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madam [21]
3 years ago
8

I take half of Jeremy's money and divide it into 7 equal piles. Six of these piles blow away in the wind, but from the seventh p

ile, I take 2 dollars and hand Jeremy the rest, which is 8 dollars. How much money, in dollars, did Jeremy begin with?
Mathematics
1 answer:
madreJ [45]3 years ago
5 0
$140 dollars,
Using the equation (1/2)J/7=x. J=Jeremy's total money.7 because it was divided into 7 piles. Then, since 6 piles are blown away, we don't need to care about that for now. After that, you take 2 dollars and give the rest to Jeremy which is 8 dollars. You can create the equation x-2=8. Solve for x which is $10. Finally substitute that into the first equation to get (1/2)J=70. Multiply 2 to both sides to cancel out the (1/2) and the 70 by 2 to get Jeremy's total money which is $140

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Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur
Bad White [126]

Looks like you have most of the details already, but you're missing one crucial piece.

\sigma is parameterized by

\vec r(u,v)=\langle u\cos3v,u\sin3v,v\rangle

for 0\le u\le7 and 0\le v\le\frac{2\pi}3, and a normal vector to this surface is

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left\langle\sin3v,-\cos3v,3u\right\rangle

with norm

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{\sin^23v+(-\cos3v)^2+(3u)^2}=\sqrt{9u^2+1}

So the integral of f(x,y,z)=x^2+y^2+z^2 is

\displaystyle\iint_\sigma f(x,y,z)\,\mathrm dA=\boxed{\int_0^{2\pi/3}\int_0^7(u^2+v^2)\sqrt{9u^2+1}\,\mathrm du\,\mathrm dv}

6 0
3 years ago
9. Aaron has a lemonade business. If he sells each glass of lemonade for $2.75, and he sold 11
marin [14]

Answer:

$27.75

Step-by-step explanation:

Multiply $2.25 by 11 to get the answer

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3 years ago
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25% of 80 and that MULTPLIED by 4
icang [17]

Answer:

80

Step-by-step explanation:

25% of 80 is 20

20 x 4 = 80

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2 years ago
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For sixth subtracted by two third
scZoUnD [109]
4/6 - 2/3 = 2/2 which reduces to 1 WHOLE
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3 years ago
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Find the equation of the line passing through the point (2,−4) that is parallel to the line y=3x+2
Naily [24]

Hey there! :)

Line passes through (2, -4) & parallel to y = 3x+ 2

Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope. "M" is simply a place mat so if we look at our given line, the "m" value is 3. Therefore, our slope is 3.

We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our slope for our new line will be 3.

Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (2, -4) with a slope of 3.

y-y₁=m(x-x₁)

Let's start by plugging in 3 for m (our slope), 2 for x1 and -4 for y1.

y - (-4) = 3(x - 2)

Simplify.

y + 4 = 3x - 6

Simplify by subtracting 4 from both sides.

y = 3x - 10

~Hope I helped!~

8 0
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