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expeople1 [14]
3 years ago
8

Please tell me this is my final please!!!!!!!!!!!

Mathematics
1 answer:
Vlad1618 [11]3 years ago
3 0

Answer:

B) A≈841.78

Step-by-step explanation:

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Let the curve C be the intersection of the cylinder  



16x^2+y^2=16



and the plane



x+y+z=1



The projection of C on to the x-y plane is the ellipse



16x^2+y^2=16



To see clearly that this is an ellipse, le us divide through by 16, to get



\frac{x^2}{1}+ \frac{y^2}{16}=1



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\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1,



We can write the following parametric equations,



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z=1-x-y



This implies that,



z=1-sin(t)-4cos(t)



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The length of the curve of the intersection of the cylinder and the plane is now given by,



\int\limits^{2\pi}_0 {|r'(t)|} \, dt



But  



r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))



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Therefore the length of the curve of the intersection  intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

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Roman55 [17]

Answer:

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Step-by-step explanation:

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