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yarga [219]
3 years ago
5

D'Naisa mixed her favorite shade of orange paint. She had 111 gallon of orange paint and added 222 quarts of yellow paint and 33

3 pints of red paint.
Mathematics
2 answers:
tatiyna3 years ago
6 0

I Hate it when Khan academy does this... The Answer is 7 1/2

belka [17]3 years ago
5 0
What’s the question though?
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Which of the following are geometric sequences?
Nana76 [90]
B. 10, 5, 2.5, 1.25, 0.625, 0.3125
5 0
3 years ago
Find the gcf of 14,35,84
Paha777 [63]

Answer:

7

Step-by-step explanation:

3 0
2 years ago
Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li
Sophie [7]
Consider the closed region V bounded simultaneously by the paraboloid and plane, jointly denoted S. By the divergence theorem,

\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV

And since we have

\nabla\cdot\mathbf f(x,y,z)=1

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV
=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr
=\dfrac\pi2

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by D, we have

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS

Parameterize D by

\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k
\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k

which would give a unit normal vector of \mathbf k. However, the divergence theorem requires that the closed surface S be oriented with outward-pointing normal vectors, which means we should instead use \mathbf s_v\times\mathbf s_u=-u\,\mathbf k.

Now,

\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du
=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du
=-2\pi

So, the flux over the paraboloid alone is

\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2
6 0
3 years ago
Find the centroid of the region bounded by the given curves y=8sin(4x), y=8cos(4x)
Luba_88 [7]
A cosine is just a sine shifted to the left by π/2. A cosine of 4x is shifted to the left by only π/8 because of the factor 4. Sketch them.

The region we're looking for is this sausage-shaped part between the cos and the sin.

The x intercepts are at π/8 for the cosine and π/4 for the sine. The midpoint between them is at (π/8 + π/4)/2 = 3/16π.

The region is point symmetric around the x axis, so the y coordinate of the centroid is 0.

So the centroid is at (3/16π, 0)
5 0
3 years ago
BRAINLIEST TO CORRECT ANSWER!!! NO links as answers, or you will be reported!! (question 4)
In-s [12.5K]

Answer:

Hello! Your answer would be, C) Divide by 2

Step-by-step explanation:

And plz don't be mean. :(

Hope I helped! Brainiest plz!♥ Have a nice afternoon. Hope you make a 100%! -Amelia

8 0
2 years ago
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