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A 3-ft by 5-ft table is placed on an outdoor patio measuring x ft by ( x+1 ) ft. Find a polynomial for the remaining open space the patio (in square feet)
Find all maximal normal subgroups of Z[p] × Z[q], where p and q are relatively prime. Would the elements from Z[p] have to be one that are relatively prime to q and vice versa?
if the sides of a square are lengthened by 5cm, the area becomes 100cm^2. What is the length of a side of the original square?
show that the number of different triples that can be chosen from N items is precisely N(N-1)(N-2)/6..(use mathematical induction)
Find the probability that during any given day three machines will break down.
In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities?
Set up and solve using Management Scientist, Excel Solver, or an online LP solver. What are the values of X and Y at the optimal solution?
Consider a rectangular box of volume 100 cubic centimters. Suppose that the base is a rectangle with sides x centimeters and 2x centimeters. Let hx give the height of the box in centimeters and let Ax be the total area of the six sides of the box.
A paint mixture contains 23 gallons of base for every gallon of color. In 552 gallons of paint, how many gallons of color are there?
A downtown parking lot is 360 feet long. It's length is 4 times its width. How wide is the parking lot? Let the width = x
trapezoid has an area of 80.75 sq. in., and its two bases are 7 and 12 inches long. find the height of the trapezoid.
Let R be a principal ideal domain and a, b, in R, not both zero. Prove that a, b have a greatest common divisor that can be written as linear combination of a and b.
Find the radian measure of the central angle of a circle of radius 245 feet that interecepts an arc of 150 feet.
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