Find a solution to the following initial-value problem: dy dx = y(y − 2)e x , y (0) = 1.

Answers

Answer 1
Answer:

This equation is separable, as

(\mathrm dy)/(\mathrm dx)=y(y-2)e^x\implies(\mathrm dy)/(y(y-2))=e^x\,\mathrm dx

Integrate both sides; on the left, expand the fraction as

\frac1{y(y-2)}=\frac12\left(\frac1{y-2}-\frac1y\right)

Then

\displaystyle\int(\mathrm dy)/(y(y-2))=\int e^x\,\mathrm dx\implies\frac12(\ln|y-2|-\ln|y|)=e^x+C

\implies\frac12\ln\left|\frac{y-2}y\right|=e^x+C

Since y(0)=1, we get

\frac12\ln\left|\frac{1-2}1\right|=e^0+C\implies C=-1

so that the particular solution is

\frac12\ln\left|\frac{y-2}y\right|=e^x-1\implies\boxed{y=\frac2{1-e^(2e^x-2)}}


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Find the equation of a line through (1,1) whichisperpendicular to a line through (1,3) and (2,5).
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Gi gi's bakery has total assets of $425 million. its total liabilities are $110 million. its equity is $315 million. calculate the debt ratio.

Answers

the answer:
debt ratio formula can be found with

debt ratio = total liabilities / total assets,  
debt ratio= $110 million /$425million = 0.25 = 1/4

A survey of 800 students yielded the following information: 519 were seniors, 430 were commuters, and 300 of the seniors were commuters. How many of the 800 surveyed students were seniors or were commuters?

Answers

Answer:

The number is  (S \ u \  C  ) = 649

Step-by-step explanation:

From the question we are told that  

      The sample size is  n =  800

       The number of seniors is  S  =  519

         The number of  commuters is  C =  430

         The number of of seniors that are commuters is  (S\  n \ C )=  300

Generally the number of 800 surveyed students who were seniors or were commuters is  mathematically evaluated as

     (S \ u \  C  ) =  S + C  -  ( S \  n  \  C )

=>   (S \ u \  C  ) =  519  + 430   - 300

=>   (S \ u \  C  ) = 649

Determine the slope of the line that has the following coordinates: (5, 9)(11, - 3)

Answers

Answer:

x_1 = 5, x_2 =11, y_1 =9, y_2 = -3

The slope can be founded with this formula:

m =(y_2 -y_1)/(x_2 -x_1)

And replacing we got:

m =(-3 -9)/(11-5)= -2

And the best answer for this case would be :

m=-2

Step-by-step explanation:

For this case we have the following two points given:

x_1 = 5, x_2 =11, y_1 =9, y_2 = -3

The slope can be founded with this formula:

m =(y_2 -y_1)/(x_2 -x_1)

And replacing we got:

m =(-3 -9)/(11-5)= -2

And the best answer for this case would be :

m=-2

An automobile purchased for 22,000 is worth 2500 after 5 yrs. Assuming that the cars value deprecited steadily from year to year, what was it worth at the end of third year

Answers

Original price = 22000
New price = 2500
Amount depreciated in 5 years = 22000 - 2500
                                                  =19500
Amount depreciated in 1 year = 19500/5
                                                = 3900
Worth after 3 years = 22000 - 3(3900)
                               = 10300

1. The Hamiltons are installing a new pool in their backyard. The scale drawing below represents the new pool, where 1 centimeter represents 5 feet. 4 cm 6 cm If the area of the Hamiltons' backyard is 900 square feet, how many square feet of their backyard will NOT be taken up by the pool? Round your answer to the nearest whole number.​

Answers

The number of square feet of their backyard will NOT be taken up by the pool should be 100 square feet.

Calculation of the number of square feet;

Since 1  centimeter represents 5 feet. 4 cm 6 cm And, the area of the Hamiltons' backyard is 900 square feet.

So here it can be like

4cm (5) = 20ft

6cm (5) = 40ft

Now

20ft : 40ft pool

20(40) = 800 square ft

So,

= 900sq ft - 800sq ft

= 100 square feet

Learn more about area here: brainly.com/question/17758676

Answer:

175

Step-by-step explanation:

Because why would i lie?

How does 3.71 round up to 3.7​

Answers

Answer:

Step-by-step explanation:

cuz 7 is greater then 5