Sequences & Series Questions and Answers

points) Find the sequence generated by the following exponential generating function: f(x)=e^x- e^-2x +1-5x³

On the grids below, sketch a graph of a function that a) VA at x = 2 HA at y = -3 f(x) is increasing on the intervals x < 2 and 2<x< 4 f(x) is decreasing on the interval x>4

Rewrite 7" = n as a logarithmic equation. b) log, m = n a) log, 7 = m n log 7 = n d) log, n = m

Which of the following local/global truncation errors are correct for the 2nd order Adams-Bashforth method? (At³) local, O(At²) global (At²) local, O(At²) global (At³) local, O(At³) global (At5) local, O(At4) global (At) local, O(At²) global (At) local, O(At) global None of the above

Solve the absolute value inequality. |x+6| ≤9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is (Simplify your answer.) B. The solution set is Ø.

How many grams are in 1 decigram? 1 dg = [?] g A. 1/10 g or 10¹ g B. 1/1000 g or 10-³ g C. 100 g or 10² g D. 1000 g or 10³ g

Evaluate x/y for x = -5 and y = -1. Select the correct choice below and fill in any answer boxes in your choice. A. x/y = B. The answer is undefined.

Bryan, Michael, and Han are painting a house. Working together, they can paint the house in 6 hr. Working alone, Bryan can paint a similar sized house in 15 hr and Han can paint a similar sized house in 18 hr. How many hours would it take Michael to paint a similar sized house working alone? Enter the answer to the nearest tenth.

Using an absolute value inequality, describe all the z-values within a distance of 1 units from the number 7. Your answer should be of the form lx-al ≤ b.

What is the least common denominator of fractions with the given denominators? 14 and 21

Solve the absolute value inequality. |2x - 4| >8 Rewrite the inequality without absolute value bars. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. <2x-4< B. 2x-4< or 2x-4> C. 2x-4>

A student provided the solution for solving the following equation. Click on the part in which an error was made. 7x /x-3 = 48/x-3 + 1

A text message plan costs $10 per month plus $0.41 per text. Find the monthly cost for x text messages. The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.)

Evaluate 2x-y for the given replacement values. x = 6 and y = -17

Evaluate x-y for the given replacement values. x=6 and y=-37

Use a sum or different identity to find the exact value of the expression. Tan = 7x/12

Find the slope of the line that passes through the given points. (1,-3) and (3,-4) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is (Type an integer or a simplified fraction.) B. The slope is undefined.

Find the slope of the line. 4x-3y = 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The slope of the line is B. The slope of the line is undefined. (Simplify your answer.)

The basic fee for a sailboat rental is $75. There is an additional $20 fee for each additional hour over 2 hours. The explicit rule a, = 75 + 20n gives the amount of the rental for n hours over 2 hours. Write a recursive rule for the amount of the rental for n hours over 2 hours.

Answer this questions by True or False For full row rank matrix A, Ax = b can be unsolvable.

Determine whether each ordered pair is a solution of x=7/8y. Is (0,0) a solution of the given linear equation? No Yes

A bathtub is being filled with water. The height of the water increases by 1 inch each minute. What is the independent quantity in the relationship between time and the height of the water? The time that has passed since the water was turned on The time it takes to fill the tub with water The height of the water when the tub is full The height of the water after a certain amount of time has passed

A certain product has supply and demand functions given by p = 40q+ 300 and p = 9300-50q, respectively. (a) If the price p is $1300, how many units q are supplied and how many are demanded? (b) What price gives market equilibrium, and how many units are demanded and supplied at this price? (a) When the price p is $1300, there are (Simplify your answer.) ... units supplied and units demanded.

For the functions f(x) = sinx and g(x) = cos x, (f/g) (x) would be equal to: a) (f/g) (x) = cos²x b) (f/g) (x) = sin² x c) (f/g) (x) = sin x cos x d) (f/g)(x) = tanx

A water tank can be filled by an inlet pipe in 9 hours. It takes 4 times as long for the outlet pipe to empty the tank. How long will it take to fill the tank if both pipes are open?

Find the slope of the line x= 1. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is B. The slope is undefined. (Type an integer or a simplified fraction.)

Solve the following inequality. 8-5y ≥ 10 What is the best first step to solve the given inequality? Choose the correct answer below. A. Use the addition principle to isolate the y-term on one side of the inequality. B. Use the multiplication principle to isolate the y-term on one side of the inequality. C. Use the addition principle, so that one side of the inequality is zero. D. Use the multiplication principle, so that one side of the inequality is zero. To solve the given inequality, use the addition principle for inequalities. Which number or expression should be subtracted to get the terms without variables on the right side of the inequality? 8 Subtract 8 from both sides of the inequality. 8-5y ≥ 10 8-5y- 10 - Simplify. (Type the terms of your expression in the same order as they appear in the original expression.)

Find the compound interest on a sum of Rs.12.000 at the rate of 8% per annum for 1 year compounded quarterly.

Write using exponential notation. 3-3-6-6-6 3-3-6-6-6=

Write the sentence as an equation. Two times the difference of -15 and 3 amounts to -36. The sentence "two times the difference of -15 and 3 amounts to -36" written as an equation is

Which of the following is the correct way to express 1.37 in scientific notation? 1 A.37 x 10-1 B 1.37 x 10⁰ C 1.37 x 101

For the function, y=-4x³ +2x²-x+5, a) State which finite difference will be constant? b) Determine the value of the constant finite difference.

Evaluate the following expression for x= -2, y=4, and z= -1. 3x - 5y-6z 3x-5y-6z= 0

A coffee shop is selling their donuts for $1. In an average week they sell 300 donuts. For every $0.05 increase in price, the coffee shop will sell 20 less items. Which of the following revenue functions with respect to price increase is correct? a) R(n) = (1+0.05n) b) R(n)= (300 -0.05n)(1+20n) c) R(n) = (300- 20n) d) R(n)= (300-20n)(1+0.05n)

a Given that sin²(θ/2)=2 sinθ, show that √17 sin (θ+a)= 1 and state the value of a, where θ<a</7/2 (-/-) = 2 sin 0, (3 ma (2) for 0° ≤θ ≤ 360° b Hence, or otherwise, solve sin² (4 ma

Translate the phrase and then simplify. Subtract 21 from - 20. The phrase translates to the expression _. (Do not simplify.) The result of the subtraction is (Simplify your answer.)

Factor the expression completely or state that the polynomial is prime. 4x³ - 4x Select the correct choice below and fill in any answer boxes within your choice. A. 4x³ - 4x = (Factor completely.) B. The polynomial is prime.

Given tan(θ)=8/9, find the exact value of sin(2θ).

Evaluate x-y for the given replacement values. x = -3 and y=9 x-y=

Find the slope of the line. - 9x - 4y = 5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is (Simplify your answer.) B. The slope is undefined.

Evaluate the following statement as true or false: A negative a value in f(x) = a sin(x) reflects the function in the x-axis a) True b) False

Solve the system of equations by the addition method. 3x + y = 1 - 12x - 4y = -4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions; {(x,y) |3x+y=1} or {(x,y) - 12x - 4y = -4}. C. There is no solution; or Ø.

A liquid sample has a mass of 2.56 kg and a volume of 0.820 L What is the density of this liquid in kilograms per liter? density=[?] kg/L Round your answer to the hundredths place. Density (kg/L)

Determine if the following ordered pairs are solutions to the equation 3x+y=18. (3,8) (6,0) (0,18) Is (3,8) a solution to the equation 3x+y=18? Select the correct choice below and fill in the answer box to complete your choice. A. No, because when 3 is substituted for x and 8 is substituted for y, simplifying the left side results in __ which does not equal the right side. B. Yes, because when 3 is substituted for x and 8 is substituted for y, simplifying the left side results in___ which equals the right side.

The granite sample has a mass of 24.31 g and a volume of 9.35 cm3. What is the density of the granite? d = [?] g/cm³ density (g/mL)

Does the system below have a unique solution, no solution, or many solutions? What does this mean graphically? 2x + 3y = 16 x + 1.5y = 8 Does the system have a unique solution, no solution, or many solutions? A. no solution B. many solutions C. a unique solution

Plot the ordered pair (5,3). State in which quadrant or on which axis the point lies. Plot the ordered pair on the graph to the right.

At St. John's, Newfoundland, the time of sunrise on the nth day of the year (Jan. 01 is n=0) is given by the equation: T(n) = 1.89 sin 2π(n-80/365) +6.41 When will the sun rise on Oct. 20th? a) 5:40 am b) 5:45 am c) 5:28 am d) 5:46 am

Par on a golf course is 72. If a golfer shot rounds of 76, 67, and 70 in a tournament, what will she need to shoot on the final round to average par?

Let P be a polynomial with integer coefficients. Suppose that for n = 1,2,3,..., 1998 the number P(n) is a three-digit positive integer. Prove that the polynomial P has no integer roots.