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>
The slope is the constant rate of change. In this case, the number is being multiplied by 3 each time
The slope is 3
“x represents number of chocolate truffles sold each day”
Represents amount of chocolate truffles sold per day
Answer:
Option 1 is correct that is square root of 18.
Step-by-step explanation:
We will use pythagoras theroem to find the length of hypotenuse
Here, c is hypotenuse,a is one leg and b is the other leg.
Here, a=b=3
On substituting the values in the formula we get:
Hence, Option 1 is correct that is square root of 18.
The answer is the last one the one that starts with king’s speech
