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A bucket that weights 4 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 36 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 lb/s. Find the work done W in pulling the bucket to the top of the well.
A mortgage at 9% interest compounded monthly with a monthly payment of $1125 has an unpaid balance of $10,000 after 350 months. Find the unpaid balance after 351 months.
Find the dimensions of the rectangle of the largest area that has its base on the x axis and its other two vertices above the x axis and lying on the parabola y=8-x^2.
List the coordinates of any two points on the graph in (x, y) form. The numbers on the horizontal axis are 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0.
A rectangular is to be fenced off and divide in two by another fence parallel to one side of the playground. 720 feet of fencing is used. what are the dimensions and maximum area.
Calculate the mean and variance of profit where the mean and variance for the number of units produced are 500 & 900 respectively.
the perimeter of a standard high school basketball court is 268 feet. the length is 34feet longer than the width. Find the dimension of the court.
Find the gradient of f(x,y) at (3,2). Compute the directional derivative (triangle u) f(3,2) where u is the unit vector in the direction of v =
Find the equation of the tangent line to the curve
The total cost of the fencing along three sides comes to $1950. What are the lot's dimensions?
let f(x)=x^3+1. Find the point(s) on the graph of f where the slope of the tangent line is equal to 12, and find the equations of the tangent line at these points.
a plane flies 435 miles with the wind and 375 against the wind in the same length of time. if the speed of the wind is 10 mph. find the speed of the plane in still air?
Profit for each big shelf is $85 and for each medium shelf is $75. What is the constraint on money to invest?
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