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Let P(n) be the proposition "If a and b are positive real numbers, then (a+b)^n >_ a^n + b^n." Prove that P(1) is true. What kind of proof did you use?
Determine the correct degree of freedom
How much should the bank invest in each possible category? Let x, y, and z, respectively, be the amounts invested in bonds, certificates of deposit, and first mortgages. Solve the system of equations by the Gauss-Jordan elimination method.
A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 200ft.
a twin-engine aircraft can fly 1050 miles from city a to city b in 5 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?
A 410-ft weather tower used to measure wind speed has a guy wire attached to it 175 ft above the ground. The angle between the wire and the vertical tower 57degrees. Determine the lengh of the guywire.
By reading values from the given graph of f, use five rectangles to find a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 40.
Show that log(r), where this is log base 10, is irrational when r is a positive rational that is not an integral power of 10
Calculating the first derivative and critical point.
Evaluate the coordinate of centroid using multiple integral method - Find the z- coordinate of the centroid of T
Calculate the probability of drawing a King or a diamond
Show that f is a homeomorphism. Isn't a homeomorphism by definition a bijection? And since M is compact, will it not be true that N will be compact too?
Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, 2) and the second going from (-1, 2) to (-2, 0)
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