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A 20 ft ladder leans against a wall. The bottom of the ladder is 4 ft from the wall at time t=0 and slides away from the wall at a rate of 3 textrm{ft/sec}.
Find the velocity of the top of the ladder at time t=3.
Find the equation of the tangent plane to the ellipsoid 7x2 + 5y2 + 3z2 = 60 which pass through the line 5y - 3z = 0 = 7x + 10y - 30.
Suppose u(x, y) and v(x, y) are harmonic in a region under? Under what condition is the product u(x, y) . v(x, y) harmonic? In particular, when is (u^2)(x, y) harmonic?
Using a suitable change of variables, find the solution of (1/4)y''-((4z 2 +3)/(4z))y'+(z 2 +1)y=z 4 e (2z) , y(0)=y(1)=0.
A dietician has decided to go on a steady diet of only two foods for all his meals: Potatos and Steak. He realizes that this isn't the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key..
What is the probability of getting an A on the paper? What is the probability of getting an A on the exam?
Write a linear-time Boolean function HEAP(T:BINARY_TREE) which returns TRUE is T is a heap, i.e., it is partially ordered. Assume that T is represented using pointers to left and right children.
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to describe the lighter coin using this number of weighings.
Choose the largest subset for cover, and then remove all its elements from universal set. Repeat by adding subset consisting of largest number of uncovered elements until all is covered.
If it costs Acme Manufacturing C dollars per hour to operate its golf ball division, and an analyst has determined that C is related to the number of golf balls produced per hour, x, by the equation C = 0.009x squared - 1.8x + 100.
Find the solutions of the exponential equation
Suppose that a body moves in a straight line through a resisting medium with resistance proportional to the square of it's speed v with initial speed v_0 and initial position x_0.
A domestic auto producer is facing intense competition in the US market from Asian imports. The CFO decides that the solution is to produce at the point at which average cost is minimized, i.e. where TC/Q is at a minimum. The firm's cost structure..
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