Answer:
The maximum volume of the open box is 24.26 cm³
Step-by-step explanation:
The volume of the box is given as 
, where 
and 
.
Expand the function to obtain:
Differentiate wrt x to obtain:
To find the point where the maximum value occurs, we solve
Discard x=3.54 because it is not within the given domain.
Apply the second derivative test to confirm the maximum critical point.
, 
This means the maximum volume occurs at 
.
Substitute into to get the maximum volume.
The maximum volume of the open box is 24.26 cm³
See attachment for graph.
Y= f(x)= ax+b
when x= -1, y= -1
-1= -a+b | * ( -1)
when x= -3, y=2
2= -3a+b
-3a+b= 2
a - b= 1
--------------
2a=3
a=3/2 is the slope
Answer:
23. 0.4583 seconds
24. 0.0107 seconds
Step-by-step explanation:
The problem statement tells you how to work it. You need to convert speed from miles per hour to feet (or inches) per second.
90 mi/h = (90·5280 ft)/(3600 s) = 132 ft/s = (132·12 in)/s = 1584 in/s
__
23. The time it takes for the ball to travel 60.5 ft is ...
time = distance/speed
time = (60.5 ft)/(132 ft/s) = 0.4583 s
It takes 458.3 milliseconds to reach home plate.
__
24. time = distance/speed
time = (17 in)/(1584 in/s) = 0.0107 s
The ball is in the strike zone for 10.7 milliseconds.
715 miles / 11 hours = 65 mph
845 miles / 65 mph = 13 hours
It would take 13 hours to drive 845 miles.
