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A sphere of fixed radius R is enclosed in a cone of height h and radius r. Express the volume V of the cone as a function of the slant angle of the cone.
Let f be Lebesgue integrable on [0,1]. Prove that the limit, as k goes to infinity, of the integral from 0 to 1 of (x^k)f(x)dx is equal to 0.
Use rules of differentiation.
At East Zone University there are 627 students taking College Algebra or Calculus. 417 are taking College Algebra, 261 are taking Calculus,and 51 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra?
Determine the number X for the given table and evaluate the number x so that the preceding independence relations hold.
Exactly one of the three contestants will win a game show. The probability that Terry wins 0.25 and the probability that Chris wins is 0.65. What is the probability that Toni wins?
John is intending to put $10,000 into investment. He picked a fund that grows at 5% per annum. Assuming his profit is compounded annually, how much money would he have from this investment after 5 years and how long would it take for his money to ..
You follow the same pattern for every fourth, fifth locker and so on up to every thousandth locker. Which locker doors will be open when the process is complete?
Find the rate at which the distance bewtween the planes changes when the southbound plane is 31 km away from the airport and the westbound plane is 24 km from the airport.
Find the x-intercept and the y-intercept for 2x-6y=4?
Suppose a given container has 2 non-working engines. Find the probability that the container will not be shipped.
Let V be an n-dimensional vector space over F. What is the characteristic polynomial of the Identity operator on V? What is the characteristic polynomial for the zero operator?
Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
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