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3 years ago

I need to know this asap thanks

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

7 0

1. 1 7/8

wait a minute for me to answer number 2

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Find the solution of the initial value problem<br><br> dy/dx=(-2x+y)^2-7 ,y(0)=0

Leokris [45]

Substitute $v(x)=-2x+y(x)$ , so that $\dfrac{\mathrm dv}{\mathrm dx}=-2+\dfrac{\mathrm dy}{\mathrm dx}$ . Then the ODE is equivalent to

$\dfrac{\mathrm dv}{\mathrm dx}+2=v^2-7$

which is separable as

$\dfrac{\mathrm dv}{v^2-9}=\mathrm dx$

Split the left side into partial fractions,

$\dfrac1{v^2-9}=\dfrac16\left(\dfrac1{v-3}-\dfrac1{v+3}\right)$

so that integrating both sides is trivial and we get

$\dfrac{\ln|v-3|-\ln|v+3|}6=x+C$

$\ln\left|\dfrac{v-3}{v+3}\right|=6x+C$

$\dfrac{v-3}{v+3}=Ce^{6x}$

$\dfrac{v+3-6}{v+3}=1-\dfrac6{v+3}=Ce^{6x}$

$\dfrac6{v+3}=1-Ce^{6x}$

$v=\dfrac6{1-Ce^{6x}}-3$

$-2x+y=\dfrac6{1-Ce^{6x}}-3$

$y=2x+\dfrac6{1-Ce^{6x}}-3$

Given the initial condition $y(0)=0$ , we find

$0=\dfrac6{1-C}-3\implies C=-1$

so that the ODE has the particular solution,

$\boxed{y=2x+\dfrac6{1+e^{6x}}-3}$

5 0

3 years ago

PLEASE HELP ME<br> Answer the question in the picture.

Sati [7]

Answer:

3^-2=1/9

3^0=1

3^1=3

3^2=9

7 0

3 years ago

Read 2 more answers

1. What is the prime factorization of 402? *<br> Your answer

docker41 [41]

Answer:

Step-by-step explanation:

Prime factorization requires dividing by primes starting with smallest prime number

402/2=201

201/3=67, 67 is prime so we cannot go further so the prime factorization of 402 is

2X3X67

3 0

3 years ago

You decide to record the hair colors of people leaving a lecture at your school. What is the probability that the next person wh

Mekhanik [1.2K]

Answer:

38/195 or 0.1949

Step-by-step explanation:

The data of the distribution of hair colors of people in the lecture in question is provided bellow.

$\begin{array}{cccccc}Blonde&Red&Brown&Black&Gray&Total\\29&30&38&49&49&195\end{array}$

The probability that the next person who leaves the lecture will have brown hair is determined as the number of brown-haired people divided by the number of people in class.

$P(brown) = \frac{38}{195}=0.1949$

The probability is 38/195 or 0.1949.

5 0

3 years ago

Find the value of the expression. (m + n)3 for m = 1 and n = 1

charle [14.2K]

Answer:

Step-by-step explanation:

Given

(m + n)³ ← substitute m = 1, n = 1 into the expression

= (1 + 1)³ = 2³ = 2 × 2 × 2 = 8

7 0

4 years ago

Read 2 more answers