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Your firm has been asked to design a storage tank for liquid petroleum gas. The customer's specifications call for a cylindrical tank with hemispherical ends, and the tank is to hold 8000 cubic meters of gas. The customer also wants to use the smallest amount of material possible in building the tank. What radius and height do you recommend for the cylindrical portion of the tank? Use Lagrange multipliers.
Plot x.vs. x for h = a12/4a2, h a12/4a2 , What is the significance of h = a12/4a2 with respect to the phase diagrams?
Does body weight have an influence on the blood cholesterol level? To answer this question what variables do you think the researcher would measure? Which would be the i.v. and which the .d.v.? Why?
Determine the number of turns made by a wheel to cover a well known distance using perimeter of circle.
A child applies the brakes on a bicycle by applying a downward force of 20 pounds on the pedal when the crank makes a 40 degrees angel with the horizontal. The crank is 6 inches in length. Find the torque at P.
Prove the triangle inequality starting with: |V+W|^2. You must use Re (less than or equal to) | | and the Schwarz inequality.
an empty bin in the shape of a rectangular prism has sides 1.2m, 1.5m and 2.0m, a. calculate the volume of the empty bin in m3
Let v1 and v2 be vectors in R^n. Show that (prove) the set of all vectors w, an element of R^n such that w is orthogonal to both v1 and v2, is a subspace of R^n.
Prove that the function f(x) = C (a constant function) is Reimann integrable over [a,b] and calculate its Reimann integral over [a,b]
Probability on normal distribution
A rancher wants to fence in a rectangular area of 124416 square feet and then divide the enclosed area in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
what is the probability of getting a sample proportion this small or smaller? Do you think she actually has 55% of the vote? Why or why not?
the mean and the standard deviation of a random sample of n measurements are equal to 33.4 and 3.7 respectively.a. find
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