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2 years ago

13

Simplify 5+ W equals eight

1 answer:

shepuryov [24]2 years ago

3 0

Answer:

3

Step-by-step explanation:

5+3=8

8-5=w

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2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=Factor%3A%20x%5E2-9" id="TexFormula1" title="Factor: x^2-9" alt="Factor: x^2-9" align="absmidd

Bezzdna [24]

Answer:

x²-9=x²-3²=(x+3)(x-3)

Step-by-step explanation:

use formula

a²-b²=(a+b)(a-b)

7 0

2 years ago

Help with 2 and 5 plzzzzz

Katyanochek1 [597]

Multiply all the numbers on 2

4 0

2 years ago

Bab needs help please!

schepotkina [342]

Answer: it's 3.14 in^3

6 0

2 years ago

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Graph the six terms of a finite series where a1 = −3 and r = 1.5.

s344n2d4d5 [400]

We are given the first term and the common ratio, this means they belong to a geometric series.

For the given series:

$a_{1}=-3 \\ 
r=1.5$

Each term of the geometric series is obtained by multiplying the previous term by common ratio.

So the next terms will be:

-4.5, -6.75, -10.125, -15.1875, -22.78125

The general formula for the G.P would be:

$a_{n}=-3(1.5)^{n-1}$

On plotting the series, the result will be like this:

6 0

3 years ago

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