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adoni [48]
3 years ago
14

Alina's bus runs every 20 minutes if she arrives at her bus stop at a random time what is the probability that she will have to

wait at least five minutes for the bus if it is running on schedule
Mathematics
1 answer:
Nesterboy [21]3 years ago
4 0
If Alina's timing is ppperfect her probabilies are low but she has to wait at least 5 min because the bus has a cordinated schedule and it was its timing
:) Hope I helped

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X + 3y = -3 solve for Y (ex. y= 3 + 5x
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Answer:

y = -1/3x - 1

Step-by-step explanation:

Let's solve for y.

Step 1: Add -x to both sides.

x+3y+−x=−3+−x

3y=−x−3

Step 2: Divide both sides by 3.

y=-1/3x-1

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\frac{-1}{3} x-1

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Hiroto solved the equation 6 – 4|2x – 8| = –10 for one solution. His work is shown below.
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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
3 years ago
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