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2 years ago

8

How do I do angles of triangles

1 answer:

BigorU [14]2 years ago

7 0

Answer:

What kind of angles?

Step-by-step explanation:

What is your question?

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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

The log of x cubed times y squared simplified

tresset_1 [31]

Answer:

$log(x^{3}y^{2}) = 3 log x+2 log y$

Step-by-step explanation:

Step 1:-

using logarithmic formula $log(ab)=log a+log b$

so given $log(x^{3} y^{2} ) = log (x^{3} )+log(y^{2} )$

now simplify

= $3 log x+2 log y$

<u>Answer:</u>-

$log(x^{3}y^{2})= [tex]3 log x+2 log y$

4 0

3 years ago

a sandwich shop has 60 stores and 70 percent of the stores are I California. How many stores are in California and Nevada

Aliun [14]

Answer:

The number of stores in California 42

The number of stores in Nevada 18

Step-by-step explanation:

Given as :

The total sandwich shop in California and Nevada = 60

The percentage of shop in California = 70%

So, The percentage of shop in Nevada = 100% - 70% = 30%

Let The number of stores in California = c

And The number of stores in Nevada = n

Now, According to question

The number of stores in California = 70% of the total number of shops

I.e c = $\frac{70}{100}$ × total number of shops

Or, c = $\frac{70}{100}$ × 60

∴ c = $\frac{70\times 60}{100}$

or, c = $\frac{4200}{100}$

or, c = 42

So, The number of stores in California = c =42

Again

The number of stores in Nevada = 30% of the total number of shops

I.e n = $\frac{30}{100}$ × total number of shops

Or, n = $\frac{30}{100}$ × 60

∴ n = $\frac{30\times 60}{100}$

or, n = $\frac{1800}{100}$

or, n = 18

So, The number of stores in Nevada = n = 18

Hence The number of stores in California 42

And The number of stores in Nevada 18 Answer

8 0

3 years ago

Write each power as a product of the same factor. Then find the value.

Leona [35]

Answer:

its answer is option b 15.625

4 0

2 years ago

Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosin

kodGreya [7K]

Answer:

B

Step-by-step explanation:

Just read and you will see why i say that

3 0

1 year ago