentially with a half-live of 5700 years. (a) Find the value of r in A(t) = anert for t in years. Give the exact value and a decimal approximation. (b) An Egyptian mummy is discovered in which the amount of carbon -14 present is only about two- thirds the amount found in the atmosphere. How long ago was the mummy buried? (c) Another Egyptian mummy is estimated to contain 59% of the carbon-14 in contained originally. How long ago was the mummy buried?

The sum of the first three terms in an arithmetic series is -6 and the product of these terms is 24. Find the first three terms.

A neighborhood carnival has a Ferris wheel with a radius of 30 feet. You measure the time it takes for one revolution to be 70 seconds. What is the linear speed (in feet per second) of this Ferris wheel? What is the angular speed in radians per second?