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Mkey [24]
3 years ago
15

What is half of 3672

Mathematics
1 answer:
tekilochka [14]3 years ago
6 0

Half of 3672 is 1836

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99 POINT QUESTION, PLUS BRAINLIEST!!!
sattari [20]
We know, that the <span>area of the surface generated by revolving the curve y about the x-axis is given by:

\boxed{A=2\pi\cdot\int\limits_a^by\sqrt{1+\left(y'\right)^2}\, dx}

In this case a = 0, b = 15, y=\dfrac{x^3}{15} and:

y'=\left(\dfrac{x^3}{15}\right)'=\dfrac{3x^2}{15}=\boxed{\dfrac{x^2}{5}}

So there will be:

A=2\pi\cdot\int\limits_0^{15}\dfrac{x^3}{15}\cdot\sqrt{1+\left(\dfrac{x^2}{5}\right)^2}\, dx=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\left(\star\right)\\\\-------------------------------\\\\&#10;\int x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\,dx=\int\sqrt{1+\dfrac{x^4}{25}}\cdot x^3\,dx=\left|\begin{array}{c}t=1+\dfrac{x^4}{25}\\\\dt=\dfrac{4x^3}{25}\,dx\\\\\dfrac{25}{4}\,dt=x^3\,dx\end{array}\right|=\\\\\\

=\int\sqrt{t}\cdot\dfrac{25}{4}\,dt=\dfrac{25}{4}\int\sqrt{t}\,dt=\dfrac{25}{4}\int t^\frac{1}{2}\,dt=\dfrac{25}{4}\cdot\dfrac{t^{\frac{1}{2}+1}}{\frac{1}{2}+1}= \dfrac{25}{4}\cdot\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}=\\\\\\=\dfrac{25\cdot2}{4\cdot3}\,t^\frac{3}{2}=\boxed{\dfrac{25}{6}\,\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}}\\\\-------------------------------\\\\

\left(\star\right)=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\dfrac{2\pi}{15}\cdot\dfrac{25}{6}\cdot\left[\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}\right]_0^{15}=\\\\\\=&#10;\dfrac{5\pi}{9}\left[\left(1+\dfrac{15^4}{25}\right)^\frac{3}{2}-\left(1+\dfrac{0^4}{25}\right)^\frac{3}{2}\right]=\dfrac{5\pi}{9}\left[2026^\frac{3}{2}-1^\frac{3}{2}\right]=\\\\\\=&#10;\boxed{\dfrac{5\Big(2026^\frac{3}{2}-1\Big)}{9}\pi}

Answer C.
</span>
3 0
3 years ago
F(x) = 9x2 - 4<br><br> Find the zeros of the function
Delvig [45]

Answer:

I believe that the answer is 14.

Step-by-step explanation:

hope it helped

4 0
3 years ago
Please help will give brainliest<br> options are <br> w=v/lh<br> w=lh/v<br> w=vl/h<br> w=vm/l
RUDIKE [14]

Answer:

B

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Trevor and Marissa together have 26 t-shirts to sell. If marissa has 6 fewer t shirts than trever, how many t shirts does Trevor
Soloha48 [4]
The answer is most likely 20, if together, they have 26. Basically, 26 - 6 = 20.
3 0
3 years ago
Please help what are the answers
krok68 [10]
Part b is 64 i think
hope this helps:))
4 0
2 years ago
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