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:
1,440 degrees (10 interior angles of 144 degrees)
Step-by-step explanation:
Answer:
The answer is c, a, b, d
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
Given
See attachment
Required
Find x
The figure in the attachment is a quadrilateral and the angles in a quadrilateral add up to 360.
So, we have:
90 + 6x + 5+ 10x - 40 + 4x + 5 = 360
Collect like terms
6x + 10x + 4x = 360 - 90 - 5 + 40 - 5
20x = 300
Divide both sides by 20
x = 15
Hence, the value of x is 15
Answer:
Number 4, the last one
Step-by-step explanation: