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3 years ago

3) Michael is getting dinner for his drama club on the evening of their final rehearsal.

Mathematics

1 answer:

bagirrra123 [75]3 years ago

5 0

Answer:

5.5p + 5 ≤ 60

10 pounds

Step-by-step explanation:

a) The maximum total cost he can spend is $60.

5.5 * p + 2 * 2.5 ≤ 60

Simplify.

5.5p + 5 ≤ 60

b) Solve 5.5p + 5 ≤ 60

Subtract 5 from both sides

5.5p ≤ 55

Divide both sides by 5.5

p ≤ 10

So, the maximum he can buy is 10 pounds of food

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Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
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4 0

3 years ago

How far from an airport can an airplane fly and return in 8 hours, if it's outgoing speed is 160 km per hour and it's returning

PilotLPTM [1.2K]

speed = distance/time
total time is 8 hours

outgoing speed is 160 km per hour,
so time = d/160

returning speed is 240 km per hour,
so time = d/240

d/160 + d/240 = 8

3d/480 + 2d/480 = 8
5d/480 = 8
5d =480 (8)
5d = 3840
d=3840/5
d=768

answer: so the distance is 768 km

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3 years ago

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Mama L [17]

Answer:

Infinite solutions

Step-by-step explanation:

Simplify both sides, subtract 9x, and add 21x to both sides and you will get 0 = 0 so there is infinite solutions.

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3 years ago

Evaluate the expression: (1/3)⁴ = ?

vlabodo [156]

Answer:

1/81

Step-by-step explanation:

$\frac{1*1*1*1}{3*3*3*3}$ multiply them

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3 years ago

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What is the center and radius of the circle that has the equation x+72+y-42=49? Explain.

balu736 [363]

Answer: The center is (-7, 4) and the radius is 7.

Step-by-step explanation:

The equation for a circle usually is:

(x - a)^2 + (y - b)^2 = R^2

where R is the radius, and (a, b) is the center of the circle.

I guess that the equation in this case is:

(x + 7)^2 + (y - 4)^2 = 49

then, in this case we have:

a = -7 and b = 4, then (a, b) = (-7, 4)

this means that the center of our circle is in the point (-7, 4)

and we know that:

R^2 = 49

R = √49 = 7

Then the radius is equal to 7.

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3 years ago