Sequences & Series Questions and Answers

Given that f(x) = 3x - 1 and g(x) = x2 - 2x. Find g(-3) and then evaluate f(x) at that value. -80 -10 44 120

The expression (5-1) 2-4 is equivalent to A) 5-2-4 B) 5-1+4 C) 5-2+5 D) 5-2-5

Solve for x in tan² x cscx - √2 tan² x = 0. A. x = 180°k, x = 45° +180°k, or x = 315° +180° k B. x = 360°k, x = 45° +180°k, or x = 315° +180° k C. x = 180°k, x = 135° +360°k, or x = 225° + 360° k D. x = 180°ºk, x = 45° +360°k, or x = 315° + 360° k E. NO correct choices

Given the vector u= (10√2, 10√2), find the magnitude and direction of u. Select the correct answer below: Olut= 10;0= 45° Olut= 10;0= 135° Out= 10:0=315° Olut= 20;0= 45° Olut= 20;0= 135"

Prove the following identity: [4] cos (x) sin(2x) cos(2x)cot (2x) = 2- cos(x)csc(2x). 2sin (x) cos(x) sin(2x) + sin(x)csc(2x)

A bacteria culture starts with 100 bacteria and grows at a rate proportional to its size. After 2 hours the population grows to 200 bactería. (a) Express the population A after t hours as a function of t. (b) What will be the population after 4 hours? (c) How long will it take for the population to reach 2090? (a) Express the population A after t hours as a function of t. A(t) = Round k to 4 decimal places.) (b) What will be the population after 4 hours? Approximately bacteria. (Do not round until the final answer. Then round to the nearest whole number as needed.) (c) How long will it take for the population to reach 2090? in approximately hours. (Do not round until the final answer. Then round to the nearest hundredth as needed)

Use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. (If a triangle is not possible, enter IMPOSSIBLE in each corresponding answer blank.) A = 130°, a = b = 15 B = C = C =

An object undergoes uniform linear motion on a straight path from point A to point B in At sec. Write parametric equations over an interval I that describe the motion along the path. Express numbers in simplest form. A-(2,4), B (8, 2), and At=2 The parametric equations are.x= and y= for 0≤t≤2.

Let f(x) = 6x-8 and g(x)=x²-4x+8. (If an answer is undefined, enter UNDEFINED.) (a) Find f(7)+g(7). (b) Find f(7)-g(7). (c) Find f(7)g(7). (d) Find f(7)/g(7).

The solution of the following system of linear equation (SLE) is unique. True or false? x-y-z = 3 2x − 3y + z = 2 3x - 4y = 5 O TRUE O FALSE

Assume that the recursively defined sequence converges and find its limit. a₁ = -20, an+1 = √20+ an The sequence converges to. (Type an integer or a decimal.)

If f(x)=|4+x|−1 is not a one-to-one function, restrict the domain of the function to quarantee the existence of the inverse, and plot the graph of both functions on the same same system of coordinate axes indicating their domain and range.

4 burgers and 4 tacos cost $12,7 burgers 2 tacos cost $16.50 find the cost of 1 burger and 1 taco.

An amount of $4500 is invested at 12% interest, compounded daily. a. Find the future value in 8 years. b. Determine whether more or less money would have accrued if the money had been compounded quarterly. a. The total amount is $ (Round to the nearest cent as needed.)

An amount of $4500 is invested at 14% interest, compounded daily. a. Find the future value in 6 years. b. Determine whether more or less money would have accrued if the money had been compounded quarterly. a. The total amount is $ (Round to the nearest cent as needed.)

The angle of elevation to a nearby tree from a point on the ground is measured to be 74°. How tall is the tree if the point on the ground is 54 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.

Rajani wants to use a sheet of fiberboard 31 inches long to create a skateboard ramp with a 19° angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.

Mamadou leans a 18-foot ladder against a wall so that it forms an angle of 75° with the ground. What's the horizontal distance between the base of the ladder and the wall? Round your answer to the nearest tenth of a foot if necessary.

A giant tortoise can travel 0.14 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles? It would take the tortoise approximately (Round to the nearest tenth as needed.)

7. (Periodic compounding) If $3,500 is invested at 4% interest compounded monthly, then how much will be in the account in 5 years? Setup an equation and solve. Label your answer and round to two decimal places. P = r= k= t = S = ?

Given triangle ABC, angle A is 40 degrees, sides b = 7 m and a = 6 m. Find angle B. Round the angle(s) to two decimal places.

Three moons are in the same circular orbit around a planet. The moons are each 98,000 kilometers from the surface of the planet, located at points A, B, and C. The planet is 12,000 kilometers in diameter and m∠ABC = 90°. How far is point A from point C? km

A parallelogram has sides of 20 cm and 30 cm with an angle of 80° between the two sides. What is the length of each of the diagonals?

Solve the rational equation: 10m/m² - 9+1/m-3=1/m+3 Answer: m = Enter your answer as an integer or rational number in the form A/B, using.

Nell has a sales clerk job that pays $12.00 per hour for regular work hours (less than or equal to 40 hours per week). She gets double time (or $24 per hour) for any hours over 40 that she works in a week. Which of the following functions can be used to represent Nell's weekly pay for working h hours in a week? Is the answer P(h) = {12(40) 0<h<_40 over 24h h.40

If 20100 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent. (a) Annual: $ (b) Semiannual: $ (c) Monthly: $ (d) Daily: $

Convert the angle 90° to radians. Give the exact value and use pi for π.

Express the equation in exponential form (a) log2 16= 4 That is, write your answer in the form 2^A= B. Then A= and B= . (b) log5 125 = 3. That is, write your answer in the form 5^C = D. Then C = and D=

Let P be the plane with equation x+2y+2z = 8. Find four distinct points on P at distance 6 √2 to the point Q = (0, 6, 7). R1 = (0, 0, 0) R2 = (0, 0, 0) R3 = (0, 0, 0) R4 = (0, 0, 0)

The variables x and y vary directly. Use the given x and y values to write a direct variation equation and find y given that x = 12. Enter any fractional answers in the form 1/2.

Without graphing the function y = 7 sin(2x), determine its amplitude, period, and section width (distance between critical points. Leave answers in exact form; type pi for π.

A bank loaned out $33,000, part of it at the rate of 4% annual interest, and the rest at 8% annual interest. The total interest earned for both loans was $1,960.00. How much was loaned at each rate?

Total emissions of carbon dioxide from the burning of fossil fuels have been increasing at about 7% per year (data from 2010 to 2011). If emissions continue to increase at this rate, about how much higher will total emissions be in 2050 than in 2010? Using the approximate formula, emissions will increase by a factor of between 2010 and 2050. Using the exact formula, emissions will increase by a factor of between 2010 and 2050.

Let g be the function g(x) = { 2- |x| if -2 ≤ x ≤ 2 { 0 otherwise Find the Fourier transform ĝ(u) of g, using the definition of the Fourier transform (set up and find the integral).

Given the function f(x) = 3x² - 3x + 7. Calculate the following values: f(-2) = ƒ( − 1) = f(0) = f(1) = f(2)=

Montana invests $10600 in two different accounts. The first account paid 5 %, the second account paid 13% in interest. At the end of the first year he had earned $938 in interest. How much was in each account? $ at 5% $ at 13%

If f(-2) = 5, then the point is on the graph of f. Enter an n-tuple [more..]

Write an equation for a line parallel to y = -2x + 4 and passing through the point (1,-6) y =

If 88 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.5 and total receipts for the concert was $161.25, how many of each went to the concert?

The Nutty Professor sells cashews for $6.60 per pound and Brazil nuts for $5.50 per pound. How much of each type should be used to make a 27 pound mixture that sells for $6.11 per pound? Round answers to the nearest pound. pounds of cashews pounds of Brazil nuts

In 1990 the average family income was about 36000, and in 2000 it was about 46094. Let = 0 represent 1990, x = 1 represent 1991, and so on. Find values for a and b (rounded to one decimal place if necessary) so that f(x) = ax + b models the data What was the average family income in 1995?

Write an equation for a line perpendicular to y = 3x + 2 and passing through the point (-3,-2) y =

Let A, B, C and D be non-zero digits, such that CD is a two-digit positive integer. BCD is a three-digit positive integer generated by the digits B, C and D. ABCD is a four-digit positive integer generated by the digits A, B, C, and D. Suppose that CD BCD ABCD + 4679 The value of A + B + C + D is .... (A) 16 (B) 17 (C) 18 (D) 19

Find the exact length of the curve. y = (x + 4) ³/2, 0≤x≤ 4

(1 point) Let f(x) = 36 - x². a) Compute each of the following expressions and interpret each as an average rate of change:

Write the sum using sigma notation: -1+5+ 11 + ... + 29 Σ i=1

The exponential model A = 497.6 e^ 0.004t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 561 million. The population of the country will be 561 million in (Round to the nearest year as needed.)

If the standard quota for how many new schools will open in the 5 boroughs are: Bronx: 20.73 Brooklyn: 10.12 Queens: 35.44 Manhattan 25.16 Staten Island 5.44 Use Jefferson's plan to apportion the Queens

Consider an object moving along a line with the following velocity and initial position. v(t)=9-3t on [0.5]; s(0)=0 Determine the position function for t20 using both the antiderivative method and the Fundamental Theorem of Calculus. Check for agreement between the two methods.

There is a mound of g pounds of gravel in a quarry. Throughout the day, 300 pounds of gravel are added to the mound. Two orders of 500 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,500 pounds of gravel. Write the equation that describes the situation.