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Amy plans to paint both sides of a fence whose base is in the xy-plane and is given by the points (x,y) where x = 30cos^3(t) and y = 30sin^3(t) for 0 <= t <= (PI/2), and whose height z at (x,y) is given by z = 1+(1/3)y, all measured in feet. How many gallons of paint will Amy need if a gallon covers 200 ft^2?
Determining the maximum area of a Norman window with the fixed perimeter of 16 feet - Evaluate the dimension of a Norman window of maximum area if the total perimeter is 16 feet.
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
Assume f is continuous on the interval (a,b) that contains x0 and f(x0)>0. Show there is an open interval J that contains x0 and m>0 such that f(x)>=m for each x in J.
If the minute hand and the hour hand on the clock both start at 12:00 when will the two hands first coincide? How many times will they coincide in 12 hours?
What is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?
Factorize the given expression - Evaluate the perfect square
Suppose that a probability distribution has a mean 20 and standard deviation 3. The Chebychev inequality states that the probability that an outcome lies between 16 and 24 is
Let f be continuous on the closed interval [a,b] and differentiable on the open interval (a,b). Also, suppose that f(a) = f(b) and that c is a real number in the interval such that f'(c) = 0.
Please show me how to solve this first order linear differential equation:
Find whether the given expression is a function or not - Which of the following are functions? The last two problems, i.e., b & c, are multi part relations consider all parts when determining whether or not these relations are functions.
Can people really identify their favorite brand of cola.
A pendulum is 18 feet long. Its central angle is 44º. The pendulum makes one back and forth swing every 12 seconds. Each minute, the pendulum swings _____ feet.
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