Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x = w/3 - 2/3
The general solution of <span>y' + 2xy = (x^3) is y(x) = c1e^(-x^2)
The general solution of </span><span>ydx = (y(e^y) - 2x)dy is x = c1/(y(x))^2 + (e^y(x) ((y(x))^2 - 2y(x) + 2)/(y(x))^2
</span>
The general solution of<span> (dP)/(dt) + 2tP = P + 4t - 2 is P(t) = c1e^(t - t^2) + 2</span>
Vertical asymptotes happen at x=a if the function is undefined at x=a.
This is a rational functions, and rational functions are not defined when the denominator is zero, since you can't divide by zero.
In this case, the denominator is zero if

And thus the function has a vertical asymptote at x= -3/2
Answer:
The expression that can be used to calculate the rate per second at which the machine launches the balls is fraction 20 over 4.
Step-by-step explanation:
The x-axis label is Time in seconds, and the x-axis values are from 0 to 20 in increments of 4 for each grid line.
And the y-axis label is Number of Balls and the y-axis values from 0 to 100 in increments of 20 for each grid line.
If the ordered pairs (4,20) and (8,40) are on the graph, then the slope of the line will be represented by
Therefore, the expression that can be used to calculate the rate per second at which the machine launches the balls is fraction 20 over 4. (Answer)
Plug in the values
3(5) - 5(1)
15 - 5 = 10
Solution: 10