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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.
Find the radius of convergence of the series. Provide complete and step by step solution for the question and show calculations and use formulas.
What is the height of each tower above the roadway? What is the length of z for the cable bracing the tower?
Find, in terms of a, the equation of the line tangent to the curve at x = -1 (use point slope)
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.
A solid metal sphere at room temperature of 20 degrees Celsius is dropped into a container of boiling water (100 degrees Celsius).
Find the width of the box that can be produced using the minimum amount of material . Round to the nearest tenth , if necessary.
Continuous function on the interval (a,b). Find the solution to this differential equation in the form u = integral from a to b (G(x,s) r(s) ds) and determine G
Find the eigenvalues and eigenfunctions of the boundary-value problem.
A wholesaler that sells computer monitors finds that selling price "p" is related to demand "q" by the relation p=280 - .02q where p is measured in dollars.
Let f(x) = x + sin 2x on [0, 2 pie] find two numbers (c ) that satisfy the conclusion of the Mean Value Theorem.
Use the function V(x,y) = x2 + y2 to analyze the stability properties of the zero solution of the nonlinear system.
Solve y'' + y = v2Sin(t v2), with y(0) = 10 and y' (0) = 0 using the method of the LaPlace Transform.
Let A be any constant. Write down a differential equation satisfied by g(x)=f(A)f(x), and also give the value of g(0).
Find the limits using L'hopitals rule where appropriate. If there is a more elementary method, consider using it.