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A piece of molding 168 centimeters long is to be cut to form a rectangular picture frame. What dimensions will enclose the largest area? Round to the nearest hundredth, if necessary.
Description of Directional Derivative and how the dot product can be used to justify that the gradient points in the direction of maximum of a function.
These questions are about the quadratic function which takes the form: Choose the false statements.
Determine whether the following assertion is true or false: if you integrate the Fourier series for the delta function d(x) term by term you obtain the Fourier series for the step function s(x).
A particle's position is give by s = 3t^3 - t^2 + 2t. What is it's acceleration at t=2? This seemed too easy.
Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (4, 80), and the x-axis.
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve.
When n is a positive integer by using mathematical induction and the formula of d/dz[f(z)g(z)]=f(z)g'(z)+f'(z)g(z) for the derivative of the product of 2 functions.
Find the critical value for this hypothesis test.
There are 45 participants in the triathlon. The first three finishers will receive prizes. How many ways can the three prizes be given?
Write a goal equation that represents the fluctuations in the production level from May to June, June to July, and July to August.
The surface area S of a right prism is given by S = 2B + Ph. The length of a rectangle is five times its width. If the area of the rectangle is 500m², find its perimeter.
Construct a truth table and determine the truth value of the statement ~ q = { ~r ^ ( p v q) }, when p is false, q is true and r is true.
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