Help me solve this problem

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

luda_lava [24]

We write the equation in terms of dy/dx,
y'(x)=sqrt (2y(x)+18)
dy/dx = sqrt(2y + 18)
dy/dx = sqrt(2) ( sqrt(y + 9))

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

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

C = sqrt(18) - 5/sqrt(2) = sqrt(2) / 2

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

sqrt(y+9) = (2x + 2) / 2sqrt(2)

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

y = ((2x+2)^2) / 8 - 9

7 0

4 years ago

Find the value of 7xº - (6x)".

docker41 [41]

7x - 1 + 6x - 1 = 180
13x - 2 = 180
13x = 182
x = 14

6 0

2 years ago

Read 2 more answers

Grade 7 math extra credit

Nonamiya [84]

2400 in prize money...

the first winner will receive 1/3 of the money..
1/3 * 2400 = 2400/3 = 800
leaving 2400 - 800 = 1600

the next 10 winners will receive 1/10 of the remaining amount
1/10 * 1600 = 1600/10 = 160 <== each will receive $ 160

3 0

3 years ago

(1.1.8 in the book) Let P be the proposition ’I bought a lottery ticket this weekend’ and Q be the proposition ’I won the millio

Karolina [17]

Answer:

~ is for negation

^ is for "and"

v is for "or"

=> for "if then"

<=> for "if and only if"

Step-by-step explanation:

(a) ~P (negation of P)

I didn't buy a lottery ticket this weekend.

(b) P v Q (P is in disjunction Q)

I have either bought a lottery ticket this weekend or won the million dollar jackpot.

(c) P => Q (Q is a consequence of P)

I won the million dollar jackpot because I bought a lottery ticket this weekend.

(d) P ^ Q (P is in conjunction with Q)

I bought a lottery ticket this weekend, and I won the million dollar jackpot.

(e) P <=> Q (P and Q are dependent on each other)

If only I had bought a lottery ticket this weekend, I would have won the million dollar jackpot.

(f) ~P => ~Q (negation of Q is a consequence of negation of P)

I didn't win the million dollar jackpot because I didn't buy a lottery ticket this weekend.

(g) ~P ^ ~Q (negation of P is in conjunction with negation of Q)

I neither bought a lottery ticket this weekend nor won the million dollar jackpot.

(h) ~P v (P ^ Q)

This is logically equivalent to (~P v P) ^ (~P v Q) (negation of P is in disjunction with P, and also with disjunction with Q), and can be best expressed as:

It didn't matter that I bought a jackpot ticket or not, I won the million dollar jackpot.

8 0

3 years ago

Greg needs $51 to go on a field trip. He has saved $12.75. He earns $6.50 per hour cleaning his neighbor's garden, and he earns

Schach [20]

B.)Yes, because the total will be $52

5 0

4 years ago