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3 years ago

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]

Answer:

$f(g(x))$ = $\sqrt{8x - 4}$

Step-by-step explanation:

• $f(x) = \sqrt{x + 8}$

• $g(x) = 8x - 12$

$f(g(x))$ 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? 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

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