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3 years ago

The graph shown compares the number of feet equal to a given number of yards.

Mathematics

1 answer:

Flauer [41]3 years ago

6 0

I believe the answer is B , One yard equals three feet .

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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

Km=m/2+p. Solve for m

kirill [66]

M=2p over2k+1Km=m/2+p. Solve for m

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3 years ago

How do you know when to find area or circumference

const2013 [10]

Hello there,

To find the area of a circle you use an equation:

A = πr²

For the circumference you use:

C = 2πr

These two equations would help you find the area as well as the circumference of a circle.

Hope I helped,

Amna

5 0

4 years ago

2 5 9 I need help please

Airida [17]

Answer:

where is the question?

7 0

3 years ago

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The ratio of wolves to cougars in a forest is 5:3 find and interpret the value of the ratio

Iteru [2.4K]

Answer:

There are 5 wolves per 3 Cougars

Step-by-step explanation:

4 0

2 years ago