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stiks02 [169]
2 years ago
13

Simplify 5+ W equals eight

Mathematics
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
Read 2 more answers
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 \\ &#10;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
Read 2 more answers
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