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A radio transmission tower is 574 feet tall. A guy wire is to be attached 6 feet from the top and is to make an angle of 25o with the ground. How many feet long should the guy wire be?
Five ounces of shrimp and 3 ounces of scallops contain 45 milligrams of cholesterol less than the suggested maximum daily intake. Determine the cholesterol content in an ounce of each item.
A particle is moving along the curve y= 2 sqrt{4 x + 4}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this i..
How do you explain why vectors QR and RQ are not equivalent? Explain when the elimination method for solving a system of equations is preferable to the substitution method.
Prove the following theorem: If x y + for any > 0 then x y.
Integration by parts method - How much longer would the worm be at t = 2, if it always grew at the maximum rate? Use Integration by parts.
Suppose that Phi (f) is an isomorphism. Is f then an isomorphism? Alternatively, suppose that Phi (G) and Phi (G')
Can a linear equation and a linear inequality be solved in the same way? Explain why? What makes them different?
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
Prove that a graph G is a forest if and only if every induced subgraph of G contains a vertex of degree at most 1.
A group of people share in a $5,000,000 lottery. Before the money is divided, 3 more winning ticket holders are declared. As a result, each person's share is reduced by $375,000. Write and solve an equation to determine how much $ each winner rece..
Use mathematical induction to prove that 2-2*7+2*7^2-.....+2(-7)^n=(1-(-7)^n+1)/4 whenever n is a nonnegative integer. Show that 1^3+2^2+....n^3=[n(n+1)/2]^2 whenever n is a positive integer.
If I treat the upper block as a 2x2 matrix, I can find P = [1 0; 1 1] (Note: Using Matlab notation here). This correctly results in INV(P)AP = [3 1; 0 3] which is in the form needed.
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