1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
timofeeve [1]
3 years ago
14

(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution s

atisfying the initial condition y(5)=9.
Mathematics
1 answer:
luda_lava [24]3 years ago
7 0
We write the equation in terms of dy/dx,
<span>y'(x)=sqrt (2y(x)+18)</span>
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9)) 

Separating the variables in the equation, we will have:
<span>1/sqrt(y + 9) dy= sqrt(2) dx </span>

Integrating both sides, we will obtain
<span>2sqrt(y+9) = x(sqrt(2)) + c </span>
<span>where c is a constant and can be determined by using the boundary condition given </span>
<span>y(5)=9 : x = 5, y = 9
</span><span>sqrt(9+9) = 5/sqrt(2) + C </span>

<span>C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2</span>

Substituting to the original equation,
sqrt(y+9) = x/sqrt(2) + sqrt(2) / 2

<span>sqrt(y+9) = (2x + 2) / 2sqrt(2) 
</span>
Squaring both sides, we will obtain,
<span>y + 9 = ((2x+2)^2) / 8</span>

y = ((2x+2)^2) / 8 - 9
You might be interested in
Convert the decimal below into a rational number.
LekaFEV [45]
The answer is D.1/10
3 0
2 years ago
ace car rental rents cars for x dollars per day plus y dollars for each mile driven carlos renteda car for a 4 days drove 100 mi
Yuliya22 [10]
T=xd+ym\\x(4)+y(100)=(120)\\x(1)+y(240)=(80)\\\\4x+960y=320\\4x+100y=120\\860y=200\\y=\frac{200}{860}\\y=\frac{10}{43}\\\\x+240(\frac{10}{43})=80\\x+\frac{2400}{43}=\frac{3440}{43}\\x=\frac{1040}{43}

x = 1040/43 = $24.19 per day.

y = 10/43 = $0.23 per mile.
4 0
3 years ago
Giving brainlist to whoever answers
AURORKA [14]

Answer:

false

Step-by-step explanation:

False

5(9)(3.2)

45*3.2=144

Hope this helps :)

6 0
2 years ago
Fill in values for a, b and c so that the answer to this equation is x = 4.<br>a(bx+3)=c​
den301095 [7]

Answer:

A=1, B=3, C=15

Step-by-step explanation:

I think that

1(3x+3)=15

3x+3=15

3x=12

x=4

7 0
3 years ago
Analyzing Patterns This table shows the ratio of parts of red paint to parts of Complete this statement about the ratios. white
Andrew [12]

Answer:

the answer is 3

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • Help. divide and simplify(104i)/(3+i) express a in a + bi form
    13·1 answer
  • Complete the statement with the choice that best
    12·2 answers
  • What are the domain and range of each relation? Drag the answer into the box to match each relation. A mapping diagram. Element
    10·1 answer
  • Salvador wrote 15 letters to friends each month for p months in a row. Write an expression to show how many total letters Salvad
    8·1 answer
  • The U.S. Bureau of Labor Statistics reports that 11.3% of U.S. workers belong to unions. Suppose a sample of 400 U.S. workers is
    14·1 answer
  • Help me with this hehe
    7·2 answers
  • A laptop is bought for $1380 VAT inclusive. If VAT was charged at 15%, what
    14·1 answer
  • Which is the best way to use compatible numbers to estimate
    5·2 answers
  • 6у – 6 = 4у + 16<br> A.y=2.2<br> B. y= -2.2<br> C. у= 11<br> D. у= 5
    6·1 answer
  • Please help on this question :) tyyy
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!