What is the equation of the axis of symmetry for the function shown below?

Mathematics

1 answer:

Alinara [238K]3 years ago

4 0

The squared term and the function are symmetrical about the value of x that makes (x+5)^2 = 0. That value is ...
D. x = -5

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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

Usimov [2.4K]

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

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

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

$\implies x=0,x=8\implies y=0,y=8$

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