The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
Answer:

Step-by-step explanation:
In order to solve this problem we can make use of the following formula:

where θ is the total angle the basket has turned, ω is the angular velocity and t is the time.
Generally theta is written in radians and omega is written in radians per second. Now, since the revolutions are directly related to the radians and they want us to write our answer in revolutions, we can directly use the provided speeds in the formula, so we can rewrite it as:

where n represents the number of revolutions and f is the frequency at which the basket is turning.
The movement of the cylindrial basket can be split in two stages, when it accelerates and when it decelerates. So let's analye the first stage:

and now let's analyze the second stage, where it decelerates, so we get:

So now that we know how many revolutions the cylindrical basket will take as it accelerates and as it decelerates we can add them to get:
n=18rev+26rev=44rev
So the basket will turn a total of 44 revolutions during this 22s interval.
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Answer:
see attached
Step-by-step explanation:
The first two x-values, -4 and 0, fall in the first part of the function definition.
There is no function definition for x = 4, as the second part only applies for x > 4.
The last x-value, 8, falls in the second part of the function definition.
The function is evaluated by putting the x-value where x is in the expression and doing the arithmetic. For example, ...
h(-4) = -(-4+1)^2 +7 = -(-3)^2 +7 = -9 +7 = -2
h(0) = 6
h(4) = undefined
h(8) = -8/3
Gary gets 4 marbles, because 12/3 is 4. So for the ratio 3:1 to apply, Jo gets 12 marbles and Gary gets 4.
<span><u>PLAN</u>
</span>(2,4) and (2,-3)
<span><u>SOLVE</u>
</span>. 2
. |4|= 4 |-3|=<span> 3
</span>. Distance from (2,4) to the x-axis= <span>6
</span>. Distance from (2,-3) to the x-axis=<span> -1
. 6 + (-1) = 5 blocks
</span>