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.
The expression (−81)(−9) will give the value of 729.
<u>Step-by-step explanation:</u>
The given expression is (−81)(−9)
.
The both numbers in the expression are negative numbers and they are given inside the brackets.
This means that, the negative numbers must be multiplied to get a final value.
<u>The rules in multiplication are :</u>
- Positive number × Positive number = positive number
- Negative number × Positive number = negative number
- Positive number × Negative number = negative number
- Negative number × Negative number = positive number
From the rules, it can be determined that the result of any two negative numbers will be a positive number.
So, eliminate option A) and B) because they have negative sign.
The expression (−81)(−9) = -81 × -9
⇒ 729.
Therefore, the option C) and D) are not in match with 729. None of the options are not the value of the given expression (−81)(−9).
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