What is the first year in which franklins sign shows a larger number than chester’s sign

in one day a movie rented out 35 comedies. If the ratio of comedies rented action movies rented was 5:2 how many action movies w

aksik [14]

14 35/7 equals 5 so 7x2 equals 14

7 0

3 years ago

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

Find the total surface area.

Ede4ka [16]

Hey love! <3

Answer:

The right answer is A = 49.6 π ft^2

Step-by-step explanation:

(Let pi = 3.1415926535898)

The formula for calculating the surface area of a cylinder is A=2πrh+2πr^2

So if r = 4 ft

and h = 2.2 ft

A= 2π(4)(2.2)+2π(4)^2

Once we've plugged in our formulas our final surface area is A = 49.6 π ft2

Hope this helped you calculate the surface area! ◃┆◉◡◉┆▷ Sincerely, Kelsey from Brainly.

~ #LearnWithBrainly ~

8 0

3 years ago

Read 2 more answers

How many meters in 1 kilometer

mixas84 [53]

1 kilometer = 10000 meters
1 kilometer = 100000 centimeters
I can so more and explain more is you want Hope it helps

7 0

3 years ago

Read 2 more answers

What is the maximum number of snowmen they can make?

Anastasy [175]

To answer this question, you do 5 2/3 divided by 1/2. First, change 5 2/3 to 17/3. Then, use the reciprocal method by doing 17/3 times 2/1, which gives you 34/3. That’s 11.3 repeating, so they can make 11 whole snowmen.

3 0

3 years ago