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pishuonlain [190]
3 years ago
7

PLZZ HELP Will give brainlist plz help its for my 9 week exam

Mathematics
1 answer:
kotykmax [81]3 years ago
4 0

Answer:

Its commutative property

Step-by-step explanation:

It means u can move stuff around so ya

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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
The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the pop
lora16 [44]

Answer:

  year 2139

Step-by-step explanation:

The population will double when the factor e^(.005t) is 2.

  e^(.005t) = 2

  .005t = ln(2)

  t = ln(2)/0.005 = 138.6

The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.

7 0
3 years ago
Need 19 plz don’t rlly understand but if u can help that would be amazing thanks &lt;3
Neko [114]

Answer:

I got zero but I am not sure if that is right

Step-by-step explanation:

3 0
2 years ago
If 400 bricks measuring 81" by 31" are required to build a wall 42 ft. high, how long is the wall​
musickatia [10]
Idek lol but yeah have a good day
7 0
2 years ago
HELp mEEEEEEE pLssssssss
EastWind [94]

Answer:

its #3

Step-by-step explanation:

hope this helps

8 0
3 years ago
Read 2 more answers
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