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3 years ago

Simplify the expression: 2x-5-x-8/x+4

Mathematics

1 answer:

Sergio [31]3 years ago

7 0

$2x-5-\dfrac{x-8}{x+4}=\dfrac{(2x-5)(x+4)}{x+4}-\dfrac{x-8}{x+4}\\\\=\dfrac{(2x)(x)+(2x)(4)+(-5)(x)+(-5)(4)-x-(-8)}{x+4}\\\\=\dfrac{2x^2+8x-5x-20-x+8}{x+4}=\dfrac{2x^2+2x-12}{x+4}$

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3 years ago

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telo118 [61]

Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

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which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

$\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy$

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

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2 years ago

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this would not be the case if it wasn't parallel

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1 year ago

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The answer is C. 20. Hope this helps!

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2 years ago

Read 2 more answers

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Answer:

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Step-by-step explanation:

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