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3 years ago

WILL MARK brainiest answer

Mathematics

1 answer:

lyudmila [28]3 years ago

5 0

Answer:

i Think it would be B

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

A family uses 1,303 kWh of electric energy in a month. If the power company charges $0.08 per kilowatt hour, what is the total e

prisoha [69]

The total electric energy bill for the month is $\$104.24$

Solution: 

Given that

Electric energy consumed by family in a month = 1303 kWh

Power Company charges $\$0.08$ per kilowatt hour

Need to calculate total electric energy bill for the month.

Price of 1 kilowatt hour = $\$0.08$

$\text { Price of } 1303 \text { kilowatt hour }=1303 \text { x Price of } 1 \text { kilowatt hour }=1303 \times 0.08=\$ 104.24$

Total electric energy bill for the month = Price of Electric energy consumed by family in a month = Price of 1303 kilowatt hour = $\$104.24$

5 0

3 years ago

the sum of three times one number, x, and five times a second number,y, is 77. if the sum of the two numbers is 19, find the two

HACTEHA [7]

Answer:

x=9, y=10. (9, 10). The two numbers are 9 and 10.

Step-by-step explanation:

3x+5y=77

x+y=19

------------------

3x+5y=77

-3(x+y)=-3(19)

---------------------

3x+5y=77

-3x-3y=-57

-------------------

2y=20

y=20/2

y=10

x+10=19

x=19-10

x=9

5 0

3 years ago

What is the GCF of 24a^3 b and 36ab^2? 2ab 4a^3b 12ab 72a^3b^2

Oksi-84 [34.3K]

12ab will be the right answer.

Since 24a^3 = 12ab(2a^2)

And 36ab^2 = 12ab(3b)

6 0

3 years ago

Read 2 more answers

A person earns 23,000 one year and gets a 5% raise in salary. Calculate the new yearly salary using a percent greater than 100

Kazeer [188]

Answer:

24,150

Step-by-step explanation:

Given that :

Salary earned this year = 23,000

Percentage Raise in salary for the new year = 5%

The new yearly salary can be obtained thus ;

(100% + percentage raise in salary) * salary earned this year

(100% + 5%) * 23,000

105% * 23000

1.05 * 23000

24,150

4 0

3 years ago