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4 years ago

Write an equation for the nth term of the arithmetic sequence: 28,25,22,19#42

Mathematics

1 answer:

ratelena [41]4 years ago

7 0

As its going down by -3 , it would be -3n. If you try to find the zeroth term, you will have to add three to 28, which gives you 31. So the answer is -3n+31

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Are the length of a side of a square and the area of the square related proportionally? Why or why not?

Sliva [168]

Answer:

Yes, the length of a side of a square and the perimeter of the square are related proportionally.

Step-by-step explanation:

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3 years ago

PLEASE HELP ANSWER 4 AND 5.

kumpel [21]

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3 years ago

The probability of drawing a green marble from a marble bag is 40%. What are the odds in favor of drawing a green marble?

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4 years ago

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Masja [62]

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3 years ago

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