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:
5 - 1/12x.
Step-by-step explanation:
1/4x + 3 - 1/3x + (2)
= 1/4 x - 1/3 x + 3 + 2
= 3/12 x - 4/12 x + 5
= -1/12 x + 5.
I got 21% at selecting a point outside.
Explanation: Since the perimeter is 16sqrt (6), each side must be 4sqrt (6)
This also means that the diameter is 4sqrt (6).
To find the area of a circle, we need to find the radius (2sqrt (6)).
Area of circle is pi × (2sqrt (6))^2 = 24pi or approximately 75.4 units^2
Area of square is 4sqrt (6)^2 = 96
Thus, let's take the area of the circle and subtract that from the area of our square to yield approx. 20.6 units^2
and now divide through by 96 to yield 21%
Answer:
$69
Step-by-step explanation:
80 x 75% (0.75) = 60
60 x 15% (0.15) = 9
60 + 9 = $69
Answer:
As few as just over 345 minutes (23×15) or as many as just under 375 minutes (25×15).
Imagine a simpler problem: the bell has rung just two times since Ms. Johnson went into her office. How long has Ms. Johnson been in her office? It could be almost as short as just 15 minutes (1×15), if Ms. Johnson went into her office just before the bell rang the first time, and the bell has just rung again for the second time.
Or it could be almost as long as 45 minutes (3×15), if Ms. Johnson went into her office just after the bells rang, and then 15 minutes later the bells rang for the first time, and then 15 minutes after that the bells rang for the second time, and now it’s been 15 minutes after that.
So if the bells have run two times since Ms. Johnson went into her office, she could have been there between 15 minutes and 45 minutes. The same logic applies to the case where the bells have rung 24 times—it could have been any duration between 345 and 375 minutes since the moment we started paying attention to the bells!
Step-by-step explanation:
