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Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A = 27x - x2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.
S4 means symmetric group of degree 4, A4 means alternating group of degree 4, e is the identityIs there a group homomorphism $:S4 -> A4, with kernel $ = {e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}?
What is your monthly mortgage payment? How much does your house cost per month including principal, interest, real estate taxes, and insurance?
A population of protozoa develops with a constant relative growth rate of 0.8329 per member per day. On day zero the population consists of six members. Find the population size after eight days. (Round your answer to the nearest whole number.)
Suppose that the simultaneous equations F(x,y,z)=0 and G(x,y,z)=0 define x=f(z) and y=g(z) implicitly, Determine expressions for dx/dz and dy/dz in terms of partial derivatives of F and G
For what value of the parameter b will the following system of equations fail to have a unique solution?
Use the disk method to find the volume of the solid of revolution formed by revolving the region about the x-axis. Solid region is a semi circle from 0,4 to 16,0 find the solid amount between 5,0 and 6,0
Write a recursice algorithm to find x^n mod m whenever n,x and m are positive integers based on the fact that : x^n mod m = (x^(x-1) mod m * x mod m)mod m
Prove that any two universal (initial) objects in a category C are equivalent. Prove that any two couniversal (terminal) objects in a category C are equivalent.
What do we gain by studying geometry? Do you see any geometric concepts being used in your area of expertise or in your day-to-day experiences? Explain
How do you write a system of linear equations in two variables? Explain this in words and by using mathematical notation in an equation.
Write an equation of a line parallel to y= 3x + 8 if the line intercepts the y axis at (0,3). Use the slope-intercept form.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
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