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blondinia [14]
3 years ago
11

Hello I’m new here ! But I’m having trouble understanding how my teacher factored out the A from a-a(1.2^4)? And made it to A(1-

1.2^4)?
I attached a picture !

Thank you everyone :)

Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0

This is the distributive property:

<em>ab</em> + <em>ac</em> = <em>a</em> (<em>b</em> + <em>c</em>)

In this case, you have

<em>a</em> - <em>a</em> (1.2⁴)

and <em>a</em> is a common factor to both <em>a</em> and <em>a</em> (1.2)⁴, so you can pull it out as

<em>a</em> (1 - 1.2⁴)

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A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u
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Answer:

The volume of the ball with the drilled hole is:

\displaystyle\frac{8000\pi\sqrt{2}}{3}

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

x^2+y^2=15^2\to y=\sqrt{225-x^2}

Then we set the integral for the volume by using shell method:

\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx

That can be solved by substitution:

u=225-x^2\to du=-2xdx

The limits of integration also change:

For x=5: u=225-5^2=200

For x=15: u=225-15^2=0

So the integral becomes:

\displaystyle -\int_{200}^{0}\pi \sqrt{u}du

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

\displaystyle \int_{0}^{200}\pi u^{1/2}du

Then applying the basic rule we get:

\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}

Since that is just half of the solid, we multiply by 2 to get the complete volume:

\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}

=\displaystyle\frac{8000\pi\sqrt{2}}{3}

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Please help!!!! I don’t get this
Stella [2.4K]
The trig function sine, often abbreviated as "sin" (pronounced the same way as "sine"), is essentially the ratio or fraction of the opposite side and the hypotenuse. See the attached image for a reference.

The leg opposite angle B is side AC. Note how B is not present in the sequence "AC". Visually, we are as far away as possible from point B. This side is 16 units long. So AC = 16

The hypotenuse is the longest side of the right triangle. Always always always. This longest side is opposite the largest angle (90 degrees). Therefore the hypotenuse is BC = 17.46

In summary so far, we have,
opposite side = AC = 16
hypotenuse BC = 17.46

Let's use those values to compute sin(B)

sin(Angle) = opposite/hypotenuse
sin(B) = AC/BC
sin(B) = 16/17.46
sin(B) = 0.916 (this is approximate)
sin(B) = 0.92 (rounding to nearest hundredth)

This points to the final answer of choice A) 0.92

--------------------------------

Edit: Sorry nearly forgot about the reference image. I attached it just now.

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