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2 years ago

7

Select other ways to write 0.125

1 answer:

dangina [55]2 years ago

5 0

Answer:

1/8

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

2 years ago

Plz help for financial algebra

serious [3.7K]

Answer: $277.91

<u>Step-by-step explanation:</u>

The average of the 2 highest salaried quarters is:

$\dfrac{\$13,500+\$12,775}{2}=\dfrac{\$26,275}{2}=\$3,137.50$

Divide that by 26 (weeks) to find out her average weekly salary:

$\dfrac{\$3,137.50}{26}=\$505.29$

Multiply that by 55% (0.55) to calculate her weekly unemployment benefit:

$\$505.29(0.55)=\$277.908$

Round to the nearest penny --> $277.91

4 0

2 years ago

Help me please a girl neeeds help

konstantin123 [22]

Answer: B) reflection over the y-axis

6 0

2 years ago

For each relation, decide whether or not it is a function<br>

Digiron [165]

Answer:

Relation 1,2,and 4 are functions, but relation 3 not is a function.

Step-by-step explanation:

function 1 input, no function with the same input like m in relation 3.

5 0

2 years ago

If I bought an outfit for $24.50 and sales tax is 8%, how much will I have to pay in all? *

aleksley [76]

Answer:

26.46

Step-by-step explanation:

24.50 x .08 = 1.96 (this is our sales taxes)

1.96 + 24.50 = 26.46

8 0

2 years ago