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3 years ago

Y varies directly as x. If x=7 then y = 56. Find ybwhen x=3

Mathematics

1 answer:

marshall27 [118]3 years ago

6 0

When something varies directly as something else, their ratio of change always stays the same.

56 / 7 = 8

Therefore,

8 * 3 = 24

If x = 3 then y = 24

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2 years ago

What is the cube root of -729a^9b^6?<br> -9a^3b^2<br> -9a^2b^<br> -8a^3b^2<br> -8a^2b^3

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Answer:

$= 9a^3b^2$

Step-by-step explanation:

$\sqrt[3]{-729a^9b^6} =$

$= ((-9)^3a^9b^6)^{\frac{1}{3}$

$= (-9)^{3 \times \frac{1}{3}} \times a^{9 \times \frac{1}{3}} \times b^{6 \times \frac{1}{3}}$

$= (-9)^{1} \times a^{3} \times b^{2}$

$= -9a^3b^2$

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1 year ago

A recipe for a large batch of brownies uses one kilogram of sugar. Another recipe uses 800 grams of flour. How much sugar is nee

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3 years ago

Point m lies between points l and n on line segment l n . the space between l and m is 10 x 8. the space between m and n is 5 x

Ivenika [448]

The length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.

<h3>What is the length of line segment?</h3>

Length of a line segment is the distance of both the ends of it.

Point m lies between points l and n on line segment l n .

The space between l and m is 10x 8.

The space between m and n is 5x -4.

The value of line segment LN is,

$LN = 12x +16$

The sum of LM and LN is equal to the line segment LN. Thus,

$LM+MN=LN\\10x +8+(5x-4)=12x+ 16\\10x +8+5x-4=12x+ 16\\10x+5x-12x=16 -8+4\\3x=12\\x=\dfrac{12}{3}\\x=4$

Put this value of x in the equation of line segment LN,

$LN = 12(4) +16\\LN=48+16\\LN=64\rm\; units$

Thus, the length of line segment l n on which point m lines in between is 64 units. Option 4 is the correct option.

Learn more about the line segment here;

brainly.com/question/2437195

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2 years ago

Evaluate the integral by changing to polar coordinatesye^x dA, where R is in the first quadrant enclosed by the circle x^2+y^2=2

34kurt

$\displaystyle\iint_Rye^x\,\mathrm dA=\int_{\theta=0}^{\theta=\pi/2}\int_{r=0}^{r=5}r^2\sin\theta e^{r\cos\theta}\,\mathrm dr\,\mathrm d\theta$

which follows from the usual change of coordinates via

$\begin{cases}\mathbf x(r,\theta)=r\cos\theta\\\mathbf y(r,\theta)=r\sin\theta\end{cases}$

and Jacobian determinant

$|\det J|=\left|\begin{vmatrix}\mathbf x_r&\mathbf x_\theta\\\mathbf y_r&\mathbf y_\theta\end{vmatrix}\right|=|r|$

Swap the order, so that the integral is

$\displaystyle\int_{r=0}^{r=5}\int_{\theta=0}^{\theta=\pi/2}r^2\sin\theta e^{r\cos\theta}\,\mathrm d\theta\,\mathrm dr$

and now let $\sigma=r\cos\theta$ , so that $\mathrm d\sigma=-r\sin\theta$ . Now, you have

$\displaystyle\int_{r=0}^{r=5}\int_{\sigma=0}^{\sigma=r}re^\sigma\,\mathrm d\sigma\,\mathrm dr=\int_{r=0}^{r=5}r(e^r-1)\,\mathrm dr=4e^5-\dfrac{23}2$

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3 years ago