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3 years ago

A circle has a radius of 16 units. What is the area in square units of the circle in terms of pi

Mathematics

1 answer:

m_a_m_a [10]3 years ago

6 0

Step-by-step explanation:

area= (pi)r^2

a = (pi)×16^2

a= 256pi square units

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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

Your balance sheet shows $6,400 worth of inventory in hair products. Items are recorded in inventory at cost, and the average co

andreyandreev [35.5K]

Answer:

Units of hair products = 2634 units

Step-by-step explanation:

Given that:

Worth of products in the inventory = $6400

Average cost per unit = $2.43

Number of units = $\frac{Total\ worth}{Per\ unit\ cost}$

Number of units = $\frac{6400}{2.43}$

Number of units = 2633.73

Rounding off to nearest whole number = 2634 units

Hence,

Units of hair products = 2634 units

4 0

3 years ago

Witch Decimal is equal to six-tenths?<br><br> 0.6 0.15 0.2 0.3 0.4

miss Akunina [59]

0.6 matches with six-tenths because if you divide 6 and 10 together you will get 0.6

Hope this helped! :)

~Shadow

6 0

3 years ago

List all the factors of 16

Olenka [21]

Answer:

There are 5 factors of 16, which are 1, 2, 4, 8, and 16.

5 0

3 years ago

Read 2 more answers

!!50 POINTS!! Please answer all, don't just answer to get the points or you'll be reported. And please, do not copy from the int

diamong [38]

G. The shape would be similar since dilation at the origin is just a translation and a translation doesn't affect the shape's size or shape.

h. They will still be similar because adding length to each side will just make the shape larger, and if the shape hasn't changed (which it hasn't) it will remain similar.

I. This is simple, just write an equation of the changes you could do the shape and it would be similar. You would have to explain how many you should move and from which sides (should be all sides). It is better for you to do this because there are millions of possible equations, and if you use the same one then it might be striked.

8 0

3 years ago