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A hemisphere of radius 5 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the center of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.
Use the point-slope form of the linear equation to find an equation of the line with the given slope and passing through the given point. Then write the equation in standard form.
The temperature(at a randomly selected time) is normally distributed with mean 83 degrees Fahrenheit and standard deviation 5 degrees. Find the following probabilities:
The same experiment as in part (a) above is done with the 7 letters from CHICAGO. Find the probability that the result spells CHICAGO. Find probability that the result spells NEW YORK
Problem on speed.
Two fires towers are 30 kilometers apart, tower A being due west of tower B. A fire is spotted from the towers, and the bearings from A and B are E 14 N and W 34 N. Find the distance d of the fire from the line segment AB.
Calculate the ambiguity function of a signal with an envelope u(t) = Bexp(-t^2)T^2). What should be the value of B that will make the signal of the unit energy?
Two circles of different radii touch internally at C. A tangent at P on the smaller inner circle touches the larger circle at A and B. Join ABC. Prove that CP bisects angle
With the definition that pi is the area of the unit circle, explain why pi equals 8 times the integral from 0 to 1/sqrt(2) of (sqrt(1 - x^2) - x) dx. use the Romberg algorithm to approximate the integral.
Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G,
Solving problems conditional probability
Give the horizontal asymptotes. Graph the function by dividing the axis and tell if the graph is above or below the axis for it's intervals.
Normal Approximations to Binomial Probabilities, Mathematics Study Centre was established to help students to solve mathematics and statistics problems
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