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My name is Ann [436]

2 years ago

6

Ratio 90kg to 2 : 3 : 7

1 answer:

adoni [48]2 years ago

3 0

Answer:

Please follow me back

Step-by-step explanation:

The Answer is 158

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Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

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

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

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

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

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

Pre college need help

AVprozaik [17]

Answer:

sorry I can't answer that because I need points very3× sorry

3 0

3 years ago

Steve can run 3.5 miles in 30 minutes. If Steve increases his rate by 1/2 mile per hour, how far will he run in 2 hours?

Sati [7]

Answer:

15 miles

Step-by-step explanation:

Steve runs 3.5 miles in 30 minutes (0.5 hours). So his speed is:

r = 3.5 mi / 0.5 h

r = 7 mi/h

If his rate increases to 7.5 mi/h, the distance he runs in 2 hours is:

d = 7.5 mi/h × 2 h

d = 15 mi

7 0

4 years ago

Read 2 more answers

What value makes the equation 11-3x=-7 true?

o-na [289]

The answer is x=6. 11-3x6=-7

3 0

3 years ago

Read 2 more answers

What are the roots of the quadratic equation below 3x2+15x-5=0

fomenos

Answer:

<h2>A</h2><h2 />

Step-by-step explanation:

$3x^2+15x-5=0\\a = 3\\b = 15\\c = -5\\ x = -b\±\frac{\sqrt{b^{2} -4ac} }{2a} \\x = -(15)\±\frac{\sqrt{15^{2} -4(3)(-5)} }{2(3)} \\x = -15 \±\frac{\sqrt{225+60} }{6} \\x = -15\±\frac{\sqrt{285} }{6} = A$

8 0

3 years ago