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Using integration to derive geometric formulas-
Problem 1- Derive the formula for the circumference of a circle of radius r by computing the arc length of the curve √(r2 - x2) from x = -r to x = r.
Problem 2- Derive the formula for the area of a circle of radius r by computing the area between the curves √(r2 - x2) and -√(r2 - x2) between x = -r and x = r.
Problem 3- Derive the formula for the volume of a sphere of radius r by computing the volume of "the object obtained by rotating the curve √(r2 - x2) above the x-axis".
Problem 4- Derive the formula for the volume of a cone whose height is h and whose base has area A by "integrating along the height".
Find an equation of the planes tangent to the following surfaces at given points, x2 - 2y2 + z2 / 4 = 3, at (√2, 0, 2). z = xy - 25 at (1, 16, -9).
Janet can shovel her driveway in 30 minutes, Bill can shovel his driveway in 35 minutes. How long would it take if they worked together?
A poster is to have an area of 250 in2 with 1 inch margins at the bottom and sides and a 3 inch margin at the top. What dimensions will give the largest printed area? (Give your answers correct to one decimal place.)
the revenue and cost functions for producing and selling quantity x for a certain production facility are given
The bus averaged 40 mph on the drive from Columbus to Athens but averaged 60 mph during the return trip. What was the average speed of the bus for the entire trip?
A printed poster is to have a total area of 750 square inches with top and bottom margins of 6 inches and side margins of 2 inches. What should be the dimensions of the poster so that the printed area be as large as possible?
Evaluate double integral: (int from 0 to 1). (int from 0 to cos inverse y). [square root (1 + sin x) dx dy.
Project: Create and interpret a line graph. Project Description: A line graph, sometimes called a run chart, is used to show changes in performance measurement data over several time periods
Events occur according to a Poisson process with rate lambda=2 per hour. Starting at noon, what is the expected time at which the fourth event occurs?
Find the composition of the following cycles representing permutations on N. Write your answer as a composition of one or more disjoint cycles
Remember that the perimeter is the sum of all sides of the rectangle. Is there another shape that would be more efficient( higher area to perimeter ratio?)
Service station cars arive randomly at a rate of 1 car every 30 min. the average time to change oil on a car is 20 min. both the time between arrivals and service time can be modeled using the negative exponential Poisson distribution.
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