Answer:
V0 = 48 feet per second is the answer.
Step-by-step explanation:
The given function which represents height of a golf ball in feet after x seconds after a player hits it.
y = -16x² + v0x
here v0 is the initial velocity and we have to calculate initial velocity. The ball returns to the ground 3 seconds after it is hit.
After 3 seconds height of the ball will be 0.
Now from the given function
0 = -16(3)² + v0×3
3v = 16×9
v0 = 16×9/3 = 48 feet per second.
Steps:
1) determine the domain
2) determine the extreme limits of the function
3) determine critical points (where the derivative is zero)
4) determine the intercepts with the axis
5) do a table
6) put the data on a system of coordinates
7) graph: join the points with the best smooth curve
Solution:
1) domain
The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0
=> x > 3 <-------- domain
2) extreme limits of the function
Limit log (x - 3) when x → ∞ = ∞
Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote
3) critical points
dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)
4) determine the intercepts with the axis
x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4
y-intercept: The function never intercepts the y-axis because x cannot not be 0.
5) do a table
x y = log (x - 3)
limit x → 3+ - ∞
3.000000001 log (3.000000001 -3) = -9
3.0001 log (3.0001 - 3) = - 4
3.1 log (3.1 - 3) = - 1
4 log (4 - 3) = 0
13 log (13 - 3) = 1
103 log (103 - 3) = 10
lim x → ∞ ∞
Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.
Answer:
$90,200
Step-by-step explanation:
Airlines usually try to sell their all seats before they fly the airplane. They do wish to sell maximum available seats in order to maximize their revenue. If the airplane takes off with less occupancy then there is opportunity cost for the airline companies. There are 200 seats available to the current flight and they wishes to sell it completely. If they sell all the 200 seats at the price of $451 per seat then their total revenue will be $90,200.
Expression would be
46 - 2v
