12. What steps do you need to take to solve

Find the domain for the rational function:

jenyasd209 [6]

Answer:

3rd Option

Step-by-step explanation:

Since the denominator cannot equal 0, x ≠ 5. Therefore, our domain stops and starts again at 5. So our answer is 3rd option.

3 0

2 years ago

Caroline is making some table decorations.

jolli1 [7]

Answer:

Caroline buys 3 packs of candles and 5 packs of holders.

Step-by-step explanation:

1.) You need to add numbers of candle packs together until they both reach the same number, for example, multiples of 30 are 30, 60, 90.

2.) Then you add multiples of the holders. 18, 36, 54, 72, 90.

3.) You find that Caroline buys 3 pakcs of candles and 5 packs of holders to have the same number of both.

6 0

2 years ago

Solve each equation y-6.72=253

diamong [38]

You just need to have the variable by itself, so move the -6.72 to the other side (that will make it +6.72)
So you should have this equation now: y = 253+6.72
Then just add them and you have this: y = 259.72
And that is your answer!

Hope I helped! <3

7 0

2 years ago

Read 2 more answers

Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.

This requires

$\dfrac{\partial f}{\partial x}=\sin x\implies f(x,y)=-\cos x+g(y)$

$\dfrac{\partial f}{\partial y}=\cos y=\dfrac{\mathrm dg}{\mathrm dy}\implies g(y)=\sin y+C$

So we have

$f(x,y)=-\cos x+\sin y+C$

which means $\vec F$ is indeed conservative. By the fundamental theorem, we have

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=f(2,-\pi)-f(1,0)=-\cos2-(-\cos1)=\boxed{\cos1-\cos2}$

3 0

2 years ago

Every 2 seconds, the distance the mouse travels ___by ___feet!

Mrac [35]

(answer)increases, 22

(explanation)the numbers show that they increase going from 22 to 44 to 66. subtract 22 from either number (44 or 66) and youll get 22. add 22 to each number (44 and 66) and youll get the numbers 44 and 66, meaning the mouses travel increases by 22 feet.

8 0

1 year ago