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:
36% of 240
=36/100*240
=6640/100
=86.4
Step-by-step explanation:
Answer:
x=20
Step-by-step explanation:
In scientific notation, to obtain the original whole number. Move the decimal to the left if the exponent is negative and to the right if the exponent is positive.
So 1 inch = .00001578 miles
1225 / .00001578 = 77629911.28
To obtain the answer in scientific notation, move the decimal to the left until you have a single digit whole number and the rest of teh digits are to the right of the decimal. In this case 7 places. Now show it multiplied by 10 to an exponent equal to the number of places you moved the decimal. In this case the 7th exponent.
7.763 x 10^7
