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An airplane is flying in still air with an airspeed of 475 miles per hour. If it is climbing at an angle of 25°, find the rate at which it is gaining altitude. (Round answer to four decimal places.)
Discuss the convergence and divergence sets of each of those Laurent series. Find two non-zero terms of the Laurent series which represents this f for all z outside some circle |z| = R but diverges inside the circle and find the numerical value of..
A box with a square base and open top must have a volume of 500000 cm3. Find the dimensions of the box that minimize the amount of material used.
To two decimal places, what is the value of the positive root in the auxiliary equation?
Find the absolute minimum and maximum values of the function f(x,y) = 1+4x-5y on the closed triangular region with the vertices (0,0),(3,0), and (0,3).
Explore and find a real-world application of a quadratic equation, whether it is from the realm of physics, finance, or anything else. Write a paragraph about what you find. In your description,
Let P : C -> R be defined by P(z) = Re z; show that P is an open map but it is not a closed map. ( Hint: Consider the set F = { z : Imz = ( Re z)^-1 and Re z doesn't equal to 0}.) Please explain every step and justify.
Automorphism of a Group, Let G be a group, T an automorphism of G, N a normal subgroup of G. Prove that (N)T is a normal subgroup of G.
A square garden plot measures 125 square feet. a second square garden plot measures 405 square feet. how many more feet of fence will the second garden plot require over that required for the first garden plot.
Probability amd Mutually Exclusive Events, A fair dice is rolled. What is the probability of rolling an odd number OR a number less than 3?
Reals with the "finite complement topology:" U open in X if U - X is finite or is all of X. Why compact? Why not regular? Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X. Why not compact? Why not regul..
An irrigation canal has the shape of a trapezoid. Let x = the bottom width, y = the water depth, and theta = the angle of inclination of the sides from the horizontal.
Find the average temperature during the period from 6 am to 6 pm.
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