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3 years ago

Do you have a favorite color?

Mathematics

1 answer:

Amanda [17]3 years ago

3 0

Answer:

Purple. red, blue, green, orange

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How many times larger is 7 x 106 than 3.5 x 10°?

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Simplify: 5x + 4 + 9x

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Korolek [52]

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3 years ago

Order the rational numbers below from greatest to least. -3/4 , .8, 1, -5.3 , 9. I'm not that smart so imma try to get this answ

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3 years ago

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Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

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3 years ago