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
Answer:
-4+10v
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
The numbers on a six-sided die are as shown:
1, 2, 3, 4, 5, 6
The even numbers are:
2, 4, 6
The numbers greater than 3 are:
3, 4, 5, 6
Both lists together are:
2, 3, 4, 5, 6
Because 5 out of 6 numbers satisfy these conditions, the probability of satisfying these conditions is 5/6.
Answer:
Step-by-step explanation:
Answer:
47/12, or 3 11/12
Step-by-step explanation:
9 1/2 - 5 7/12 > convert to improper fractions
19/2 - 67/12
make same denominator (12)
19/2 * 6 = 114/12
114/12 - 67/12 = 47/12
