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vampirchik [111]
3 years ago
9

How many solutions can be found for the equation −4x − 11 = 2(x − 3x) + 13?

Mathematics
1 answer:
nignag [31]3 years ago
5 0

Answer:

None

Step-by-step explanation:

-4x-11=2(x-3x)+13

-4x-11=2x-6x+13

-4x-11=-4x+13

-11=13

Therefore, there are no solutions for the equation as both sides will never be equal to each other.

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2 years ago
Hello! I don't understand how to do this question Triangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle
Katen [24]

ANSWER

EXPLANATION

Given that

X (-2, 1)

Y (-4, -3)

Z (0, -2)

The transformation rule of the triangle is given as

(x, y) ----------------> (x - 1, y + 3)

From, the given transformation rule, we can now find the new coordinates

X (-2, 1) --------------> X' (-2 -1, 1 + 3)

X(-2, 1 ----------------> X' (-3, 4)

Y(-4, -3) -----------------> Y'(-3-1, -3+1)

Y(-4, -3)-------------------> Y' (-4, -2)

Z(0, -2) --------------------Z'(0-1, -2+3)

Z(0, -2) -------------------> Z'(-1, 1)

Therefore the new coordinates of the triangles are

X' (-3, 4)

Y' (-4, - 2)

Z' (-1, 1)

8 0
1 year ago
Hey guys happy Tuesday ! I need some home work help ASAP work and answer pls love y’all ❤️
Strike441 [17]
1. Multiply 5 by 2 since the piece is twice as long. That is 10. 
Multiply 4 by 3 since the piece is 3 times as long. That is 12. 
Her piece is 10 x 12. 
2 sides of 10 & 2 sides of 12.
Multiply 10 & 12 by 2 to get 20 and 24. Add them together to get 44 inches, which is the perimeter. 

2. Multiply 4 x 2 since length is twice width. That is 8. 
Multiply 8 x 4 to get the area of the red paper. That is 32. 
Multiply 3 x 7 to get the area of the blue paper. That is 21.
Subtract 21 from 32 to get the amount of red paper that wasn't covered up.
11 square cm were not covered up. 

Hope this helps!
8 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

5 0
3 years ago
When a person 6 feet tall casts a shadow
yan [13]

Answer:

75 feet

Step-by-step explanation:

5 0
3 years ago
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