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Find the vertex of the parabola defined by the function y=4x^2+2x-3 by completing the square.
A Norman window has the shape of a rectangle capped by a semicircle. What is the length of the base of a Norman window of maximum area if the perimeter of the window equals 10?
dance team knows 18 routines of which 8 are tap, 7 are ballet, and 3 are modern. The program can consist of any four routines. In how many ways can the manager choose which routines to present if there are no restrictions?
1. determine the value of c if any so that the system of equations with the following augmented matrixhas the requested
A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years.)
Prove that the intersection of any collection of closed sets in X is a closed set and prove that the union of finitely many closed sets in X is a closed set.
in a game of ice hockey it took the puck 0.8 seconds to travel 89 feet to the goal line, determine the average speed of the puck in feet per second.
the length of a rectangle is 4 less than twice the width. The are of the rectangle is 70. Find the dimensions of the rectangle.
the equation a=25000 - 1500t, where t is the time in minutes and a is the altitude in feet, represents the steady decent of a certain aiplane. Graph the equation using the x- and the y- intercepts. How long will it be before the airplane reaches t..
Assume the probability that a person has the desease is 0.04 for all people, independently of each other, and compute the expected number of tests necessary for each group.
some appropriate equilibrium price. Label the horizontal axis as x and the vertical as p. Shade in the area which represents the producer's surplus.
how to solve problem-5 out of 6 people will eat vanilla ice cream . total amt of people is 144. How many will eat vanilla ice cream.
Which of the following is the elementary matrix corresponding to the row operation.
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