What is the least 1/2 x 3/4, 3/4 + 1/8, 1/2 + 1/4

bezimeni [28]

This is the answer in exact form

4 0

3 years ago

Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k) she can drive with 12 li

masya89 [10]

Answer:

132 kilometers

Step-by-step explanation:

Given: Pamela drove her car 99 kilometers and used 9 liters of fuel.

To find: Number of kilometers Pamela drove in 12 liters of fuel.

Solution:

It is given that Pamela drove her car 99 kilometers and used 9 liters of fuel. Also the relationship between kilometers and fuel is proportional.

So, let us assume that she can travel x kilometers in 12 liters of fuel.

By proportionality we have,

$99:9 :: x:12$

$\frac{99}{9} =\frac{x}{12}$

$11=\frac{x}{12}$

$x=12\times11$

$x=132$

Hence, she can travel 132 kilometers in 12 liters of petrol.

7 0

3 years ago

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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

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

5 0

3 years ago

PLEASE HELP?! <br><br> Polygon LMNOP ~ Polygon QRSTU What is TU?

ycow [4]

Answer:

The answer is B.

Step-by-step explanation:

9 : 12 = 3 : 4

12 : 16 = 3 : 4

6 0

3 years ago

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A cooler contains ten bottles of sports drink: four lemon-lime flavored, three orange-flavored, and three fruit-punch flavored.

Alika [10]

Since there are a total of 10 bottles, the probability of getting a certain one is based on the number of those bottles in the cooler.

The probability of getting a lemon-lime flavored drink is 4/10 or 40%.

The probability of getting a orange flavored drink is 3/10 or 30%

The probability of getting a fruitpunch flavored drink is also 3/10 or 30%.

If the question is asking what the probability is of choosing lemon-lime, fruit punch and fruit punch again in that order, you would multiply the probabilities together.

.4 * .3 * .3 = .036, so there’s a 3.6% chance of picking these exact 3 flavors happening again.

6 0

3 years ago

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What is the least 1/2 x 3/4, 3/4 + 1/8, 1/2 + 1/4​

What is the least 1/2 x 3/4, 3/4 + 1/8, 1/2 + 1/4