Factors of 84: 1, 2<span>, </span>3<span>, 4, 6, </span>7<span>, 12, </span>14<span>, </span>21<span>, </span>28<span>, </span>42<span>, 84. Prime factorization: 84 = </span>2<span> x </span>2<span> x </span>3<span>x </span>7<span> which can also be written (</span>2^2<span>) x </span>3<span> x </span>7<span>.</span>
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:
There are 5000 mililitres in 5 litres
Therefore option A.
Hope u got the answer............
X = Juan's age
y = Eliza's age
Some key words/phrases we can use to help us make the equation are:
-is (whatever comes after this word usually equals the end result, or what it equals)
-two years younger
-than
-half her brother's age
.
just break it down :)
x/2 (half her brother's age) - 2 (two years younger) = y (Eliza is...)
| basically,
v
x/2 - 2 = y
So if Juan is 6, then we need to plug in 6 for x.
6/2 - 2 = y
3 - 2 = y
1 = y
ANSWER: Eliza is one year old.
The answer is B. Hard to explain but it is B.
