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3 years ago

Help ASAP I’ll mark branliest

Mathematics

1 answer:

sveticcg [70]3 years ago

8 0

Answer:

C - 129

Step-by-step explanation:

180-51=129

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Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

4 years ago

Solve for x. <br><br> 3x = 2/5

Elena-2011 [213]

X = 0.4/3
x = 13
if answer is wanted in decimal form.

6 0

4 years ago

Translate each sentence into an equation.

mihalych1998 [28]

Answer:

1. 1/2x = 4

2. x - 6 = 9

3. 2x = 5x + 12

4. 2x + 5 = x - 5

5. 2x + 11 = x - 5

Hope this helps you!

3 0

3 years ago

What is the volume of this prism?

Fiesta28 [93]

Answer:

36 cubic inches

Step-by-step explanation:

v=(3)(6)(2)=36

Hope this helps

3 0

3 years ago

Please help need answer fast‼️

Bess [88]

Answer:

The second one is D.

Step-by-step explanation:

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3 years ago