An open-top rectangular box is to be constructed with 300 in2 of material. If the bottom of the box forms a square, what is the largest possible box, in terms of volume, that can be constructed?

1. You plan to calculate the volume of a tall, thin cylinder from measurements of its radius and height. Which dimension should you measure more carefully? Give reasons for your answer.

Let S be the surface with equation x2+y2-z2=1. (a) In a single xy-plane, sketch and label the trace curves z=k for k = -2,-1,0,1,2. In words describe what types of curves these are and how they change. (b) In a single yz-plane, sketch and label the trace curves x=k for k= -2,-1,0,1,2. In other words, describe what types of curves these are and how they change as k varies.

Find the consumer and producer surpluses by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions). Demand Function Supply Function p = 1005 − 25x p = 42x consumer surplus $ producer surplus $

A company manufactures and sells x television sets per month. The monthly cost and​ price-demand equations are

​C(x)=75000+50x and p(x)=300-x/30, 0 ≤ x ≤ 9000

​(A) Find the maximum revenue.

​(B) Find the maximum​ profit, the production level that will realize the maximum​ profit, and the price the company should charge for each television set.

​(C) If the government decides to tax the company ​$5 for each set it​ produces, how many sets should the company manufacture each month to maximize its​ profit? What is the maximum​ profit? What should the company charge for each​ set?

Find the Taylor series of f(x)=ln(3+2x) about x=0.

Find the equilbrium solutions of x'(t) = [2x^2 − 8y; -8x + 16y] . What is the types for each equilibrium solutions

1. Jacobs & Johnson, an accounting firm, employs 15 accountants, of whom 9 are CPAs. If a delegation of 3 accountants is randomly selected from the firm to attend a conference, what is the probability that 3 CPAs will be selected? (Round your answer to three decimal places.)'

2. Among 500 freshmen pursuing a business degree at a university, 301 are enrolled in an economics course, 220 are enrolled in a mathematics course, and 130 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)

(a) an economics and/or a mathematics course

(b) exactly one of these two courses

(c) neither an economics course nor a mathematics course

• Find the volume of the solid obtained by revolving the area under y=cosx on [0,π/2] around the y-axis.

• The total weight of a cable hanging from the ceiling plus the bucket of coal it is attached to is F(x)=1800−2x pounds when the bucket is xx feet off the ground (the cable gets shorter as the bucket is lifted, so the weight decreases). Find the total work done in lifting the bucket from the ground to 100 feet off the ground.

You want to be able to withdraw $50,000 from your account each year for 20 years after you retire. If you expect to retire in 30 years and your account earns 5% interest while saving for retirement and 4.1% interest while retired: Round your answers to the nearest cent as needed. a) How much will you need to have when you retire? $ b) How much will you need to deposit each month until retirement to achieve your retirement goals? $ c) How much did you deposit into you retirement account? $ d) How much did you receive in payments during retirement? $ e) How much of the money you received was interest? $

(a) Estimate the area under the graph of f(x) = 3 + 4x² from x = −1 to x = 2 using three rectangles and right endpoints.

R₃ =

Then improve your estimate by using six rectangles.
R₆ =

Sketch the curve and the approximating rectangles for R_{3 and}R₆.

(b) Repeat part (a) using left endpoints.

Sketch the curve and the approximating rectangles for L₃ and L_6.

(c) Repeat part (a) using midpoints.

Sketch the curve and the approximating rectangles for M₃ and M_6.

(d) From your sketches in parts (a)-(c), which appears to be the best estimate?

A) L6

B) M6

C) R6

Find the measures of the marked angles in the triangle below if you know that a/c=10/11 and a/2=b/3. Hint: if x/y=w/z then xz=wy. In other words, if two fractions are equal, the products you obtain from cross-multiplying will also be equal. (Do not use a protractor to measure the angles below since the diagram is not drawn to perfectly match the angles of your answer.)

​D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​ item, and​ S(x) is the​ price, in dollars per​ unit, that producers are willing to accept for x units. Find ​(a​) the equilibrium​ point, ​(b​) the consumer surplus at the equilibrium​ point, and ​(c​) the producer surplus at the equilibrium point. ​D(x)=(x-8)^2​, ​S(x)=x^2+4x+24

Equation 4x²+9y²-xy=25

a. find x-intercepts

b. find y-intercepts

c. check for all symmetries