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:
12
Step-by-step explanation:
3^n=27
Solve Exponent.
3^n=27
log(3n)=log(27)(Take log of both sides)
n*(log(3))=log(27)
n=log(27) / log(3)
n=3
Answer:
-3.9% I.e there is decrease in the population
Step-by-step explanation:
Population @ 1990 = 1585577
Population @ 2010 = 1526006
% change =
(1526006-1585577)/1526006 × 100%
= -59571/1526006 ×100%
= -3.9%
Answer:
The dimensions are 5 and 10 inches
Step-by-step explanation:
The area is 50 square inches and the length is twice the width. 10 is the length, which is two times 5. 10 times 5 is 50.
The length is 10 and the width is 5.
