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2 years ago

9

Is this graph proportional?

1 answer:

LenKa [72]2 years ago

3 0

Answer:

Yes it is. becaus its even

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The area of a parallelogram is 125 square inches and the height of the parallelogram is 10 inches. What is the lenght of the bas

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12.5 inches is the answer

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3 years ago

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A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. The central angle formed by the peach co

Vsevolod [243]

Answer:

D. 5 inches

Step-by-step explanation:

Given:

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.

That means complete angle having 360° is divided into 3 section.

The central angle formed by the peach cobbler is 105 degrees.

The central angle formed by the pasta is 203 degrees.

<u>Question asked:</u>

What is the approximate length of the arc of the section containing the peas?

<u>Solution:</u>

The central angle formed by the peas = 360° - 105° - 203°

= 52°

$Ridius,r=\frac{Dameter}{2} =\frac{12}{2} =6\ inches$

As we know:

$Length\ of\ arc=2\pi r\times\frac{\Theta }{360}$

$=2\times\frac{22}{7} \times6\times\frac{52}{360} \\ \\ =\frac{13728}{2520} \\ \\ =5.44\ inches$

Therefore, the approximate length of the arc of the section containing the peas are 5 inches.

6 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 $v(x)=\dfrac{y(x)}x$ :

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

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

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

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3 years ago

A silo is a storage bin that is a cylinder with a hemisphere on top.A farmer has a silo with a base radius of 30 feet and a stor

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1000 square feet of wheat produces 250 pounds of grain.

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3 years ago

kupik [55]

Answer:

True

Step-by-step explanation:

~Is SAA side-angle-angle

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2 years ago