Answer:
p=4.1
Step-by-step explanation:
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
Okay for this question, you make a simple equation: (1/3)x=(1/4)y to represent the ratio between the milk and water. Then to find how many cups of water are needed for each cup of milk, you plug in 3 for x (because 1/3 times 3 equals one cup) and solve for your y value. Your final equation for solving should look like: (1/3)(3)=(1/4)y
Check attached file for solution.
<u>Answer</u>
-5/3, -1, 0.7, √2, √5
<u>Explanation</u>
√5 = 2.236
-1 ⇒ this is less than 1.
-5/3 = -1.666667 this is less than 1. -5/3 < -1
0.7 > -1
√2 = 1.414 ⇒ √5 > √2
Arranging them from the least to the greatest;
-5/3, -1, 0.7, √2, √5
