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3 years ago

I will give brainliest

Mathematics

1 answer:

alina1380 [7]3 years ago

5 0

Answer:

3532.5

Step-by-step explanation:

The formula for the volume of a cylinder is 3.14 times R^2 times H

I calculated it

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Which graph represents a function with direct variation

Amanda [17]

Where’s the graph????

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3 years ago

What transformation of the parent function f(x) is made to get 4f(x+2)

LenKa [72]

Answer: A vertical stretch of 4 and a translation of -2 units in the x-direction.

Step-by-step explanation:

Changes of the parent function can be written, in this case as af(x)(x - k) where a is the stretch factor and k is the movement left or right on the x-axis.

In this case, a = 4 and k = 2. Since the k is negative, the function will be moved -2 units on the x-axis.

Learn more about transformations of a parent function here:

brainly.com/question/13822715

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2 years ago

Help me i'll help you back

Dmitriy789 [7]

Answer:

A, C, B, respectively

Step-by-step explanation:

science(density and buoyancy)

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3 years ago

Pleas help !!! Choices X= -1 Y = -1 X = 1 Y= 1

____ [38]

Answer:

x=-1

Step-by-step explanation:

The axis of symmetry is along the vertex

The vertex is at (-1,-2)

The x coordinate is -1

x=-1

6 0

3 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

4 years ago