Sequences & Series Questions and Answers

Use the given conditions to find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. cos u = -4/5, π/2<u<π sin 2u = ________ cos 2u =________

Use a calculator to solve the equation on the interval 0≤x< 27. Round the answer to one decimal place if necessary. x²-3 sin(2x) = 2x______________ 1.

Prove that f(x)=|x|−|x + 1| is a continuous function.

Evaluate 2x -y for the given replacement values. x = 2 and y = - 19 2x - y =

Shanika has invested in three different stocks. Stock A is currently worth $4.50 per share. Stock B is worth $6.00 per share, while stock C is worth $10.00 per share. Shanika purchased half as many shares of stock B as stock A and half as many shares of stock C as stock B. If her total investments are currently worth $760, how many shares of each stock does she own?

Four times a number, subtracted from nine, is twice the number. Find the number. The number is __ (Simplify your answer.)

Which of the following statements is true? A. Every term of a sequence must be nonzero. B. The terms of a sequence can never be fractions. C. It is possible for the terms of a sequence to alternate in sign. D. The domain and range values of a sequence must be positive integers.

The Scenario The Tortoise and the Hare finally have their long awaited rematch. The Tortoise gets a 1,000 foot lead and runs 9 inches per second. The Hare begins at the starting line and runs at a rate of 6 feet per second. There is also a rat in this race. The Rat starts 1,200 feet ahead of the Hare and runs back Cowards the starting line at a rate of 2 feet per second. The finish line is 1,320 feet way. *Note: it may be helpful to graph this scenario as well. If you scan and upload your graph, you could earn extra credit. Question 3 When will the Tortoise and Rat pass each other and how far will they be from the starting line? Explain your thought process. Time: Distance from start: seconds feet

If the accumulated value of an investment that is growing at 3.11% compounded monthly is $70,912.40, and the interest earned on this investment is $20,912.40, calculate the time period of this investment. years months

3^2x-1 = 6^1-x solve and explain the process

Consider the quadratic function below and (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or a minimum value, and find that value; and (d) graph the function. f(x)=x²-14x+48 (a) The vertex occurs at (Type an ordered pair, using integers or fractions.)

Find the solutions by factoring. Choose all that apply. x² + 4x² = 12 Select one or more: a. +√6 b. ti√6 C. +√2 d. ti√2 e. +2 f. +6

Explain why synthetic division cannot be used to simplify: x³ -3x+1/x² + 1

On the axis below, plot the points C= (2, 9) and D= (8,1) and connect them. Find the length of this segment.

State the number of complex roots and the number of real roots. Choose all that apply. -12 + x + 10x² + 3x³ = 0 Select one or more: a. 3 complex roots b. 2 complex roots c. 1 real root d. 3 real roots e. 2 real roots f. 0 complex roots

Find the approximate area of a sector whose central angle measures 19π/12 in a circle of radius 8 ft to the nearest hundredth.

Given f(x) = 4 ln(x), find the average rate of change of f(x) on the interval (5, 5+ h]. Your answer will be an expression involving h. Don't try to simplify.

katie has a job offer to be a jewelry salesperson that pays $3,100 per plus 1.5% of all sales. What total sales are required to earn between $4,900 and $6,150 per month? Between $1,800 and $3,150 Between $27 and $47.25 Between $209,767 and $413,100 Between $120,000 and $210,000 Between $533,333 and $616,667

Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

The function f is defined as follows. f(x) = -x+4 if x<1 4x-1 if x ≥ 1 (a) Find the domain of the function. (b) Locate any intercepts (c) Graph the function (d) Based on the graph, find the range

Find the first five terms in sequences with the following nth terms. a. 2n² +5 b. 6n + 2 c. 10n - 8 d. 2n-1

Solve the equation. 3[2(x13)-2(2x + 2)]=4[-(x-6)-5(3x-4)]

If P = 4 +6+8+10+...+100 and Q=8+10+12+14+...+102 are sums of arithmetic sequences, determine which is greater, P or Q, and by how much.

A student claims that 1, 2, 3, and 4 are the zeros of a cubic polynomial function. Explain why the student is mistaken. Select one: a. A cubic function can have at most 3 zeros. b. A cubic function will have at least one imaginary zero. c. A cubic function has zeros that are conjugates of each other. d. A cubic function has zeros that are additive inverses of each other.

Given (x³ + 13x2 -12x - 8)/(x + 2). What number would you put in the box on the left when using synthetic division?

Suppose a company has fixed costs of $42 and variable cost per unit of 7x +13 dollars, where x is the total number of units produced. Write a cost function C(x). a. C(x)=42+6x² +10x b. C(x)=42+7x²+ 13x c. C(x) = 42+2x² +15x d.C(x)=42+5x² + 12x e. C(x)=42+3x²+14x

Air temperature decreases as elevation increases. Suppose the weather at the bottom of Whistler Mountain in British Columbia is 25°F one winter day. The temperature x feet above the base of the mountain is given by t = 25-0.0054x. How many feet above the mountain's base will the temperature be less than 8.8°F?

Describe the shape of the graph including the end behavior, turning points, and increasing/decreasing intervals. y = 3x³ - x - 3

A business advertises that everything in the store is an additional 10% off the already reduced prices. Marcus picks out 2 shirts that are on a 30% off rack. If the shirts are originally priced at $28.99 and $30.29 and there is 6% sales tax, how much does Marcus end up paying for them? a. $39.59 b. $37.70 c. $37.35 d. $35.57

6. Determine which statements are true about the function below. If false, change the statement so it is true. a. the function approaches positive infinity as x approaches negative infinity b. the only zeros of the function are -1 and 5 c. there are two turning points

The population of a city in Arizona is 7200 in 2010. The city's population is increasing at a rate of 8% per decade. Using this information, predict the population of the city in the year 2040. Round your answer to the nearest person.

Determine the sign of the leading coefficient and the least possible degree of the polynomial function for the graph. Select one: a. positive, 2 b. positive, 3 c. negative, 2 d. negative, 3

Find the present value of the given future amount. Assume 360 days in a year. $22,948 for 171 days at 9.5% simple interest. What is the present value?

Kathy stood on the middle rung of a ladder. She climbed up 3 rungs, moved down 5 rungs, and then climbed up 9 rungs. Then she climbed up the remaining 3 rungs to the top of the ladder. How many rungs are there in the whole ladder?

Heather held a loan of $1,900 for 8 months and was charged interest of $146.93. What was the annual simple interest rate on this loan? 0.10% 7.73% 11.60% 0.12%

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n = 3; 3 and 2 i are zeros; f(2)= -8 f(x) = (Type an expression using x as the variable. Simplify your answer.)

Find the interest on the following loan. $1400 at 9.5% for 3 months The interest is $ (Round to the nearest cent as needed.)

Use the modular multiplication property to calculate (876 x 978) mod 10 and show your work.

Teri goes shopping for some new clothes and then out to lunch with a friend. She spends $32.94 on some shirts, $15.89 for a belt and $19.99 each for two dresses that are on sale. For lunch, Teri has a salad that is $6.95, iced tea for $1.49 and dessert for $3.49. Teri pays 7% sales tax on both her shopping items and lunch. She tips her server 15%. How much has Teri spent all total for the day? a. $121.52 b. $109.58 c. $107.79 d. $88.19

Taking successive discounts of 15% off and then 25% off is the same as taking a one time discount of 40%. Please select the best answer from the choices provided T F

Find the zeros of the function. State any multiplicity. y = (x + 1)²(x - 1)(x - 2)

Enter the value of each expression in the blank provided. If the expression is undefined, enter undefined in the blank. a. -5(-4)= b. 20(-3) = c. (-12/5).(10/3)= d. -3÷0=

Byron's income last year was $61,700. He made $48,000 at his plumbing job and had income from an apartment that he rented out. If Byron earned the same amount of rent each month for the entire year, approximately how much per month did he collect? a. $940 b. $1,140 C. $4,000 d. $5,140 Please select the best answer from the choices provided A B C D

In a typical diabetic, the level of insulin might be given by the following function: 55t+100 if Osts4 320 if 4<t≤11 -85t+1255 if 11<ts 14 65 if 14<t≤24 Here f(t) is the blood sugar level, in appropriate units, at time t measured in hours from the time of insulin injection. Suppose a patient takes insulin at 5AM. Find the blood sugar levels at 10AM and at 5PM. f(t)= At 10AM, the blood sugar level is: A. 650 C. 320 At 5PM, the blood sugar level is: A. 320 C. 830 B. 65 D. 375 B. 65 D. 235

The final grade in an algebra course is based on a weighted average- homework counts 10%, quizzes count 10%, tests count 50%, and the final exam counts 30%. A student has a homework average of 96, quiz average of 88, and a test average of 84. What is the minimum score a student needs to score on the final exam to earn at least a 90 for the final course grade? (Round to the nearest tenth.)

Determine whether the value of c that makes ax² + bx + c a perfect square trinomial is sometimes, always, or never negative. Explain your reasoning.

Allen bought 1,350 shares of stock for $12 per share. If he sold all his shares for $27,000, how much profit on each share did he make? a. $6 b. $8 C. $10 d. $12

Kai had a gross weekly paycheck of $616 last week. Kai worked 6 hours for 4 of the days and 8 hours on 1 day. What is Kai's hourly rate of pay? a. $16.21 b. $19.25 C. $20.53 d. $25.67 Please select the best answer from the choices provided A B C D

Write the number as a product of a real number and i. Simplify all radical expressions. √-7

The formula S = 16t² is used to approximate the distance S, in feet, that an object falls freely from rest in t seconds. The height of a building is 1288 feet. How long would it take for an object to fall from the top? The object would fall for seconds. (Simplify your answer. Type an integer or a decimal rounded to the nearest tenth.)