Answer:
The particular solution satisfying the initial condition, , of the differential equation is .
Step-by-step explanation:
A separable differential equation is any differential equation that we can write in the following form.
We may find the solutions to certain separable differential equations by separating variables, integrating with respect to x, and ultimately solving the resulting algebraic equation for y.
To find the solution of the differential equation you must:
Separate the differential equation and integrate both sides.
Solving
Therefore,
Now, we use the initial condition to find the value of the constant E.
Thus,
and we solve for x,
Answer:
A
Step-by-step explanation:
He graphed (7, 17) incorrectly making his not a function. But the correct numbers make a function.
PART A:
The x-intercept at 0 shows the location where the ball was kicked. The x-intercept at x = 16 shows the location where the ball hit the ground.
The maximum value represents the highest point of the ball.
The interval where the function is increasing is 0<x<8. Between this interval, the height of the ball measured from the ground is increasing.
The interval where the function is decreasing is 0<x<16. Between this interval, the height of the ball is decreasing.
PART B:
Reading from the graph
When x = 8, y = 10 ⇒ let this be x₁ = 8 and y₁ = 10
When x = 13, y = 6 ⇒ let this be x₂ = 13 and y₂ = 6
The rate of change = (y₂-y₁) / (x₂-x₁)
The rate of change = (6 - 10) / (13 - 8)
The rate of change = -4 / 5 = -(4/5)