5q ≥ 8q - 3/2
<em><u>Add 3/2 to both sides.</u></em>
3/2 + 5q ≥ 8q
<em><u>Subtract 5q from both sides.</u></em>
3/2 ≥ 3q
<em><u>Multiply both sides by 2.</u></em>
3 ≥ 6q
<em><u>Divide both sides by 6.</u></em>
0.5 ≥ q.
The value of q is less than or equal to 0.5.
I've already been complemented twice on my previous answer, but then I discovered that I mis-read the question. My entire original answer was wrong, and I have to delete it.
I don't believe that any number can satisfy both of those conditions.
I'll say the question has no answer.
the answer is 16
8^(4/3) can be written in different ways. You can first simplify it by breaking the exponents down into 1/3 and 4. You can write it as (8^1/3)^4 (it still means the same thing). When you raise something to the one over something fraction, the denominator tells you what the root is. Because it says 1/3, it means that you're finding the cube root of something. So you can rewrite it as (3√8)^4 (the three should be sitting on top of the sign to signify that it's cube root). You then just solve from there. The cube root of 8 is 2 (2*2*2=8) so it'll simplify to (2)^4. You then solve it from there and get 16 as your answer (2*2*2*2=16).
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<span>(t) = 0 gives
</span><span>-24t + 60 = 0
</span><span>t = 2.5
</span><span>For this t, the second derivative s"(t) = -24 is negative. And so, s(t) is maximum for t = 2.5.
</span><span>Maximum height is S = -12(2.5)^2 + 60(2.5) +8 = 233ft</span>
