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Yuliya22 [10]
3 years ago
15

Y=x+4 Y=2x+6 Solve for x and y

Mathematics
1 answer:
gladu [14]3 years ago
7 0

Answer:

X = -2

y = 2

Step-by-step explanation:

Substitute y=x + 4 in the second equation to find x

x+4 = 2x + 6

subtract x from both sides

4 = x + 6

subtract 6 from both sides

-2 = x

put -2 in for x in the first equation

y= 2

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. f(x) = Square root of quantity x plus eight. ; g(x) = 8x - 12 Find f(g(x)). (1 point) f(g(x)) = 2 Square root of quantity two
frozen [14]

<u>Answer:</u>

f(g(x))  = \sqrt{8x - 4}

<u>Step-by-step explanation:</u>

• f(x) = \sqrt{x + 8}

• g(x) = 8x - 12

f(g(x)) is the combination of the functions f(x) and g(x) such that g(x) is the input to the function f(x) .

This means, we have to replace the original input of  f(x), which is x, with the function  g(x).

∴  f(g(x)) = f(8x - 12)

               ⇒ \sqrt{8x - 12 + 8}

               ⇒ \sqrt{8x - 4}

3 0
1 year ago
Hi can someone please answer this question? <br><br> Thank you :)
Archy [21]

Answer:

\frac{7}{8}

Step-by-step explanation:

Remember that slope, or in this case pitch, is equal to rise divided by run. In other words:

m=\frac{rise}{run}

where m is the slope.

From looking at the image, we can see that the rise 21 feet and the run is 24 feet. By plugging this information into the equation, we get:

m=\frac{21}{24}=\frac{7}{8}

So the slope, or pitch, of the roof id 7/8.

I hope you find my answer and explanation to be helpful. Happy studying.

7 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
GenaCL600 [577]

Close off the hemisphere S by attaching to it the disk D of radius 3 centered at the origin in the plane z=0. By the divergence theorem, we have

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

where R is the interior of the joined surfaces S\cup D.

Compute the divergence of \vec F:

\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2

Compute the integral of the divergence over R. Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

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

So the volume integral is

\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5

From this we need to subtract the contribution of

\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S

that is, the integral of \vec F over the disk, oriented downward. Since z=0 in D, we have

\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k

Parameterize D by

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

where 0\le u\le 3 and 0\le v\le2\pi. Take the normal vector to be

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

Then taking the dot product of \vec F with the normal vector gives

\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v

So the contribution of integrating \vec F over D is

\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4

and the value of the integral we want is

(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>

==>  486π/5 - (-81π/4) = 2349π/20

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1. The heights of two right prisms
RoseWind [281]

Answer:

They are not similar

Step-by-step explanation:

To determine whether the prism are similar we need to calculate their volumes

Volume of a prism = Base Area * Height

Volume of the first prism = 18ft *8 * 8ft

Volume of the first prism = 1152ft^2

Volume of the second prism = 30t * 15 * 15ft

Volume of the second prism = 6,750ft^2

Since the volumes are different, the prism are not similar.

3 0
3 years ago
Antonio’s weekly allowance is given by the equation A=0.5c+10, where c is the number of chores he does. If he received $16 in al
Vedmedyk [2.9K]
A=0.5(12)+10= 16. Antonio has 12 chores.
3 0
2 years ago
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