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2 years ago

What is the greatest multiple of 99 that is less than 0?

Mathematics

1 answer:

Gekata [30.6K]2 years ago

3 0

Answer:

-1

Step-by-step explanation:

99 is the greatest factor greater than 0, but postive numbers have negative factors too, and negative numbers closer to 0 are greater.

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The hardcover version of a book weighs twice as much as its paperback version. The hardcover book and the paperback together wei

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Answer:

The 4th system (h = 4.2 − p ; h = 2p)

Step-by-step explanation:

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3 years ago

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Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

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$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

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3 years ago

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Small problem....

There is no graph!

ill be happy to solve this if i saw a graph

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2 years ago

Highest common factor of 15 30 and 45

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Step-by-step explanation:

I believe it is 15...all the numbers can be divided by 15, since 15 is the smallest number it is also the highest common factor only because 30 and 45 can be divided by 15

.......hope it helps!

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2 years ago

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In triangle ABC, the side lengths are AB = 13, AC = 21, and BC = x. Write a compound inequality that represents the range of pos

N76 [4]

There is only 1 solution for the length of BC.

We can calculate it using Pythagorean theorem.

We can conclude that triangle's hypotenuse is AC.

$AC^2=AB^2+BC^2$

If that is the case we are looking for a side BC.

$BC=\sqrt{AC^2-AB^2}$

Now put in the data.

$BC=\sqrt{21^2-13^2}=\sqrt{272}=\sqrt{272}\approx\boxed{16.49}$

Hope this helps.

r3t40

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3 years ago