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Let R be the shaded region bounded by the graphs of y=sqaure root of x, and y=e to the power of -3x, and the vertical line x=1.
a) Find the area R
b) Find the volume of the solid generated when R is revolved about the horizontal line y=1.
c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a rectangle whose height is 5 times the length of its base region R. Find the volume of this solid.
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance.
Composition of Functions and Isomorphisms, I can't prove the following statements about functions f:A->B and g:B->C, 1. If gof is one-to-one then so is f.
Write equations for the vertical and the horizontal lines passing through the point (-7,5) in (x,y)-coordinates.
A person is given 4 coins each with equal and independent probabilities of being a nickel , a penny, a dime or a quarter. What is the probability the person has been 37 cents
Graph y=sinx + cosx restricted to 0
Using the given data and chart, find the coefficients a, b, and c of the exponential model algebraically.
Multiple choice questions based on regression
Find the p-value associated with the test of hypothesis
Use Newton's Method for three steps to find the cube root - Evaluate the Newton's method discrete-time dynamical system to check your answer for the first step and compute the next two values.
Compute the integral of 4y^3 dx -2x^2 dy around the square bounded by the lines y=+/- 1 and x=+/-1. Directly by performing the line integration.
The group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n. Show that A_8 contains an element of order 15.
Describe two main differences between classical and empirical probabilities. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than t..
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