Delia measured her bathtub to be 2 meters long. Which of these is an equivalent measurement?

Mathematics

1 answer:

snow_lady [41]3 years ago

6 0

The answer would be D) 78.7 inches is equivalent to 2 meters.

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The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. Cross sections of the solid perpendicular to

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The two curves intersect at two points, (0, 0) and (8, 8):

$x^2=8y\implies y=\dfrac{x^2}8$

$y^2=\dfrac{x^4}{64}=8x\implies\dfrac{x^4}{64}-8x=0\implies\dfrac{x(x-8)(x^2+8x+64)}{64}=0$

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The area of a semicircle with diameter $d$ is $\dfrac{\pi d^2}8$ . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of $x$ between 0 and 8. Over this interval, $y^2=8x\implies y=\sqrt{8x}$ and $\sqrt{8x}>\dfrac{x^2}8$ , so the volume of this solid is given by the integral