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.
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Answer:
We know that:
Energy released by fusion of hydrogen in 1 liter of solution A = 7.6x10^10 J
Energy used daily in a certain family home = 3x10^4 J
(you did not write the units, so i suppose that are the same in both cases)
Then, if x is the number of liters of solution A used, the energy produced will be:
E(x) = x*7.6x10^10 J
And we want this equal to 3x10^4
then:
E(x) = x*7.6x10^10 J = 3x10^4 j
now we solve this for x.
x = (3x10^4 j)/(7.6x10^10 j) = 3.9x10^-7
Then you need to use 3.9x10^-7 L of solution a.
I'm sorry but it's bugging me that you aid 'one cases', you can't have the plural of something that is strictly singular.
Now: for your answer.
72*35=2520
94*23=2162
2520+2162=4682
The total wight is 4682 pounds.
Hope this helps
