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
The answer is C i did the math for you
4.2 times 39.37 = 165.354
Answer:
16, -16, 14, and -14
Step-by-step explanation:
The easiest way of solving this question is by setting up an equation. Let's use "n" to represent any random possible integer.
n (n + 2) = 224
Simplifying:
x^2 + 2n - 224 = 0
(n + 16)(n - 14) = 0
n = -16, 16 or n = -14, 14
<u>Check:</u>
16 * 14 = 224
-16 * -14 = 224
Thus, answers of 16, -16, 14, and -14 all work correctly.
(3,4) and (-5,6) are "coordinate planes".
These appear in algebra and math when you're graphing. These coordinate planes consist of "x" and "y" (x,y). The x's (which are 3 and -5 in your situation) should be graphed accordingly using the x-axis and the y's (which are 4 and 6 in your situation) should be graph accordingly using the y-axis.
