Sequences & Series Questions and Answers

Suppose f(x) is a differentiable function with f(3) = 5 and f'(3) = 4. Let g(x)= 1/f(x) Find g(3) A. 4/5 B. 5/4 C. -5/16 D. -5/8 E. -4/25

True or False: If you deposit $1,200 and earn 6% interest for 2 years, your interest is $144. True False

Solve. A cell phone that is on sale for $90 has a markdown of 35% off the regular price. What is the regular price of the cell phone? Round to the nearest cent. $ ____________

An Hem costs $2 per unit to produce and is sold for $7. If the overhead cost $350, how many items must be said to even? A. 175 B. 140 C. 50 D. 100 E. 70

Use the function to evaluate the limits below f(x) = {x+1, x<2 x-2, 2≤x<4 x+5, x≥4 a) lim f(x)= b) lim f(x) =) c) lim f(x) = d) lim f(x) =

Let A= 2 8 -2 3 -5 -3 u =2 -1 1 Define a transformation T: R^3 → R^2 by T(x) = Ax. Find T(u), the image of u under the transformation T.

Stanley has a job that pays $45,000 a year that requires he work 45 hours a week. How much money is Stanley paid per week? (A) $450 (B) $3700 (C) $937.50

n+4 <-15 A) n<-19: -24 -22 -20 -18 -16 B) n>-60 : -66 -64 -62 -60 -58 C) n>-19: -26 -24 -22 -20 -18 D) n<-60: -66 -64 -62 -60 -58

Explain how θ1,θ2,θ3,θ4 values are obtained. Explain the steps used in finding these values. Antenna normalised array factor is given by 12.5sin²((3π/4)cosθ)-sin²((15π/4)cosθ)=0 On solving θ in radians 1. θ₁ = 1.6913 (rad) 2. θ₂= 1.4503 (rad) 3. θ₃= 4.8329 (rad) 4. θ₄ = 4.5919 (rad) Explain the steps in details how above values are obtained from above main equation ?

True or False: If your new balance is $395 and you made the minimum payment of $70, your original balance was $465. O True O False

When the price of a scones is $3.20, the demand is 400. For each $0.80 increase in the price of a scone, the demand decreases by 20. Assuming a linear relationship between price and demand, find the demand function p(x) (where pis price and x is demand). O A. P(x) = -0.04x + 19.2 B. P(x) = -20x + 3.2 C. P(x) = -0.04x + 3.2 D. p(x) = -0.8x + 323.2 E. P(x) = 0.04x + 12.8

Write an exponential function with an initial value of 52 and an exponential decay of 12.4%. a. y = 52(12.4)^t b. y = 521.124)^t c. y = 52(0.876)^t d. y = 52(87.6)^t

Your purchase costs, $3,400, including tax. You sign an installment loan for $2,000 after the down payment. The remainder including the finance charge will be paid in 20 equal monthly installments of $105.95 at 17% interest. What is the amount of interest after one month?

What type of function does this graph model? 1. Exponential growth 2. Exponential Decay 3. Linear 4. none of the above

Why are fashion and clothing forms of non - verbal communicaton ?

If f(x) = 3x⁶ + x²- 4, then what is the remainder when f(x) is divided by x + 1? a. 0 b. 2 C. -32. d. 1

In the diagram below, a rectangle is rotated 360° about line t. Describe the shape of the resulting figure. Write a formula for the volume of the figure in terms of c. The rectangle is translated c units from line t and again rotated 360° about line t. Sketch the resulting figure. Write a formula for the volume of the resulting figure in terms of c.

What is the inverse of the function f(x) = 4x + 8? (a) h(x) = 1/4x - 2 (b) h(x) = 1/4x + 2 (c) h(x) = 1/2x - 2 (d) h(x) = 1/2x + 2

Use technology to find the line of best fit for the following data. You may use your own graphing calculator or this GeoGebra graphing calculator tool. (1, 5), (9, 85), (2, 10), (6, 38), (4, 3), (12, 107), (7, 64), (12, 86), (7, 47), (9, 64), (4, 27) The line is in the form y = mx + b. What is the value of m? Enter your answer as a number with two decimal places, like this: 3.14

Solve. ∛(2x-2)-6=-8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution(s) is(are) x= O B. The solution set is Ø.

Students will apply pattern recognition and past knowledge to solve new problems. This question has multiple parts. 1. Factor x³-1 2. Factor x⁵-1 1. What are the possible rational roots of this function? 2. Which of those are actually roots? 3. Now factor x⁷ - 1. 4. What is the pattern between these three problems? Based on the pattern you see in the solutions, what is your prediction for the factorization of x⁹⁹⁹-1

Use the factorization A = PDPᐨ¹ to compute Aᵏ, where k represents an arbitrary positive integer. |11 40| = |4 5| |1 0| |-1 5| | 2 -7| |1 1| |0 3| | 1 -4|

A model rocket was launched from a podium 5 meters above ground at a initial velocity of 98 m/s. The function that models height (in meters) with respect to time (in seconds) is h(t)=5+98t-4.9t². Part A: Complete the table below. Time (seconds) 0 5 10 15 20 Elevation (feet) Part B: Graph function h(t) on the following coordinate Part C: Estimate the time when the model rocket lands on the ground. Justify your answer.

Given the hyperbola with the equation (v+4)²/1 - (x + 2)²/4 =1. Find the vertices. List your answers as points in the form (a, b). 2. Find the foci. List your answers as points in the form (a, b) 3. Find the equations of the asymptotes. Separate equation(s) by commas:= 1, find the vertices, the foci, and the equations of the asymptotes.

Rationalize the denominator. 7a/(⁵√4a⁷b¹³)

Perform the following multiplications using the lattice multiplication algorithm. a. 294 x 34 b. 146 x 86

Given the equation y=7sin(2(x+3))+8 The amplitude is: The period is: The horizontal shift is: units to the Select an answer The midline is: y =

A small town has two radio stations: an AM station and an FM station. A survey of 100 residents produced 63 people that listened to the FM stations, 40 that listened to the AM station, and 25 that listened to both.

On the graph of f(x) = sin and the domain-2x≤<0, for which of the following intervals is f(x) strictly increasing? Choose all correct answers. Select all that apply: □ (-2,-) 0 (- -*) □ (*. :) □ (-1,0)

Find the latitude and longitude of the location on Earth precisely opposite of a town located at latitude 31°N, longitude 123°W. Select the correct choice below and fill in the answer boxes within your choice. S, longitude N, longitude OA. latitude B. latitude C. latitude OD. latitude N, longitude S, longitude °E °W °E "W

Choose the answer that means an angle that measures 180°. A. Right B. Complementary C. Straight

Solve the system and write the general solution. 2y + 4z -5 y 5z = -6 6z X- X - - - = 17 The system has no solution. The system has a unique solution. The solution set is {COD} The system has infinitely many solutions. {01 The solution set is ber}. is any real number

Find the radius of convergence, R, of the series. Σ(-1)^x +1 n+6 R = 1 n=1 1 ✔ Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

134080011 2 Which number is equivalent to A 2 B 9 C D 81 729 3121?

In sketching the graph of y = 2 sin(3x – π/5) + 1. Find the ordered pair of the 4th point in the graph. (A) (17π/15, 1) (B) (17π/15, -1) (C) (17π/30,-1) (D) (17π/30, 1)

Rationalize the denominator (√7)/((√10). The answer is ________ .

Explain the role of symbols in reflective activity.

A triangular swimming pool measures 38 feet on one side and 66 feet on another side. These sides form an angle that measures 40" To the nearest tenth of a foot, how long is the third side? Length of third side___ feet

A ferris wheel is 20 meters in diameter and boarded at ground level. The wheel makes one full rotation every 7 minutes, and at time t = 0 you are at the 3 o'clock position and ascending. Let f(t) denote your height (in meters) above ground at t minutes. Find a formula for f(t). f(t) = _______

The expression [(x⁴y³)⁶ (xy⁶)-³] / (x⁴y⁵) equals xᵉ/yᵈ where the exponent e of x is ____, the exponent d of y is _____.

What is the solution to the inequality -6 + |2p + 3| > 7? (a) p < -8 or p > 5 (b) -8 < p < 5 (c) p < -2 or p > -1 (d) -2 > p > -1

Rationalize the denominator of (√a-5)/(2√a-√b) Assume that all variables represent positive real numbers. (√a-5)/(2√a-√b)= ________

If (fg)(x) = h(x) such that h(x)=√4x+8, which of the following could accurately represent f and g? f(x)=√2x+4 and g(x)=√2x+4 f(x) = 4x + 8 and g(x)=√x f(x)=√x and g(x) = 4x + 8 f(x)=√2x+4 and g(x)=√2

The 12-foot ladder leaning against a building forms an angle of 58° with the ground. How far up the building does the ladder reach?

For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for an ODD function and N for a function which is NEITHER even nor odd. f(x) = x² - 6x² + 3x4 f(x) = -5x²-3x² - 2 f(x) = x² + 3x² + 2x9 f(x) = x³ + x³ + x9

The probability of event A is P(A)=67/100 Find the probability of the complement of event A. P(A‾ ) =

You conduct a survey that asks 250 students in your class whether they are planning to go on a trip this summer. One hundred thirty-five males respond, 93 of which are planning to go on a trip this summer. Twenty-two females are not planning on taking a trip this summer. a) Organize the results in a two-way table and interpret the marginal frequencies. b) What percent of females are planning to go on a trip this summer? Explain.

Find the sum of the first twelve terms of the sequence -9,3,15,...,123, where 123 is the twelfth term. The sum is

Write the electron configuration for a boron cation with a charge of +3.

You take out a 65-day single-payment loan for $609 with an interest rate of 21%. What is the amount of the maturity value? $636.72 $631.77 $613.66 $621.31