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:
Step-by-step explanation:
Quadratic formula: 
when the equation is 
The given equation is 
. Let's first arrange this so its format looks like 
:
Subtract 1 from both sides of the equation
Now, we can easily identify 3 as a, -2 as b and 0 as c. Plug these into the quadratic formula:
I hope this helps!
Answer:
Height is 1 1/24 unit.
Step-by-step explanation:
Given:
volume = 5/24 unit³
base area = 1/5 unit²
Rectangular prism:
volume = length * width * height
base area = length * width
Volume = base area * height
height = volume / base area
h = 5/24 ÷ 1/5
h = 5/24 * 5/1 = 5*5 /24*1 = 25/24 = 1 1/24 unit
(hope this helps can i plz have brainlist :D hehe)
If it took 4 miles per hour you multiply that twice cuss its traveling back then forth so you repeat the same process 30 miles times 2 which is 60 hope this helps.
The first word of the question is cut out of the picture, so we don't exactly know what the assignment is. But we can see that the graph of f(x) will do something weird when x=-3, because the denominator will be zero, and division by zero doesn't even have a definition or meaning. Just for fun, you should go ahead and calculate the numerator when x=-3, and that totally blows your mind, because the numerator is zero too. So you've got. f(-3)= 0/0 , and I can pretty much guarantee that you won't be able to plot that point anywhere on the graph. (I'm pretty sure that f(-3) is actually going to turn out to be -13, but even if I'm correct, you probably haven't learned that little calculus trick yet, so don't worry about it. As far as you're concerned, f(-3) is 0/0, and can't be plotted.)
