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3 years ago

3. At the Art Studio 3/8 were red and

Mathematics

2 answers:

AleksAgata [21]3 years ago

6 0

Answer:

⅛

Step-by-step explanation:

Let the total be X

4/8 = 1/2

X - ⅜X - ½X = ⅛X are orange

Fraction ⅛X ÷ X = ⅛

const2013 [10]3 years ago

6 0

1/8 of the Art studio is orange.

3/8+4/8=7/8

And that’s the total amount of the room that is red and blue. We subtract that from the whole room (1) and we get how much of the room is orange.

1-7/8=1/8.

Hope this is helpful!

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How do you order two numbers written in scientific notation?

kondor19780726 [428]

This should be the answer to the problem I would explain it in my own words but it would be easier to understand if you saw it from here. I hope this helps!!

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3 years ago

1. Find the equation of a line passing through the points (1,-2) and (-3,10).

liraira [26]

Answer:

Step-by-step explanation:

(1 , -2) x₁ =1 & y₁ = -2

(-3,10) x₂= -3 & y₂ = 10

First we need to find the slope.

$\boxed{Slope = $\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}$ $\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}$

$=\dfrac{10-[-2]}{-3-1}\\\\\\=\dfrac{10+2}{-4}\\\\\\=\dfrac{12}{-4}\\\\\\= - 3$

m = -3

Equation of the line: y = mx + b

y = -3x + b

To find the value of b, take one of the point and substitue in the above equaiton.

(1 , -2)

-2 = -3*1 + b

-2 = -3 + b

-2 + 3 = b

b = 1

Equation of the line:

y = -3x + 1

4 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

15. What is -130 = -9k - 4

Nostrana [21]

Answer: 14

Work: First, we must get rid of the four from the side it's currently on. So, we are going to add it on both sides. After adding four on both sides, I'll cancel on the side it was on, and the new equation is -126 = -9k. Now, we are going to divide -9 on both sides and yet again, I'll cancel on the side it was on. The answer is k = 14. It's a positive 14 because we divided a negative by a negative, and after doing so, the new number is a positive.

<em>I hope this helps, and Happy Holidays! :)</em>

8 0

3 years ago

The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercept

Dennis_Churaev [7]

The correct description that cab made of these graphs is that They have the same x- and y-intercepts.

<h3>What is the end behavior of a function?</h3>

This is the term that is used to describe the behaviors of these functions as they approach infinity.

the y-intercept of a function

This is what is used to tell us the y value when we put x to be = 0

The y-intercept of f(x) is y = -2

The y-intercept of g(x) is y = -2

the x-intercept of a function

It is the value of x when y = 0.

The x-intercept = 2

Hence statement B is correct. They have the same x- and y-intercepts.