3 years ago

Please Help!!! I know the answer but need work.

1 answer:

3 0

How do you know the answer if you don't have the work?

2/3(x+1/8) =1/6(x)
2/3×x+2/3×1/8=1/6(x)
2/3(x)+1/12=1/6(x)
2/3(x)-2/3(x)+1/12=1/6(x)-2/3(x)
1/12=1/6(x)-2/3(x)
1/12=1/6(x)-4/6(x)
1/12=-3/6(x)
1/12÷-3/6=-3/6(x)÷-3/6
-1/6=x

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What is the horizontal asymptote for y(t) for the differential equation dy dt equals the product of 2 times y and the quantity 1

marta [7]

First, we need to solve the differential equation.
$\frac{d}{dt}\left(y\right)=2y\left(1-\frac{y}{8}\right)$
This a separable ODE. We can rewrite it like this:
$-\frac{4}{y^2-8y}{dy}=dt$
Now we integrate both sides.
$\int \:-\frac{4}{y^2-8y}dy=\int \:dt$
We get:
$\frac{1}{2}\ln \left|\frac{y-4}{4}+1\right|-\frac{1}{2}\ln \left|\frac{y-4}{4}-1\right|=t+c_1$
When we solve for y we get our solution:
$y=\frac{8e^{c_1+2t}}{e^{c_1+2t}-1}$
To find out if we have any horizontal asymptotes we must find the limits as x goes to infinity and minus infinity.
It is easy to see that when x goes to minus infinity our function goes to zero.
When x goes to plus infinity we have the following:
$$$\lim_{x\to\infty} f(x)$$=y=\frac{8e^{c_1+\infty}}{e^{c_1+\infty}-1} = 8$
When you are calculating limits like this you always look at the fastest growing function in denominator and numerator and then act like they are constants.
So our asymptote is at y=8.

3 0

3 years ago

What is the slope of the line below? If necessary, enter your answer as a

Westkost [7]

9514 1404 393

Answer:

6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

m = (y2 -y1)/(x2 -x1)

m = (-1 -11)/(-5 -5) = -12/-10

m = 6/5