HellooooLH =3" 6" 9"

Mathematics

1 answer:

EleoNora [17]2 years ago

6 0

<h3>Answer: C) 6"</h3>

Explanation:

Focus on the fourth circle only.

Radius LD is 3 inches, so the diameter is 2*(radius) = 2*3 = 6 inches which is segment LH. The diameter has endpoints on the circle and the segment goes through the center of the circle.

Alternatively, you can say LD = DH are both radii, so DH = 3 and LH = LD+DH = 3+3 = 6.

Either way, LH = 6.

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alex41 [277]

Answer: $\frac{8}{3}\times \sqrt{\frac{2}{5}}$

Step-by-step explanation:

Given two upward facing parabolas with equations

$y=6x^2 & y=x^2+2$

The two intersect at

$6x^2=x^2+2$

$5x^2=2$

$x^2$ = $\frac{2}{5}$

x= $\pm \sqrt{\frac{2}{5}}$

area enclosed by them is given by

A= $\int_{-\sqrt{\frac{2}{5}}}^{\sqrt{\frac{2}{5}}}\left [ \left ( x^2+2\right )-\left ( 6x^2\right ) \right ]dx$

A= $\int_{\sqrt{-\frac{2}{5}}}^{\sqrt{\frac{2}{5}}}\left ( 2-5x^2\right )dx$

A= $4\left [ \sqrt{\frac{2}{5}} \right ]-\frac{5}{3}\left [ \left ( \frac{2}{5}\right )^\frac{3}{2}-\left ( -\frac{2}{5}\right )^\frac{3}{2} \right ]$