To find the maximum or minimum value of a function, we can find the derivative of the function, set it equal to 0, and solve for the critical points.
H'(t) = -32t + 64
Now find the critical numbers:
-32t + 64 = 0
-32t = -64
t = 2 seconds
Since H(t) has a negative leading coefficient, we know that it opens downward. This means that the critical point is a maximum value rather than a minimum. If we weren't sure, we could check by plugging in a value for t slightly less and slighter greater than t=2 into H'(t):
H'(1) = 32
H'(3) = -32
As you can see, the rate of change of the object's height goes from increasing to decreasing, meaning the critical point at t=2 is a maximum.
To find the height, plug t=2 into H(t):
H(2) = -16(2)^2 +64(2) + 30 = 94
The answer is 94 ft at 2 sec.
140 tickets sold at the door
Step by Step Explanation:
x = tickets sold in advance
y = tickets sold at the door
We use the formula ax+by=c and a+b=c
x + y = 514
17x + 20y = 9158
y = 514 - x
17x + 20(514 - x)
17x + 10,280 - 20x = 9,158
-3x + 10,280 = 9,158
-3x = -11222
x = 374
This is for tickets sold in advance so we need to find y
374 + y = 514
y = 140
140 tickets were sold at the door
Answer:
8
Step-by-step explanation:
I believe that the answer is 8
Answer:
916.1 cm^3
Step-by-step explanation:
1) find the radius of the cylinder:
radius = dimater / 2 = 7,3 / 2 = 3.65 cm
2) find the base area of the cylinder:
base area = radius^2 x 3.14 = 3.65^2 x 3.14 = 41.83265 cm^2
3) find the height of the cylinder:
height = 7.3 x 3 = 21.9 cm
4) find the volume
V = base area x height = 41.83265 x 21.9 = 916.135035 cm^3
5) round to nearest tenth:
916. 1 cm^3
Answer: 85 degrees
Step-by-step explanation: 20x+5+24x-1=180
44x+4=180
-4 -4
44x=176
division property of equality x=4
20(4)+5=
80+5= 85 degrees
