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Volumes of Solids of Revolution / Method of Rings
In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of revolution is. To get a solid of revolution we begin with a function, y = f (x ) , on an interval [a,b].
Then we rotate this curve around a given axis to get the surface of the solid of revolution. For discussion let's rotate the curve around the x-axis, although it could be any vertical or horizontal axis. Carrying out this for the curve above gives the given three dimensional region.
The length of Kara's rectangular patio can be expressed as 2x - 1 and the width can be expressed as x + 6. In the terms of x, what is the area of her patio? Since the area of a
we dont know how to do rates
Since we are going to be working almost exclusively along with systems of equations wherein the number of unknowns equals the number of equations we will confine our review to thes
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
The remainder when 5^99 is divided by 13 Ans) 8 is the remainder.
identify 4 sketch the quadric surfaces
Functional and variations.Block III, Consider the functional S[y]=?_1^2 v(x^2+y'')dx , y(1)=0,y(2)=B Show that if ?=S[y+eg]-S[y], then to second order in e, ?=1/2 e?_1^2¦?g^'
Question Solve the following functions for x (where x is a real number). Leave your answers in exact form, that is, do not use a calculator, show all working. (a) 3 x 3 x2 3
Generate G(1000,1/2) and find the largest clique you can. A clique is a complete sub graph, that is, a set of vertices each pair of which is connected by an edge.
1. Suppose the arrival times of phone calls in a help centre follow a Poisson process with rate 20 per hour (so the inter-arrival times are independent exponential random variables
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