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alina1380 [7]
3 years ago
10

Find the general solution of (x+3)y’=2y

Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

y=C(x+3)^2

Step-by-step explanation:

We are given:

\displaystyle (x+3)y^\prime=2y

Separation of Variables:

\displaystyle \frac{1}{y}\frac{dy}{dx}=\frac{2}{x+3}

So:

\displaystyle \frac{dy}{y}=\frac{2}{x+3} \, dx

Integrate:

\displaystyle \int\frac{dy}{y}=\int\frac{2}{x+3}\, dx

Integrate:

\displaystyle \ln|y|=2\ln|x+3|+C

Raise both sides to e:

|y|=e^{2\ln|x+3|+C}

Simplify:

|y|=(e^{\ln|x+3|})^2\cdot e^C

So:

|y|=C|x+3|^2

Simplify:

y=\pm C(x+3)^2=C(x+3)^2

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A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real esta
Pachacha [2.7K]

Answer:

The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Step-by-step explanation:

Let the random variable <em>X</em> represent the amount of money that the family has invested in different real estate properties.

The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = $225,000 and <em>σ</em> = $50,000.

It is provided that the family has invested in <em>n</em> = 10 different real estate properties.

Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:

\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39

Now the lowest 80% of the amount invested can be represented as follows:

P(\bar X

The value of <em>z</em> is 0.84.

*Use a <em>z</em>-table.

Compute the value of the mean amount invested as follows:

\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}

   =225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57

Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

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So, product of 16 and w can be written as 16*w or simply 16w.

Hence, B is the correct choice.

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