A manufacture has been selling 1800 television sets a week at $390 each. A market survey indicates that for each $10 rebate offered to a buyer, the number of sets sold will increase by 100 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price. p(x) =

b) How large rebate should the company offer to a buyer, in order to maximize its revenue? dollars

c) If the weekly cost function is 117000 + 130x, how should it set the size of the rebate to maximize its profit? dollars

For the first week of January 2020, Toronto Organic Coffee at Eaton Centre sold a total of 8500 cups of organic coffee. The total sales revenue for the coffee was $64,600. There are three types of organic coffee: a cup of student organic coffee costs $5.00, a cup of regular organic coffee costs $6.00, and a cup of superior organic coffee costs $8.50. How many cups of each type of coffee was sold if twice as many regular organic coffee were sold as student organic coffee?

The number of cups of student organic coffee sold by this store was

The number of cups of regular organic coffee sold by this store was

The number of cups of superior organic coffee sold by this store was

A square plot of land has a building 70 ft long and 60 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 10,200 ft2, what are the dimensions of the entire plot of land?

A wire 370 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = 2x^3 + xy^2 + 5x^2 + y^2 + 4

On this problem, you may use a computer to calculate the derivative. Consider the function f(t) = (2t^2) / (3t^2 + 1) :

(a) On what intervals is the function concave up, and on what invervals is it concave down? Why? (b) (5 points) On what intervals is the function increasing, and on what intervals is it decreasing? Why?

(b) On what intervals is the function increasing, and on what intervals is it decreasing? Why?

non-homogeneous ODE. solve this equation analytically.

-2y''+5y'+3y=exp(-0.2x) b.c y'(0)=1, y'(10)=-y(10)

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.

y = e^x, x = 0, y = 7π;    about the x-axis

Consider the function f(x)=arctan [(x+6)/(x+5)]

Express the domain of the function in interval notation: Find the y-intercept: y= . Find all the x-intercepts (enter your answer as a comma-separated list): x= . Does f have any symmetries? f is even; f is odd; f is periodic; None of the above. Find all the asymptotes of f (enter your answers as comma-separated list; if the list is empty, enter DNE): Vertical asymptotes: ; Horizontal asymptotes: ; Slant asymptotes: . Determine the derivative of f. f'(x)= On which intervals is f increasing/decreasing? (Use the union symbol and not a comma to separate different intervals; if the function is nowhere increasing or nowhere decreasing, use DNE as appropriate). f is increasing on . f is decreasing on . List all the local maxima and minima of f. Enter each maximum or minimum as the coordinates of the point on the graph. For example, if f has a maximum at x=3 and f(3)=9, enter (3,9) in the box for maxima. If there are multiple maxima or minima, enter them as a comma-separated list of points, e.g. (3,9),(0,0),(4,7) . If there are none, enter DNE. Local maxima: . Local minima: . Determine the second derivative of f. f''(x)= On which intervals does f have concavity upwards/downwards? (Use the union symbol and not a comma to separate different intervals; if the function does not have concavity upwards or downwards on any interval, use DNE as appropriate). f is concave upwards on . f is concave downwards on . List all the inflection points of f. Enter each inflection point as the coordinates of the point on the graph. For example, if f has an inflection point at x=7 and f(7)=−2, enter (7,−2) in the box. If there are multiple inflection points, enter them as a comma-separated list, e.g. (7,−2),(0,0),(4,7) . If there are none, enter DNE.

Does the function have any of the following features? Select all that apply.

Removable discontinuities (i.e. points where the limit exists, but it is different than the value of the function)

Corners (i.e. points where the left and right derivatives are defined but are different)

Jump discontinuities (i.e. points where the left and right limits exist but are different)

Points with a vertical tangent line

Upload a sketch of the graph of f. You can use a piece of paper and a scanner or a camera, or you can use a tablet, but the sketch must be drawn by hand. You should include all relevant information that has not been requested here, for example the limits at the edges of the domain and the slopes of tangent lines at interesting points (e.g. inflection points). Make sure that the picture is clear, legible, and correctly oriented.

Assume that when adults with smartphones are randomly​ selected, 49​% use them in meetings or classes. If 15 adult smartphone users are randomly​ selected, find the probability that exactly 11 of them use their smartphones in meetings or classes.

Let A0.A1,A2,A3,A4 devide a unit circle (circle of radius one) into five equal parts. Prove that the chords A0 A1, A0 A2 satisfy:

(A0 A1 * A0 A2)^2 = 5.

A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at is deepest point. A cross-section is shown in the figure. If the pool is being filled at a rate of 1.1 ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft? (Round your answer to five decimal places.)

The flat circular plate has the shape of the region ? 2 + ? 2 ≤ 4. The plate, including the boundary ? 2 + ? 2 = 4, is heated so that the temperature at the point (x, y) is: ?(?, ?) = ? 2 + ? 2 − 2? + 1. Find the temperatures at the hottest and coldest points on the plate.

Determine the interval of convergence for the power series representation of the following function.

f(x)=(69x)/(4096x^6+1)

Maricopa's Success scholarship fund receives a gift of $165,000. The money is invested in stocks, bonds, and CDs. CDs pay 3.5 % interest, bonds pay 3.1 % interest, and stocks pay 9 % interest. Maricopa Success invests $20,000 more in bonds than in CDs. If the annual income from the investments is $7,400 , how much was invested in each account? Maricopa Success invested $ in stocks. Maricopa Success invested $ in bonds. Maricopa Success invested $ in CDs.

Determine the centroid of the area bounded by x^2 − y = 0 and x − y = 0.