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.
Answer: (5.5, -4)
Step-by-step explanation:
You can use the midpoint formula to find the midpoint of point A and point B.
x₁ = 8
x₂ = 3
y₁ = -7
y₂ = -1
Midpoint = (5.5, -4)
Hope this helps!
Check the picture below.
neverminding for a few seconds the volume of the cylinder, the percentage in the height used by the water will be the same as the percentage of its volume. We know the total amount or 100% of the height is 14, so what is 11 in percentage?
Answer:
(4, 0)
Step-by-step explanation:
x=4 when y=0, and in x-intercepts, we are trying to find the value of x when y=0, which is why (4, 0) is the point of interception.