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2 years ago

Plz help! What is the surface area of the figure?

Mathematics

1 answer:

dexar [7]2 years ago

6 0

Answer:

483 ft²

Step-by-step explanation:

2(7x7)= 98

3(5x12)=180

2(12x5)=120

2(5x5)= 50

1(7x5) = 35

483

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Zuri made 2 spheres using plaster. The smaller sphere has a radius of 6 cm. The larger sphere has a radius of 24 cm.

Sliva [168]

Since we are dealing with volume, when one object is 4 times bigger than another, the difference in volume is 4^3 = 64.

6 cm sphere = 4/3 *PI * 6^3
6 cm sphere = 4/3 *PI * 216
6 cm sphere = 904.78 cc

24 cm sphere = 4/3 *PI * 24^3
24 cm sphere = 4/3 *PI * 13,824
24 cm sphere = 57,905.84 cc

Comparing the volumes: 57,905.84 / 904.78 = 64

7 0

3 years ago

I need help pleasss

butalik [34]

I think the answer is c

3 0

3 years ago

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Find the volume of the ellipsoid x^2+y^2+9z^2=64

yuradex [85]

Parameterize the ellipsoid using the augmented spherical coordinates:

$\begin{cases}x=\frac18\rho\cos\theta\sin\varphi\\\\y=\frac18\rho\sin\theta\sin\varphi\\\\z=\frac38\rho\cos\varphi\end{cases}$

Then the Jacobian for the change of coordinates is

$\mathbf J=\dfrac{\partial(x,y,z)}{\partial(\rho,\theta,\varphi)}=\begin{bmatrix}\frac18\cos\theta\sin\varphi&-\frac18\rho\sin\theta\sin\varphi&\frac18\rho\cos\theta\cos\varphi\\\\\frac18\sin\theta\sin\varphi&\frac18\rho\cos\theta\sin\varphi&\frac18\rho\sin\theta\cos\varphi\\\frac38\cos\varphi&0&-\frac38\rho\sin\varphi\end{bmatrix}$

which has determinant

$\det\mathbf J=-\dfrac3{512}\rho^2\sin\varphi$

Then the volume of the ellipsoid is given by

$\displaystyle\iiint_E\mathrm dx\,\mathrm dy\,\mathrm dz=\iiint_E|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

where $E$ denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume

$\displaystyle\frac3{512}\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\dfrac\pi{128}$

4 0

3 years ago

Given f(x) = 2x + 9, if f(x) = 15, find x.

AleksandrR [38]

Answer:

Step-by-step explanation:

$f(x)=2x+9\\\\\text{Substitute}\ f(x)=15:\\\\15=2x+9\qquad\text{subtract 9 from both isdes}\\\\15-9=2x+9-9\\\\6=2x\qquad\text{divide both sides by 2}\\\\\dfrac{6}{2}=\dfrac{2x}{2}\\\\3=x\to x=3$

4 0

2 years ago

Jeff has 4 red pens and 2 blue pens in his backpack. He also has 1 yellow highlighter and 4 green highlighters in his

Romashka-Z-Leto [24]

Answer:

$\frac{1}{15}$

Step-by-step explanation:

In probability,

"AND" means "multiplication"

"OR" means "ADDITION"

We want probability of Blue Pen and Yellow Highlighter. So we find individual probabilities and "MULTIPLY" them.

Let P(b) be probability of blue pen

Let P(y) be probability of yellow highlighter

We know probability of event is that event divided by total number of that

So,

There are 4 + 2 = 6 pens

Blue pen = 2

Hence,

P(b) = 2/6 = 1/3

And,

There are 5 highlighters

Yellow highlighter = 1

Hence,

P(y) = 1/5

Now,

P(b and y) = 1/3 * 1/5 = 1/15

Hence,

probability of grabbing blue pen and a yellow highlighter is $\frac{1}{15}$

3 0

2 years ago

Read 2 more answers

Plz help! What is the surface area of the figure?​

Plz help! What is the surface area of the figure?