Sequences & Series Questions and Answers

Find the infinite sum, if it exists: -3+ (1.2) + (-0.48)+...

Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues. {10/3, 10/9, 10/27, 10/81, 10/243.....}. Assume the first term is a1.Calculate an.

The function f(x) is graphed on the coordinate grid. The function g(x) is given by g(x) = 1.5*. What is g(2) - f(2)? 1. -1.75 2. 1.75 3. 6.25 4. 0.5

Expand (5x - 2)³ (A()125x³+50x²-20x-8 (B) 125x³-8 (C).125x³+50x²+20x-8 (D). 125x³+50x²+10x-89

Solve the system by elimination. y=-x^2-2x+2 y = 4x+2 (a)(5, 3) (b)(1, 1) (c)(0, 2) (d)(2, -9) (e)(4, -11) (f)(-7, -8) (g)(-4, 29) (g)(-6, -22) (h)Ono solutions

Evaluate the function h(x)=x^4+x^2-8 at the given values of the independent variable and simplify. a. h(1) b. h(-1) c. h(-x) d. h(3a) a. h(1)= ____ (Simplify your answer.)

Which equation does the graph below represent? y = 2x y=1/2 x y= 1/2 y = 2+x

A sinusoid reaches a maximum value of (π/2,28 )and a minimum value of (π,12) during a single cycle. What is its amplitude? (a)π/2 (b)8 (c)2π (d)20

Solve the system by elimination. y=2x–1 y = x² 1. (5, 3) 2. (1, 1) 3. (0, 2) 4. (2, -9) 5. (4, -11) 6. (-7, -8) 7. (-4, 29) 8. (-6, -22) 9. no solutions

Simplify: 2x²-x-1/x²-1 ÷ 2x+1/x²-3x+2 Use equation editor to type your answer or insert a picture of the work from your paper.

An auditorium has 79 rows of seats. The first row contains 40 seats. As you move to the rear of the auditorium, each row has 3 more seats than the previous row.How many seats are in the row 17? How many seats are in the auditorium?

Solve the inequality (x/6) < 12 (A) x < 72 (B) x < 2 (C) x > 72 (D) x > 2

Sketch the set of complex numbers such that z(i −z) — z(i + 2) = 2|z|² and justify your answer. Hint: Use (a).

Let (G,*) be a group and a, b ∈ G. Given a * b = b * a-¹ and b*a = a* b-¹. Find the identity element of G.

Simplify to a single trigonometric function: sec(t)-cos(t)/tan(t)

Simplify ∛25d¹⁵/8c⁷ 1. 5d⁵∛c/2c⁶∛c 2. 5d²/2c²∛c

Evaluate sinθ when cosθ= 3/8 and θ lies in Quadrant IV. √55/8 -√55/8 5/8 -√55/64

Consider the region given by x≤7, -x+y ≥ 5, x+2y-z≤ 9, x, y, z ≥0 (a) Formulate the problem using slack variables s1 ≥ 0, s2 ≥ 0 and 83 ≥ 0. Write down the basic solution obtained by choosing the slack variables as pivots. Enter in the form (x, y, z, s1, s2, s3). (b) Is this a feasible solution? True False (c) Write down the basic solution obtained by choosing z, s1, s2 as pivots. Enter in the form (x, y, z, s1, s2, s3) (d) Is this a feasible solution? True False (e) Write down the basic solution obtained by choosing x, y, z as pivots. Enter in the form (x, y, z, s1, s2, s3) (f) Is this a feasible solution? True False

What is an advantage of using the range to describe a data set? Why do you think the standard deviation is considered a more reliable measure of variation than the range?

Which of the following expressions is equivalent to (8³) ^2/3? √8x^9 4x² √(8x^3)3 4x^3

Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. x(t) = t + t² y(t) = t - 1

The following distribution shows the daily pocket money of 40 students of a class. If the mean pocket money is 21.7, find the missing frequencies x and y. Daily pocket money (in ₹) 10-14 14-18 18-22 22-26 26-30 30-34 34-38 Number of students 8 7 4 x 6 y 3

What power function does the polynomial f(x) = −3(x−6)^5(x+11)^7(x+5)^8, resemble for large values of x? y= please explain how to get to the answer

Use the drawing tool(s) to form the correct answer on the provided number line. What is the solution set of this compound inequality? 1 ≤ |= + 3| ≤ 4

Select the correct answer from each drop-down menu. Teresa wants to buy 2 new tires for her mountain bike. She has budgeted $120 for the tires, but after researching costs, knows she may end up spending within $25 of that amount. Write an inequality that Teresa could use to find the cost of each tire. Use the inequality to complete this statement.

Tell whether x and y show direct variation, inverse variation, or neither. x 1 2 3 4 y 7 14 21 28 a).Inverse variation b).Direct variation c). Neither

Public Service Utilities uses the equation = 6.66 + 24 log(x) to determine the cost of electricity. x represents the time in hours and y represents the cost in dollars. If a family can afford to spend $30 per month for their electricity bill, which expression represents the number of hours of electricity they can afford? (a) 6.66+ 24 log(30) (b)10^30-6.66/24 (c)30-6.66/24 (d)30+ 6.66/24

Approximate the solution of the system to the nearest thousandth. y = -x² + 3x + 2 y=-3^x The solution of the system is about

Consider the graph of y = -3 cos x-2/14 + 4 I. The amplitude is 3 II. The period is 10 III. The phase shift is 2 to the right IV. The vertical displacement is 4 up (a)I (b)ll (c)III (d)IV

Explain why it makes sense to call the expression x² + 20x + 100 a "perfect square. Solve x² + 20x + 100 = 81.

If $8000 is invested at a rate of 4.7% compounded continuously, find the balance in the account after six years. A= Pe^rt

A framed picture has a total area y, in square inches. The thickness of the frame is represented by x, in inches. The equation y = (8+2x)(10+2x) relates these two variables. 1. What are the length and width of the picture without the frame? 2. What would a solution to the equation 100 = (8+2x) (10+2x) mean in this situation?

How many solution(s) does the equation x+2/x-4-1/x=4/x² - 4x have ? (a) 0 (b)1 (c)2 (d)3

Convert 13π/6 radians to degrees. 1. 195° 2. 390° 3. 450° 4. 900⁰

Find an expression for some matrix A that has a range space equal to the null space of some matrix B

Not yet answered Marked out of 10.00 Flag question Solve the equation [6]17 X+ [10117= [13]17 X+ [7]17 for X Z17. Write your answer as X=[x]17 where 0 sx< 17. What is x?

The sum of a geometric series is 31.75. The first term of the series is 16, and its common ratio is 0.5. How many terms are the series?

You deposit # 100 in a savings account that earns 6% annual interest compounded monthly. What is the balance after 5 years.

Vanessa earns a base salary of $400.00 every week with an additional 5% commission on everything she sells. Vanessa sold $1650.00 worth of items last week. What was Vanessa's total pay last week? $ _________________

Let B={(1 1),(2 1)} a basis for R². Find the vector x if [x]β=(2 3) a) x=(-3 4) b) x=(6 5) c) x=(8 5) d) x=(1 8)

Let W be the set of all vectors {x , y , x+y} with x and y real. Find a basis of W perp.

Given y <-2x+3,y≥x-4 , which of the following describes the boundary line and shading for the first inequality in the system? a)solid line, shade above b)solid line, shade below c)dashed line, shade below d)dashed line, shade above

Find a coterminal angle between U 13) -330° 15) 640°

Connie has d dolls. Carla has 8 more dolls than Connie. Which expression represents how many dolls Carla has? a)d-8 b)d+8 c)d/8 d)8d

Sketch and find the measure of an angle in standard position for each reference angle. 13. 10° in Quadrant II 14. 35° in Quadrant IV 15. 34° in Quadrant III

Write each expression in factored form. If it is not possible, write "not possible." (a) a²-36 (b)49-256² (c)3. c² +9 (d)100/81-16d²

Find the midpoint of the segment having endpoints (6.3,-3.2) and (3.2.-6.3). The midpoint is (Simplify your answer. Type an ordered pair, using integers or decimals.)

Find dy/dt. 10) y = (1+ sin 12t)⁻⁴ A) -48(1 + sin 12t)⁻⁵ cos 12t B)-48(cos 12t)⁻⁵ C) -4(1 + sin 12t)⁻⁵cos 12t D) -4(1+ sin 12t)⁻⁵

A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. y ≥ x² + 1,000 y > 2x^2 + 50 Which points represent viable solutions? (5,3,000) (25, 2,500) (20, 2,200) (10,1,100) (30, 2,000)

Use the result of Question 17 to find the sum of the first 200 terms of the series. -3+4+11+18+25+... Type your answer into the space below.