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evablogger [386]
3 years ago
12

What is the value of m in the equation {m- n = 16, when n = 8?

Mathematics
2 answers:
TEA [102]3 years ago
8 0

Answer:

m=44

Step-by-step explanation:

ra1l [238]3 years ago
3 0

Answer:

m=44

Step-by-step explanation:

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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}

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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.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the cir
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The statements which are correct about the equation of circle x^{2} +y^{2}-2x-8=0 are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is x^{2} +y^{2} =9.

Given the equation of circle be x^{2} +y^{2}-2x-8=0.

We are required to find the appropriate statements related to the equation x^{2} +y^{2}-2x-8=0.

x^{2} +y^{2}-2x-8=0 can be written as under:

x^{2} +y^{2} -2x+1-9=0

x^{2} +1^{2}-2x+y^{2} -9=0

(x-1)^{2}+y^{2}-9=0

(x-1)^{2} +y^{2} =9

(x-1)^{2}+y^{2}  =3^{2}

Equation of a circle usually in the form x^{2} +y^{2} =a^{2} in which a is radius.

From the comparison of both the equations we get that radius is 3 units.

From the equation point will be (1,0). It is on the x axis.

Hence the statements which are correct about the equation of circle x^{2} +y^{2}-2x-8=0 are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is x^{2} +y^{2} =9.

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telo118 [61]

C. y = 1/2x - 2

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