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:
D. 1x8
Step-by-step explanation:
7/8 rounded is 1. And 8 and 1/10 rounder is 8, so therefore your answer is 1x8.
hope this helps! :)
The writing isnt so clear to me
Answer:
D. 9990 possible combinations
Step-by-step explanation:
The first digit has 10 choices (can be all of them), the second digit also has 10 choices. The third and fourth digits also have 10 choices.
Multiply them together you get 10*10*10*10 = 10000 possible combinations.
But since all 4 characters cannot be the same, we subtract 10 from 10000 (there are 10 combinations which the 4 characters are the same: 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, and 0000) and we get 9990.
<h2>pi divided by four</h2>
Step-by-step explanation:
Let the angle in degrees be 
Let the angle in radians be 
If is the angle in degrees and is the angle in radians,
It is given that the 
So,
