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Gemiola [76]
3 years ago
14

Use rounding or compatible numbers to estimate the difference 192-78

Mathematics
1 answer:
pogonyaev3 years ago
5 0
The answer would be 110
You might be interested in
7/12 × 6\14 please help
Mama L [17]
7/12*6/14
  7*6=42
  12*14=168
=42/168
=0.25 =1/4
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
3 years ago
A cylinder has a base diameter of 6 centimeters and a height of 15 centimeters. What is its volume in cubic centimeters, to the
sashaice [31]

Step-by-step explanation:

V

≈

424.12

cm³

d

Diameter

cm

h

Height

cm

5 0
3 years ago
you start a business selling bottled fruit juices. You invest $15,000 for equipment. Each bottle cost $0.40 to make. You sell ea
Inga [223]

HELP PLEASE Jackson sells lemonade for $2 per cup. he paid $20 for supplies to sell 5 cups. What is the domain for this scenario

6 0
2 years ago
if the equation y=3/2 x+5 were to be graphed in the xy-plane above, at what point would the graph intersect the line shown
adoni [48]

Answer:

if you go on https://www.geogebra.org/ it will graph it for you

Step-by-step explanation:


3 0
3 years ago
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