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3 years ago

In this swimming pool design, explain how to find the area of the pool’s surface.

1 answer:

6 0

Answer:Find the area of the rectangle. Then, find the area of the circle. The diameter is given, so take half that to get the radius. Multiply the area of the circle by half. Subtract the area of the half circle from the area of the the rectangle.

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) Set up a double integral for calculating the flux of F=3xi+yj+zk through the part of the surface z=−5x−2y+2 above the triangle

Fynjy0 [20]

The surface (call it $S$ ) is a triangle with vertices at the points

$x=0,y=0\implies z=2\implies(0,0,2)$

$x=0,y=2\implies z=-2\implies(0,2,-2)$

$x=2,y=0\implies z=-8\implies(2,0,-8)$

Parameterize $S$ by

$\vec s(u,v)=(1-v)(2,0,-8)+v\bigg((1-u)(0,2,-2)+u(0,0,2)\bigg)=(2-2v,2v-2uv,-8+6v+4uv)$

with $0\le u\le1$ and $0\le v\le1$ . Take the normal vector to $S$ to be

$\vec s_v\times\vec s_u=(20v,8v,4v)$

Then the flux of $\vec F$ across $S$ is

$\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\int_0^1\int_0^1\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^1\int_0^1(6-6v,2v-2uv,-8+6v+4uv)\cdot(20v,8v,4v)\,\mathrm du\,\mathrm dv$

$=\displaystyle8\int_0^1\int_0^1(11v-10v^2)\,\mathrm du\,\mathrm dv=\boxed{\frac{52}3}$

8 0

3 years ago

Write an equation for the line parallel to the given line that contains C.<br> Help

tangare [24]

There is no photo shown

6 0

3 years ago

Find a degree 3 polynomial with leading coefficient of 4 and zeros -2, 1, and 5

Alex Ar [27]

Answer:

4x^3-16x^2-28x+40

It will take a while to describe how i got this, but i checked the zeroes are ok.

4 0

3 years ago

What two numbers multiply to 10 and add up to 11

musickatia [10]

Answer:

1 and 10

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

$47 tie; 4.5% markup

Nuetrik [128]

Multiply the original price by the percent of markup: 47x.045=2.115. Round: 2.115=2.12. Add original price and amount of markup: 47+2.12=49.12. Answer: $49.12 :)

3 0

3 years ago