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A trough is 10ft. long and its ends have the shape of isosceles triangles that are 3ft. across at the top and have a height of 1ft. If the trough is being filled w water at a rate of 12ft3/min, haw fast is the water level rising when the water is 6 inches deep?
Define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx. is f integrable on [0,1]?
A 104 inch long piece of wire is cut into two pieces, and two squares are formed. The sum of the areas of the two squares is 388 square inches. If the sides of the squares have integer lengths, what are the lengths of the sides of each square?
Find formulas for the upper and lower limits ( u and l) as linear equation involving the age x. What is the target heart rate zone for a 20-year-old? What is the target heart rate zone for a 40-year-old?
Choose one equation of each type: linear, quadratic, polynomial, rational, exponential, and log. Plot each equation on the same graph. Discuss and compare the appearance of each graph.
the volume of a rectangular prism is 208 cm2. if the area of one end is 16cm2, what is the length of the prism.
Assuming a company is selling guitar at its list price of 1,899.90, with a cash discount of 3/10, n/30 sales tax is 7% and shipping is 30.40. What is the final price if cash discount period was met?
Find (dy/dx) by implicit differentiation for the following equation:
a manufacturer can produce cassette tape records at a cost of $40 a piece,its estimates that if the tape records are sold for p dollar a piece.consumer will buy 120-p of them a month , express the manufacturers monthly profit as a function of pric..
Plot a histogram of the variable age. Include an appropriate title to your histogram. Explain the plot.
A rancher has 1200m of fencing to enclose 2 rectangular corrals. The corrals have the same dimensions and one side in common. What dimensions will maximize the enclosed area?
(a) How many committees of six can be formed from the club membership? (b) How many committees will contain at least three men who, in the preliminary survey,favored opening membership to women?
Write the matrix of T in the standard basis of C^3. Find all eigenvalues of T. Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why.
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