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If the trough is being filled with water at a rate of 12 ft^3/min, how fast is the water level rising when the water is 6 inches deep?
A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point.
Write a short paragraph comparing and contrasting the method of undetermined coefficients and variation of parameters.
Mercury pollution in a lake (revisited): As an environmental engineer, you have been asked to analyze mercury levels in nearby Lake Arrowhead.
Calculate the curl of F=r^n*(xi+yj). For each n for which curlF=0 , find a potential g such that F=grad(g).
Find a particular solution to the differential equation: y'' - 2y' -15y = 450t3
Make a continuous model of her economic situation, i.e. write a differential equation together with initial condition for the balance B(t) .
A ping-pong ball is caught in a vertical plexiglass column in which the air flow alternates sinusoidally with a period of 60 seconds.
A water bucket is shaped like the frustum of a cone with height 24 inches, base radius of 6 inches and top radius of 12 inches.
Evaluate at least two seperate designs both of which are concave outward. The graph should be a parabolic with floating cans could be cone shapes.
Where and how do you begin to set this problem up to be solved using the Laplace transform? The value y(4)(t) is the fourth derivative of function y(t).
The rate of change of the population of a town in Pennsylvania at any time t is proportional to the population at that time.
The particle's position at time t = 0 is at the origin, and its initial velocity is 1 cm/sec. What is the position of the particle, in cm. at time t seconds?
Show that u (x, y) is harmonic in some domain and find a harmonic conjugate v (x, y) when u (x, y) = 2x (1 - y)
The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second.
A linear PDE can be written in differential operator notation L(u) = f. where L is the linear differential operator.
A right triangular plate of base 8.0 m and height 4.0 m is submerged vertically, find the force on one side of the plate. (W = 9800N/m^3)?
Find the average rate of change of the cost per case for the manufacturing between 1 and 5 cases.
State whether the function f is: increasing, decreasing, neither increasing nor decreasing, one-one or many-one.
The paddles of a defibrillator in an ambulance or the emergency room of a hospital are actually the two plates of an electronic device called a capacitor.
If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air resistance into account.
Find the average rate of change of the function over the indicated interval. Than compare the average rate of change to the instantaneous rate of change.
Let C(t)=1/t the integral from 0 to t of [f(s)+g(s)]ds. Show that the critical numbers of C occur at the numbers t where C(t)=f(t)+g(t).
Find the vertex and intercepts for the quadratic function and sketch its graph.
A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below.