Sequences & Series Questions and Answers

A business has found that it can sell 670 items if it sets its price to $66.91. However, if it lowers its price to $43.71, it can sell 950 items. (a) Find the linear demand equation (price function) for selling x items. (round to 4 decimal places) p(x)=? It costs the business $11.86 per item to produce and they have $2,150 in overhead each month. (b) Find the linear Cost, and quadratic Revenue and Profit functions for producing/selling x items: (round to 4 decimal places) C (x)___x+ _____ R(x)=____x²+ _____x+______ P(x)=____x²+______x+______ (c) Consider the maximum profit the company can make: To maximize their profit, they should sell _______items at a price of $_______each and they will make $_____ in profit.

Find the product. (3x+7) (x²-3x+2) ∞ (3x + 7)(x² - 3x + 2) =

find all positive integers n so that the base 10- representation of n! "ends with" exactly 2021

Find the following; f(x) = 3x + 1, g(x)=x²-16 (a) (f+g)(x) = (b) (f-g)(x) = (c) (fg)(x) = (d) (f/g)(x) =

A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,017.36 square feet? Use 3.14 for π The sprinkler can spread water ____ feet away.

Determine the independent and dependent variables for the following relationship: "The number of bedrooms in a home is related to the number of family members." Dependent Variable:__________ Independent Variable:________

There are 119 students in Mr. Smith's class. Fifty six of the students are female and sixty three students are male. Fill out the following chart. female male total Volleyball 20 45 Basketball 30 40 Soccer 26 8 34 total 56 63 119 Find the probability that if a student is chosen at random that they are male or play volleyball?.

Use the equation of the linear regression to interpolate and determine the value of x when y = 255. Round your answer to the nearest tenth. X 1 2 3 4 5 6 Y 84 155 241 310 405 478

Two decimal numbers are given. One digit of one of the numbers is covered. Determine whether we should reject or fail to reject the claim. See Examples 3 and 4. Claim: 8.037> 8._39

Approximate sin(2x³)/x² within 0.0001 if x = 1/3 using its Mac expansion and justify your result.

A farmer has 360 feet of fencing to make three identical adjacent rectangular pens. What dimensions of each pen will maximize the total enclosed area? What is the maximum area?

An earthquake off the coast of Vancouver Island was measured at 8.7 on the Richter Scale and an earthquake off the coast of Alaska was measured at 6.5. How many times more intense, to the nearest whole number, was the earthquake off the coast of Vancouver Island than the one off the coast of Alaska?

Use an Addition or Subtraction Formula to simplify the equation. sin(θ) cos(3θ) + cos(θ) sin(3θ) = 0 Find all solutions in the interval [0, 2x). (Enter your answers as a comma-separated list.)

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a comma-separated list.) 5 sin³ θ + 10 sin² θ - 4 sin θ - θ = 0; θ =

Convert the ordered fair in rectangular coordinates to Polar coordinates with r>o and O≤θ≤2π (4,-10)

The length 2 cos(2π/13) is a root of where a is the larger root of p(x) = x³ - ax²-x+a-1, q(x) = x² + x - 3. What center (a, b) should we use to solve the cubic? Note that the center is constructible using just a straightedge and compass.

A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 90 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Use squaring to solve the following equation over the interval [0,2x). sec 2x+tan 2x=4 Select the correct choice below and fill in any answer box in your choice, if necessary. A. The solution set is (Do not round until the final answer. Then round to the nearest thousandth as needed. Use a comma to separate answers as needed.) B. There is no solution.

Find an eigenbasis of the following linear transformation of R2: projection onto the line L spanned by [-1 5]

Find the terminal point for the following: t = -300 degrees

For each angle below, determine the quadrant in which the terminal side of the angle is found and find the corresponding reference angle θ. [NOTE 1: Enter '1' for quadrant I, '2' for quadrant II, '3' for quadrant III, and '4' for quadrant IV.] [NOTE 2: You can enter as 'pi' in your answers.]

A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 78°. How high does the ladder reach on the building?

Suppose e₁,e2, ..., en is an orthonormal basis of V and 0₁, 02, ..., Un are for each j. Prove that V₁, V2,..., Un is a vectors in V such that ||e, - vj|| < 1/ √n basis of V.

The first term of a sequence is -8. Each subsequent term equals 4 more than twice the previous term. a) Write the first four terms of this sequence. b) Represent the sequence with a recursive formula, then draw its graph.

A rectangle has a width that is 2 inches longer than its length. The area of the rectangle is 323 square inches. Write and solve an equation to find the dimensions of the rectangle.

(Polynomials) Write down an example of a 4ᵗʰ degree polynomial that has a leading coefficient of -3 and constant term of 1.

Use Table 3 (found using the Written Example button) to find the area under the standard normal curve for the given situation. a. between z = -0.33 and z = 2.67. b. for 1.34 < z < 3.22

a) Write down two examples of polynomials. b) Identify the constant term, degree, and leading coefficient of your polynomials.

1. Find the GCF of the following: a) xy, y²x, x²y b) x², x³, x³ c) y²(2y - 1), 3(2y - 1) 2. Identify the missing factors: d) 20 = (4) (?) e) -14x = (7)(?) f) x³ =x² (?)

Perform the operations and simplify. a) 5x(x+3)− 4(x² - 7x) b) (3x - 2y) (5x + y) c) (2a - b)²

1. Write the following real numbers in ascending order {i.e. from least to greatest} |-10.1| , |-21/2| , –9.8, |10|, –10, |-9,9|, |–9+7/8|, –9

Explain in your own words how to divide a polynomial by a monomial. Perform the operation and simplify: {(12x²)-(21x)/(3x)}

Use the half-angle formulas to simplify the expression. √1-cos 10x/2 Solve the equation. (Find all solutions of the equation in the interval [0, 2π). Enter your answers as a comma-separated list.) 3 sin(4x) = -6 sin(2x) X =

A farmer picks 242 apples on Monday and 118 apples on Tuesday. On Wednesday, she sells 109 of the apples at the market. Which equation can be used to find a, the number of apples the farmer has left? A) 242 + 118 + 109 = a B) 242 +118 -109 = a C) 242 -118 -109 = a D) 242 -118 + 109 = a

g(x) = 78-7x Find x when g(x) = 43. (Just type the number).________

(Restrictions, linear equations, interval notation, domain) To find the domain of a function we need to find restrictions on x by solving an equation and write our answer in interval notation. Find the domain and write your answer in interval notation. a) f(x) = {x/(x-6 )} b) g(x) = {5/+3x+1)} Domain: ___________ Domain ___________ main and range) We can also find the domain and range of a function by table of values. Use the graph

If a(3, 4) - b(2, 4) = (8, 10), determine a and b. Just enter the answers for a and b. NO NEED TO SHOW WORK!

Let n be an odd integer ≥ 25. (1) Find the number of pairs (x, y) of positive integers which satisfy the equation x + 2y = n. (2) Find the number of triples (x, y, z) of positive integers which satisfy the equation + y + 2z = n.

Which of the following graphs is the correct plot of y = - 3 cos(x)?

1 2 3 a=2 3 4 1 5 8 a)If the matrix of cofactors from A is 4 -12 7 -1 5 -3 find β -1 β -1 b)Hence, using (a), find its inverse.

Find the variation constant and an equation of variation where y varies directly as x and y = 18 when x = 3. The variation constant is k = ______.

Determine if a graph is a function. Is this the graph of a function? No Yes

Sketch a graph of the function f(x) = 0.5 sin(4x).

An object was dropped off the top of a building. The function f(x) = -16x² +484 represents the height of the object above the ground, in feet, a seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function. f(-3) = ___ meaning that ___ seconds after the object was dropped, the object was feet above the ground. This interpretation ___________ in the context of the problem. f(2.5) ___ meaning that ____ seconds after the object was dropped, the object was ___ feet above the ground. This interpretation _______ in the context of the problem. f(11)= ____ , meaning that seconds after the object was dropped, the object was ___ feet above the ground. This interpretation _______ in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is _____

Find an equation of variation where y varies inversely as the square of x, and where y = 0.76 when x = 0.1. The equation of variation is y =

Convert the angle 477° to radians. Give the exact value. This means there should be a π in your answer. Also, any fraction in your answer should be fully reduced.

Graph the trigonometric function. y = -3 cosec(2/3x) Start by drawing three consecutive asymptotes. Then plot two points, one on each side of the second asymptote. Finally, click on the graph-a-function button.

Write the series using summation notation. 1/3+1/9+1/27+1/81....

For y = 3 sin 8x, its amplitude is its period is

The maximum number of grams of fat (F) that should be in a diet varies directly as a person's weight (W). A person weighing 144 lb should have no more than 96 g of fat per day. What is the maximum daily fat intake for a person weighing 33 lb?