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3 years ago

(5x10,000) +(2x100) +(9x1) +(3x1/1000)

Mathematics

1 answer:

zubka84 [21]3 years ago

7 0

Scientific notation:
5.0209003 x 10^4

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Adam is climbing up the stairs in a building. At a certain point, Adam starts counting the steps and when he reaches the last st

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He climed 3 steps before he started counting the steps.

Step-by-step explanation:

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6. Gabriella invests $6,500 into a savings account that earns 4.5% interest, and she is investing the money for 5 years without

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Answer:

1,462.50

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3 years ago

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5/7

Step-by-step explanation:

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A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

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3 years ago

27 bags is not the answer

Alinara [238K]

Answer:

It's 27 bags your teacher just dum

Step-by-step explanation:

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(5x10,000) +(2x100) +(9x1) +(3x1/1000)​

(5x10,000) +(2x100) +(9x1) +(3x1/1000)