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Salsk061 [2.6K]
2 years ago
7

What is the factored form of x^3 - x^2 - 24x - 36 If (x+3) is a factor?

Mathematics
2 answers:
antoniya [11.8K]2 years ago
6 0

Answer:

(x + 2)(x + 3)(x - 6)

Step-by-step explanation:

dividing x³ - x² - 24x - 36 by (x + 3) gives

x³ - x² - 24x - 36 = (x + 3)(x² - 4x - 12) = (x + 3)(x + 2)(x - 6)


MAXImum [283]2 years ago
6 0

Answer:

(x + 2)(x + 3)(x - 6)

Step-by-step explanation:

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\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 k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
Use the formula for volume = ℎ to find the<br> volume of the rectangular prism shown.
Sedaia [141]

Answer: 56 / 729

Step-by-step explanation: (4 * 2 * 7) / (9^3)

3 0
2 years ago
Given that ΔPQR is similar to ΔPTS, which statement MUST be true? A) m∠PST = m∠QPR B) m∠TPS = m∠RPQ C) m∠SPT = m∠PTS D) m∠PRQ =
galina1969 [7]

Answer:

The correct option is B.

Step-by-step explanation:

Two triangle are similar if their corresponding sides are in the same proportion or the corresponding angles are same.

It is given that the ΔPQR is similar to ΔPTS. It means all corresponding angles are same.

\angle R=\angle S

\angle Q=\angle T

\angle P=\angle P

Angle P can be defined as

\angle QPR=\angle TPS

\angle RPQ=\angle TPS

Therefore option B is correct.

\angle PST\neq\angle QPR

\angle SPT\neq\angle PTS

\angle PRQ\neq\angle PTS

Therefore option A, C and D are incorrect.

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3 years ago
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Use the parabola tool to graph the quadratic function f(x)=−5x^2−2.
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Desmos.com and plug in the equation
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3 years ago
I will give the brainiest answer
Airida [17]

Answer:

D

Step-by-step explanation:

If you draw the shape in D and assemble it you will get the answer

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2 years ago
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