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3 years ago

What is another number of pennies and total mass of pennies in grams if my number of pennies is 10 and the mass in grams is 25

Mathematics

1 answer:

Angelina_Jolie [31]3 years ago

7 0

Answer:

1 penny is equal to 2.5 grams

Step-by-step explanation:

1 penny = 2.5 grams

2 pennies = 5.0 grams

3 pennies = 7.5 grams

Just add 2.5 grams every penny.

Pick any number of pennies and multiply it by 2.5 (Don't forget to add grams ( g ) at the end.

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Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

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1 year ago

Dan brought 36 vanilla cupcakes and 49 chocolate cupcakes to his school bake sale. Then his friend brought 5 more cupcakes. How

fomenos

Answer:

Step-by-step explanation:

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2 years ago

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Calculate the slope of the line using two different pairs of points.

mihalych1998 [28]

Rise/run = 20/20 = 1
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2 years ago

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What is 7 +2 = x-4/2

madam [21]

Answer:

The answer is 11.

Step-by-step explanation:

We will use PEMDAS in this situation.

7 + 2 = x - 4 / 2

7 + 2 = x - 2 [divide first

9 = x - 2 [add the 7 and 2]

+2 +2 [the 2 cancels out]

11 = x

Your answer is 11.

I hope this helped!

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

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Aliyah $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost?

MaRussiya [10]

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3 years ago

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