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3 years ago

Any one that knows this please help thanks!

Mathematics

1 answer:

Blababa [14]3 years ago

7 0

The answer is 6/7 or, in decimal form, 0.857143

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Solve the given initial-value problem. the de is of the form dy dx = f(ax + by + c), which is given in (5) of section 2.5. dy dx

shutvik [7]

$\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)$

Let $v=x+y$ , so that $\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}$ :

$\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1$

Now the ODE is separable, and we have

$\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx$

Integrating both sides gives

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx$

For the integral on the left, rewrite the integrand as

$\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v$

Then

$\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C$

and so

$\csc v-\cot v=x+C$

$\csc(x+y)-\cot(x+y)=x+C$

Given that $y(0)=\dfrac\pi2$ , we find

$\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1$

so that the particular solution to this IVP is

$\csc(x+y)-\cot(x+y)=x+1$

5 0

2 years ago

#10: find angle x and y!<br> Im struggling so much with this question please help a gurl out!

hjlf

Answers:

x = 100

y = 25

==============================================================

Explanation:

Angle y and the 25 degree angle are corresponding angle. Because the lines are parallel, this means that y = 25

Check out the attached image. Using a red pen, I extended one of the lines to form a triangle. From the alternate interior angle theorem, we know that one of the angles of the triangle is 75 degrees (alternate interior angles are congruent). Again this stems from the fact that the lines are parallel.

I've also introduced the variable z to help find x. The angles x and z add up to 180 degrees since they form a straight line. So we need to find z before we can find x.

The triangle's angles 25, 75, z add up to 180. Let's solve for z

25+75+z = 180

100+z = 180

z = 180-100

z = 80

Use this to find x

x+z = 180

x+80 = 180

x = 180-80

x = 100