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lina2011 [118]
3 years ago
10

Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your

calculator to estimate the integral. The part of the surface z=cos(x^2+y^2) that lies inside the cylinder x^2+y^2=1
Mathematics
1 answer:
love history [14]3 years ago
4 0

If we substitute x=r\cos\theta and y=r\sin\theta, we get r^2=x^2+y^2, so that

z=\cos(x^2+y^2)=\cos(r^2)

which is independent of \theta, which in turn means the surface can be treated like a surface of revolution.

Consider the function f(t)=\cos(t^2) defined over 0\le t\le1. Revolve the curve C described by f(t) about the line t=0. The area of the surface obtained in this way is then

\displaystyle2\pi\int_C\mathrm dS=2\pi\int_0^1\sqrt{1+f'(t)^2}\,\mathrm dt

=\displaystyle2\pi\int_0^1\sqrt{1+(-2t\sin(t^2))^2}\,\mathrm dt

=\displaystyle2\pi\int_0^1\sqrt{1+4t^2\sin^2(t^2)}\,\mathrm dt\approx7.4144

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weeeeeb [17]
Hi there! 

Your question: 

Sales fall from 300 per week to 270 per week what's the percentage change?

My answer:

The formula for calculating percent change is as follows: 

[(y2 - y1)/y1]*100=your percent change 

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Plug the numbers in: 

[(300-270)/300]*100

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Therefore, the percent change is 10%

Hope this helps! Let me know if it's incorrect so I can fix it:)
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For which acute angles is the following statement true? The complement of the angle is smaller in measure than either of the two
Hitman42 [59]

Let the acute angle be 2x.

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Therefore, 90 - 2x < x

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Therefore, the statement is true for all angles that are greater than 60 degrees.

7 0
4 years ago
A recipe for 4 loaves of bread use 3 tablespoons of honey.How much honey is needed for 24 loaves of bread?
frez [133]

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18 tablespoons of honey

Step-by-step explanation:

Since you need 3 tablespoons of honey for 3 loaves and you know you need 24 loaves you could do...

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