Mathematics, 23.04.2020 00:21 angel182

The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?

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Answer from: 21teunissen149

Option b) $18\pi$ is correct∴ the volume of the solid is $A(x)=18\pi$ cubic units

Step-by-step explanation:

Given that the base of a solid is the circle x^2 + y^2 = 9 and Cross sections of the solid perpendicular to the x-axis are semi-circles.

To find the the volume of the solid in cubic units:

We know that the cross sections are semicircles with the diameter in the given circle x^2 + y^2 = 9

That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.

Now the area of a semicircle is

$A=\frac{\pi r^2}{2}$ cubic units

Let r = y and y^2=9-x^2

Then area of the semicircle crossing the x-axis at x is given by

$A(x)=\frac{1}{2}\pi y^2$ cubic units

$=\frac{1}{2}\pi(9-x^2)$

Now we can find the definite integral of A(x) from x = -3 to x = 3.

Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.

We have that

$A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx$

$=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)$

$=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})]$

$=\pi[27-\frac{27}{3}]$

$=\pi[27-9]$

$=\pi[18]$

$=18\pi$

∴ option b) $18\pi$ is correct∴ the volume of the solid is $A(x)=18\pi$ cubic units

Answer from: Quest

answer: i don't understand. what are the options

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

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