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Solve the given problems by finding the appropriate derivative.
The speed of signaling by use of a certain communications cable is directly proportional to x2 to x-1 where x is the ratio of the radius of the core of the cable to the thickness of the surrounding insulation. For what value of x is s a maximum?
A right circular cylinder has a diameter of 12 in. and a height of 12 in. If water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in.
What is the angular velocity in radians per minute at the center of the propeller?
A feasible solution to an LP problem
Suppose p is a solution of Ax = b, so that Ap = b. Let vh be any solution of the homogeneous equation Ax = 0, and let w = p C vh. Show that w is a solution of Ax = b.
Model the problem of determining the equilibrium position of the mass m when loaded only by the weight of gravity. The model should be expressed as 3 equations in 3 unknowns
The base of a solid is a circle of radius ‘ a ‘, and its verticle cross section are equilateral triangles. Find the radius of the circle if the volume of the solid is 20 cubic meters.
Write down 2 equations to compute a and P, one when t=2 and the other when t= 6.
Find the unit vector perpendicular to each of a= 6i+2j+3k and b=3i-6j-2k
Determine the survival function and force of mortality of this distribution and determine the actuarial present value of a payment of 1, 000 at the moment of death of (x) providing that (y) is still alive , using δ = .04.
After solving parts A and B, assign the following parameter values and then use differential calculus to determine how long it will take for the oxygen concentration to reach the "sag" value.
Find the gradient of f at the point (2, 4, 4). Find the rate of change of the function f at the point (2, 4, 4) in the direction u = 5/√50, -3/√50, 4/√50, 4/√50.
The average SAT math scores M of potential college students can be approximated by M = 1.4t + 518, where t is the number of years since 2004.
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