1/5 of a chocolate chip cookie has 30 cal how many calories are in a whole cookie

Mathematics

2 answers:

krok68 [10]3 years ago

8 0

Answer:

150 cal

Step-by-step explanation:

5x30=150

Svetach [21]3 years ago

6 0

Answer:

150 calories.

Step-by-step explanation:

Assuming there is the same amount of chocolate as well as cookie dough throughout the whole cookie.

You know that 1/5 of a chocolate chip cookie has 30 calories.

Find one cookie, by multiply 5 to both numbers. Set the equation:

1/5x = 30

Isolate the variable. Multiply 5 to both sides:

(1/5x) * 5 = (30) * 5

x = 30 * 5

x = 150

150 calories is your answer.

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

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

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and consider a plane

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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

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