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3 years ago

15

Identify the property shown for 6+0=6

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

Answer:

Identity Property

Step-by-step explanation:

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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

3 years ago

CAN SOMONE PLS HEP WITH THIS!!!! ASAP FOR BRAINLIEST

quester [9]

Answer: How can I help?

Step-by-step explanation:

6 0

3 years ago

Terri owns a computer repair shop. Her revenue at the end of last month was $8,000. What is Terri's Run Rate?

Ilia_Sergeevich [38]

Based on the information given Terri's Run Rate is $96,000.

<h3>Run rate</h3>

Using this formula

Run rate=Revenue for the Period × Number of months in a year

Where:

Revenue for the Period =$8,000

Number of months in a year=12 months

Let plug in the formula

Run rate=$8,000×12 months

Run rate=$96,000

Inconclusion Terri's Run Rate is $96,000.

Learn more about run rate here:brainly.com/question/16134508

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2 years ago

PLISSSS HELP THIS FOR EXAM HAS A PICTURE

gizmo_the_mogwai [7]

Answer:

use mmaatthh wwaayy

Step-by-step explanation:

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3 years ago

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A jar contains only pennies, nickels, dimes, and quarters. There are 21 pennies, 26 dimes, and 15 quarters. The rest of the

pshichka [43]

Answer:

14

Step-by-step explanation:

21+26+15=62 72-62=14 :)

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2 years ago

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