N = -1/3 is the answer to the problem
Answer:
a) x=-2 then y=10
x=-1 then y=5
x=1 then y=1
x=3 then y= 5
b)x=-0.8;x=2.8
Step-by-step explanation:
a) We have the formula
Instead of x, we will plug in the given value to find y.
If x=-2:
If x=-1:
If x=1:
If x=3:
b) We know when x=0 then y=2
We need to move two boxes up to get to y=4
We can estimate that x = -0.75;x=2.75
We are supposed to round it to the 1. decimal place.
x=-0.8;x=2.8
It is impossible to work out. You don't have enough information.
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
15) 6.1
17) 0.91
19) 86.96
20) I'm not sure,but I think is 82.1%