Ask question

Ask question

All categories

3 years ago

12

The graph shows the profit per month for the 10 months during which Swanson's Restaurant has been open. Which is a valid predict

ion for the restaurant's profit during Month 12?

1 answer:

Scrat [10]3 years ago

4 0

Answer:

about $4,000 - $6,000

Step-by-step explanation:

You might be interested in

Find all the solutions for the equation:

Contact [7]

$2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0$

Divide both sides by $x^2\,\mathrm dx$ to get

$2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}$

Substitute $v(x)=\dfrac{y(x)}x$ , so that $\dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}$ . Then

$x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}$

$x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}$

The remaining ODE is separable. Separating the variables gives

$\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x$

Integrate both sides. On the left, split up the integrand into partial fractions.

$\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}$

$\implies v^2+2v+1=a(v^2+1)+(bv+c)v$

$\implies v^2+2v+1=(a+b)v^2+cv+a$

$\implies a=1,b=0,c=2$

Then

$\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v$

On the right, we have

$\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C$

Solving for $v(x)$ explicitly is unlikely to succeed, so we leave the solution in implicit form,

$\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C$

and finally solve in terms of $y(x)$ by replacing $v(x)=\dfrac{y(x)}x$ :

$\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C$

$\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}$

7 0

3 years ago

16⎯⎯⎯⎯√ – (14 + 2) : 2

ollegr [7]

Answer:

Our square root calculator estimates the square root of any positive number you want. Just enter the chosen number and read the results.

Step-by-step explanation:

8 0

2 years ago

Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 97 minutes. Billy could mow the lawn by himself in

s2008m [1.1K]

Answer:

52 minutes i think im not sure i'm not in high school

Step-by-step explanation:

5 0

2 years ago

How would eight billion, nine hundred seventy-seven thousand, thirteen be written in standard form?

zheka24 [161]

Answer:

8 billion > 8,000,000,000

977 thousand > 977,000

13> 13

8,000,977,013

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Please help me<br><br>Given: ∆NEW with NS is an angle bisector

Tatiana [17]

See attached picture:

6 0

2 years ago