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3 years ago

He table shows how the random number range is assigned to each event.

Mathematics

1 answer:

hichkok12 [17]3 years ago

8 0

Answer:

option 2nd is correct that is 2.

Step-by-step explanation:

We have been given the random number range assigned to each event

And from the given table we can see that the assigned number range of chocolate chip cookies is 0-40

So, we will consider numbers in this range 0-40 from the given random numbers which are 3,27,43,85,83.

So, 3 and 27 will come under the range 0-40

Therefore, only 2 chocolate chip cookies purchased

Therefore, option 2nd is correct that is 2.

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Given f(x)=-5x+2, find f(6)

BaLLatris [955]

It would be -5(6)+2=-28

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3 years ago

Use the least common denominator to write an equivalent fraction for each fraction. 5/6 and 2/9

olchik [2.2K]

5/6 and 2/9......least common denominator is 18
so 5/6 = 15/18 and 2/9 = 4/18

1/12 and 3/8...least common denominator is 24
so 1/12 = 2/24 and 3/8 = 9/24

5/9 and 2/15...least common denominator is 45
so 5/9 = 24/45 and 2/15 = 6/45

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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

3 years ago

Which equation is correctly rewritten to solve for x?

ikadub [295]

Answer:

Option (A)

Step-by-step explanation:

Te given equation is,

-qx + p = r

Toe find the value of x,

By subtracting p from both the sides of the equation.

-qx + p - q = r - q