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3 years ago

14

How do you model function using rules tables and graphs?

1 answer:

Oksana_A [137]3 years ago

4 0

Answer:

For X and then determine Y. So when X is equal to negative 2. Notice that Y is going to be equal to negative 2 times negative 2 plus 5. Well negative 2 times negative 2 is 4 4 plus 5 equals 9.

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Let divf = 6(5 − x) and 0 ≤ a, b, c ≤ 12. (a) find the flux of f out of the rectangular solid 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤

dusya [7]

Continuing from the setup in the question linked above (and using the same symbols/variables), we have

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV$
$=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz$
$=\displaystyle6bc\int_0^a(5-x)\,\mathrm dx$
$=6bc\left(5a-\dfrac{a^2}2\right)=3abc(10-a)$

The next part of the question asks to maximize this result - our target function which we'll call $g(a,b,c)=3abc(10-a)$ - subject to $0\le a,b,c\le12$ .

We can see that $g$ is quadratic in $a$ , so let's complete the square.

$g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)$

Since $b,c$ are non-negative, it stands to reason that the total product will be maximized if $a-5$ vanishes because $25-(a-5)^2$ is a parabola with its vertex (a maximum) at (5, 25). Setting $a=5$ , it's clear that the maximum of $g$ will then be attained when $b,c$ are largest, so the largest flux will be attained at $(a,b,c)=(5,12,12)$ , which gives a flux of 10,800.

7 0

3 years ago

The sum of the radius of the base and the height of a solid cylinder is 37m. If the total surface area of the cylinder is 1628 m

MA_775_DIABLO [31]

Answer:

4618.14 $m^{3}$ or 4618 $m^{3}$

Step-by-step explanation:

From T.S.A = 2 $\pi$ rh + 2 $\pi$ $r^{2}$

where T.S.A = 1628 $m^{2}$

1628 = 2 $\pi$ rh + 2 $\pi$ $r^{2}$

1628 = ( rh + $r^{2}$ ) 2 $\pi$

by dividing both side by 2 $\pi$

$\frac{1628}{2\pi }$ = rh + $r^{2}$

259.10 = rh + $r^{2}$

rh = 259.10 - $r^{2}$

h = $\frac{259.10 - r^{2} }{r}$ <u> </u>(1)

From Radius + Height = 37

r + h = 37 <u> </u>(2)

by substituting eqn 1 into 2

r + $\frac{259.10 - r^{2} }{r}$ = 37

by multiplying r to both side

$r^{2}$ + 259.10 - $r^{2}$ = 37r

259.10 = 37r

r = $\frac{259.10}{37}$

r = 7.00 ≅ 7

From Eqn 2

r + h = 37

7 + h = 37

h = 37 - 7

h = 30

so Volume of a cylinder = $\pi r^{2} h$

V = $\pi$ * $7^{2}$ * 30

V = 4618.14 $m^{3}$ ≅ 4618 $m^{3}$

4 0

4 years ago

Read 2 more answers

Please help giving brainliest

nata0808 [166]

I would go with 12.5

I’m more of an English person but that’s my best guess.

3/24
1/8
1 divided by 8
=12.5

Hope you get it right :)

8 0

3 years ago

Read 2 more answers

*<br> 8. Determine the rate of change (slope) in the graph

marta [7]

Answer:

Step-by-step explanation:

2 calculate rise over run

4 0

3 years ago

SOMEONE HELPP ME ASAP

Naily [24]

Answer:

k = 7

Step-by-step explanation:

The given figures are lines f(x) and g(x)

For the line f(x), we have the y-intercept at (0, -3) and slope = (-1 - (-3))/(-3 - 0) = -2/3

Therefore, line f(x) = y - (-3) = -2/3·(x - 0) which gives f(x) = y = -3 - 2·x/3

For the line g(x), the y-intercept is (0, 4), and the slope is (4 - 2)/(0 - 3) = -2/3

The equation of the line g(x) is therefore, g(x) = y - 4 = -2/3·x, which simplifies to the slope and intercept form as g(x) = y = 4 - 2/3·x

Therefore, given that the transformation of f(x) to g(x) is given as g(x) = f(x) + k, we have;

k = g(x) - f(x) = 4 - 2/3·x - (-3 - 2·x/3) = 4 - 2/3·x + 3 + 2·x/3 = 7

∴ k = 7

4 0

3 years ago