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Question 126987: The monthly sales of socks,(S on thousands of pairs) , can be calcualted by S=-t(squared)+4t+40 where t is t=0 corresponds to the first month of sales (t in months) In which months were there:
A)When were the maximum number of socks sold? For this one I used -b/2a to find the vertex and I came up with 2 months.
B) What is the maximum number of socks sold? I'm thinking you would just double the first answer and get 4 months.
C)When is the number of pairs sold equal to zero? Probably either 4 or 8 months. I think this because either I was wrong with 'B' and the maximum number was in month 2 or I was right and you just double 4.
Thanks for any help!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The monthly sales of socks,(S on thousands of pairs) , can be calcualted by S=-t(squared)+4t+40 where t is t=0 corresponds to the first month of sales (t in months) In which months were there:
:
A)When were the maximum number of socks sold? For this one I used -b/2a to find the vertex and I came up with 2 months.
:
This is correct, t = 2 is the axis of symmetry
:
:
B) What is the maximum number of socks sold?
:
To find the maximum no. of socks, substitute 2 for t and find S
S = -(2^2) + 4(2) + 40
S = -4 + 8 + 40
S = 44 thousand socks
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C)When is the number of pairs sold equal to zero?
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Solve for t when S = 0
-t^2 + 4t + 40 = 0
This requires the quadratic formula,
Positive solution: t ~ 8.6 months
:
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