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1. Find the value of g(2) when f, g are differentiable functions such that (fg)'(x) = f'(x)g(x) , f(x) > 0 , for all x, while g(0) = 4 .
2. Determine if the function f(x) = 3x + x^2/3 (2 - x)^1/3 satisfies the hypotheses of the MVT on the interval [0, 2]. If it does, find all possible values of c that satisfy the conclusion of the MVT. (MVT is Mean value theorem)
An average computer mouse inspector can inspect 60 mice per hour. The 48 computer mice inspectors at a particular factory can only inspect 55 mice per hour with a standard deviation of 10. Does the company have reason to believe that these inspect..
Find a general solution to the differential equation.
Find the x-intercept of L(x) as a way of estimating the x-intercept of f(x). Round the coefficients 3 decimal places.
Please outline the specific problem, your solution and how the specific problem solving guidelines were applied. Be sure to carefully tell us how you applied each of the guidelines to your problem.
Use partial decomposition to integrate. (2x^2-x-20)/(x^2+x-6 ). (sint)(4cos^2t-1)/(cost)(1+2cos^2t+cos^4t)
Verify that 18^3 - 1^3 = 17* 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates.
A plane is heading due south with an airspeed of 227 mph. A wind from a direction of 60 degrees blowing at 16 mph. Find the bearing of the plane.
There are 3 suspects, A, B, and C, for a robbery that presumably happened in a shop. We know that the following facts are true:
Work out what constraints in a maximum entropy problem will give rise to the true inverse Gaussian distribution.
A uniform boom AC, 4m long and weighing 50 N is smoothly hinged at C and is supported at A by a rope AB. Find the tension in the rope and the size and direction of the reaction at C.
Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t) are tonnes (metric tons) per second.
Find an equation of the tangent plane to the parametric surface x=-2rcos(theta), y=-3rsin(theta), z=r at the point (-2sqrt(2),-3sqrt(2),2) where r=2, theta=pi/4
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