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Anton [14]
3 years ago
9

F(x) = 3x^2 +12x+7 in standard form

Mathematics
1 answer:
ivann1987 [24]3 years ago
7 0

Answer:

y = ax^2 + bx + c  =>  F(x) = 3x^2 +12x+7;   F(x) = 3x^2 +12x+7 is already in standard form for the equation of a parabola.

Step-by-step explanation:

Actually, F(x) = 3x^2 +12x+7 is already in standard form, y = ax^2 + bx + c.  Double check the instructions for this problem.  Did you perhaps want "vertex form?"


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Simplify the expression.<br> (x 3/2)6
Sliva [168]

For this case we must simplify the following expression:

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We have that by definition of properties of powers that is fulfilled:

(a ^ n) ^ m = a ^ {n * m}

Then, rewriting the expression:

x ^ {\frac {3 * 6} {2}} =\\x ^ {\frac {18} {2}} =\\x ^ 9

Answer:

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3 years ago
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2 years ago
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
Tomtit [17]

Apparently my answer was unclear the first time?

The flux of <em>F</em> across <em>S</em> is given by the surface integral,

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S

Parameterize <em>S</em> by the vector-valued function <em>r</em>(<em>u</em>, <em>v</em>) defined by

\mathbf r(u,v)=7\cos u\sin v\,\mathbf i+7\sin u\sin v\,\mathbf j+7\cos v\,\mathbf k

with 0 ≤ <em>u</em> ≤ π/2 and 0 ≤ <em>v</em> ≤ π/2. Then the surface element is

d<em>S</em> = <em>n</em> • d<em>S</em>

where <em>n</em> is the normal vector to the surface. Take it to be

\mathbf n=\dfrac{\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}}{\left\|\frac{\partial\mathbf r}{\partial v}\times\frac{\partial\mathbf r}{\partial u}\right\|}

The surface element reduces to

\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\mathbf n\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\implies\mathbf n\,\mathrm dS=-49(\cos u\sin^2v\,\mathbf i+\sin u\sin^2v\,\mathbf j+\cos v\sin v\,\mathbf k)\,\mathrm du\,\mathrm dv

so that it points toward the origin at any point on <em>S</em>.

Then the integral with respect to <em>u</em> and <em>v</em> is

\displaystyle\iint_S\mathbf F\cdot\mathrm d\mathbf S=\int_0^{\pi/2}\int_0^{\pi/2}\mathbf F(x(u,v),y(u,v),z(u,v))\cdot\mathbf n\,\mathrm dS

=\displaystyle-49\int_0^{\pi/2}\int_0^{\pi/2}(7\cos u\sin v\,\mathbf i-7\cos v\,\mathbf j+7\sin u\sin v\,\mathbf )\cdot\mathbf n\,\mathrm dS

=-343\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}\cos^2u\sin^3v\,\mathrm du\,\mathrm dv=\boxed{-\frac{343\pi}6}

4 0
3 years ago
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lina2011 [118]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
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What happens to the value of the expression 80-2r as r decreases?
Ghella [55]

Answer:The value of the expression increases as r decreases.

Step-by-step explanation:

To find : What happens to the value of the expression as r decreases?

Given Expression: 80-2r

We check for different value of r as decreasing order,

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4        80-8=72

3        80-6=74

2        80-4=76

1         80-2=78

As r decreases the value of expression increases.

Therefore, the value of the expression increases as r decreases.

Hope this helps!

8 0
3 years ago
Read 2 more answers
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