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2 years ago

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A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same k

arate class for $95.

1 answer:

sleet_krkn [62]2 years ago

8 0

Answer:

215

Step-by-step explanation:

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Solve the following proportion x/3 = 6/9<br>18<br>27<br>2<br>24

Talja [164]

X/3 = 6/9
x= 6/9 x 3/1
x = 18/9 = 2

ANSWER=2

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3 years ago

Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

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2 years ago

What is 0.3636... round to the nearest tenth?

miskamm [114]

0.36.
tenth position is b in . 0.ab

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3 years ago

The distance traveled by an object divided by the time in which the distance was traveled is called the ___ of the object.

zavuch27 [327]

the Velocity of the object

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3 years ago

Read 2 more answers

Two supplementary angles are in the ratio of 31:5 find angles

ad-work [718]

Answer:

The angles are <u>155°</u> and <u>25°</u>.

Step-by-step explanation:

Given:

Two supplementary angles are in the ratio of 31:5.

Now, to find the angles.

The sum of two supplementary angles = 180°

Let the ratio of the angles be $31x\ and\ 5x$ .

So, according to question:

$31x+5x=180\°$

$36x=180\°$

<em>Dividing both sides by 36 we get:</em>

$x=5$

So, $31x=31\times 5=155\°.$

And, $5x=5\times 5=25\°.$

Therefore, the angles are 155° and 25°.

7 0

3 years ago