This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
Answer:
7.5 = 8
Step-by-step explanation:
Step 1:
30/100=0.3
Step 2:
0.3 x 25 = 7.5
Round: 8
Answer:
If you know the radius of a circular track, you can use physics to calculate how fast an object needs to move in order to stay in contact with the track without falling when it reaches the top of the loop.
Answer:
it was helpful to you ✌︎✌︎✌︎✌︎✌︎✌︎✌︎➪♧︎︎︎
The result is the perpendicular bisector of AB, perpendicular to the segment AB, and through its midpoint.
