Precalc Trig Arc Length Question

AI Thread Summary
The discussion centers around solving a precalculus trigonometry problem related to arc length, specifically question #7 from a released math exam. The equation used is a = theta * r, where the user initially calculated a = (5pi/6) * 20 but found it incorrect. Clarification on the term "total perimeter" indicates it refers to the complete distance around the area swept by a wiper. The correct approach involves adding the arc length to the lengths of other segments, leading to a revised formula. The conversation highlights the importance of carefully interpreting problem statements in math.
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Homework Statement


http://education.Alberta.ca/media/9451970/07_math30-1_released_2014-15.pdf
question #7

Homework Equations


a=theta*r

The Attempt at a Solution


I did a=(5pi/6)*20 but the answer is not A
 
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A123 said:

Homework Statement


http://education.Alberta.ca/media/9451970/07_math30-1_released_2014-15.pdf
question #7

Homework Equations


a=theta*r

The Attempt at a Solution


I did a=(5pi/6)*20 but the answer is not A
I think 'total perimeter' here means you go entirely around the area which is swept out by the wiper.
 
SteamKing said:
I think 'total perimeter' here means you go entirely around the area which is swept out by the wiper.
I agree with SteamKing's appraisal.
 
SteamKing said:
I think 'total perimeter' here means you go entirely around the area which is swept out by the wiper.

Yeah I just went back to it and I missed that word completely lol.
Its [(5pi/6)*20] + 16(2) + [(5pi/6)*4]
I was too focused on what's inside
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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