The ratio of girls to boys is 3 to 4. If there are 48 boys, how many girls are there? 24 40 47 36

Consider the following region R and the vector field F. a. Compute the two-dimensional curl of the vector field. b. Evaluate bo

Shalnov [3]

Looks like we're given

$\vec F(x,y)=\langle-x,-y\rangle$

which in three dimensions could be expressed as

$\vec F(x,y)=\langle-x,-y,0\rangle$

and this has curl

$\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle$

which confirms the two-dimensional curl is 0.

It also looks like the region $R$ is the disk $x^2+y^2\le5$ . Green's theorem says the integral of $\vec F$ along the boundary of $R$ is equal to the integral of the two-dimensional curl of $\vec F$ over the interior of $R$ :

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA$

which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of $R$ by

$\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle$

$\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt$

with $0\le t\le2\pi$ . Then

$\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt$

$=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0$

7 0

2 years ago

A railroad crew can lay 6 miles of track each day. They need ti lay 174 miles of track. The length, L (in miles), that is left t

Alex17521 [72]

X + y = 13
- x + y = 3

6 0

2 years ago

George studied 3/4 of an hour on Monday and 7/8 of an hour on Tuesday. How long did he study altogether on both days?

7nadin3 [17]

so you would add 3/4 and 7/8. so thats 1 1/2

3 0

2 years ago

Read 2 more answers

a container holds 15 pennies 8 nickels and 10 dimes you will randomly select two coins without replacement what is the probabili

AlexFokin [52]

<span>A container holds 15 pennies, 8 nickels, and 10 dimes.
You will randomly select two coins without replacement.
-->Fill in the probabilities on a tree diagram.</span>

3 0

2 years ago

Jack bought four dozen eggs at $10 per dozen six eggs were broken what percent of his money goes to waste?

Maurinko [17]

One dozen eggs is 48 eggs. Altogether that costs 40 dollars. If six of the eggs were broken then the money wasted would be 5 dollars.

The reason that it is 5 dollars is becuase it takes 10 to buy 12 eggs, and half of that is 6. So divide both 12 and 10 (separately) and you get 5 dollars for 6 eggs.

To get the percent you must divide 5 by 40.

The answer comes out to about 12.5% or 0.125.

So in the end, 12.5% of the money was wasted due to the broken eggs.

Hope this helped!

4 0

2 years ago