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guajiro [1.7K]
3 years ago
13

If y=x+2 changed to y=x-1 how would it change

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0
The line would change its y-intercept from 2, to -1 on a graph.

Blue line is original equation.
Red line is changed to -1

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Find the volume of the solid whose base is the circle x2+y2=25 and the cross sections perpendicular to the x-axis are triangles
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Triangles with height h and base b, with b=h have area \dfrac{b^2}2.

Such cross sections with the base of the triangle in the disk x^2+y^2\le25 (a disk with radius 5) have base with length

b(x)=\sqrt{25-x^2}-\left(-\sqrt{25-x^2}\right)=2\sqrt{25-x^2}

i.e. the vertical (in the x,y plane) distance between the top and bottom curves describing the circle x^2+y^2=25.

So when x=4, the cross section at that point has base

2\sqrt{25-16}=6

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In case it's relevant, the entire solid would have volume given by the integral

\displaystyle\int_{-5}^5\frac{b(x)^2}2\,\mathrm dx=4\int_0^5(25-x^2)\,\mathrm dx=\frac{1000}3

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3 years ago
Am I right?<br> I want to know if I am right
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Answer:

B $13

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8 0
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Answer:

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