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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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find 1 pencil
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3 years ago
Suppose that g(x)=f(x)+3. Which statement best compares the graph of g(x) with the graph of f(x)?
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Answer:

He said points

Step-by-step explanation:

I can get points for nothing

8 0
2 years ago
Number 1 and 2 please (25 points)
Elenna [48]

Answers:

1) (3x+2)+(4-5x)=-2x+6

(3+2i)+(4-5i)=7-3i

2) (1-3x)(2+x)=-3x^{2}-5x+2

(1-3i)+(2+i)=5-5i

Step-by-step explanation:

In mathematics there are rules related to complex numbers, specifically in the case of addition and multiplication:

<u>Addition: </u>

If we have two complex numbers written in their binomial form, the sum of both will be a complex number whose real part is the sum of the real parts and whose imaginary part is the sum of the imaginary parts (similarly as the sum of two binomials).

For example,  the addition of these two binomials is:

(3x+2)+(4-5x)=3x-5x+2+4=-2x+6

Similarly, the addition of two complex numbers is:

(3+2i)+(4-5i)=3+4+2i-5i=7-3i Here the complex part is the number with the i

<u>Multiplication: </u>

If we have two complex numbers written in their binomial form, the multiplication of both will be the same as the multiplication (product) of two binomials, taking into account that i^{2}=-1.

For example,  the multiplication of these two binomials is:

(1-3x)(2+x)=2+x-6x-3x^{2}=-3x^{2}-5x+2

Similarly, the multiplication of two complex numbers is:

(1-3i)+(2+i)=2+i-6i-3i^{2}=2-5i-3(-1)=5-5i

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3 years ago
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Answer:

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Step-by-step explanation:

12-7=5 then 5×2 =10

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3 years ago
Read 2 more answers
Describe a real world problem that you could solve using the volume of spheres
alexgriva [62]

A toy company produces rubber balls that have a radius of 1.7 cm.

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20.58 cm3

If the price of the rubber needed to produce a ball is

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Hope this helps

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2 years ago
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