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1. If f(x)=x^2-2 and g(x)=2x+4, what s the value of f(g(-3))?

 

2. A Vermont syrup-maker has 100 liters of a mixture that is 1/4 maple syrup and 3/4 base. She wants to add enough maple syrup to bring the ratio of maple syrup to base up to 1:1. If she has to evaporate 90% of the maple sap to get the maple syrup to add to that mixture, how many liters of maple sap does she need to start with?

mathtoo  May 20, 2018
 #1
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1. These are functions. First, we evaluate g(x) when g=-3, so we get: g(−3) = 2(−3) + 4 = −6 + 4 = −2.

Next, we evaluate f(x) when x=-2, so we get:  f(−2) = (−2)2 − 2 = 4 − 2 = \(\boxed{2}\)

smileysmiley

tertre  May 20, 2018
edited by tertre  May 20, 2018
 #2
avatar+2766 
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2. First, we note that the syrup maker initially has 25 liters of maple syrup and 75 liters of base. She will need to add 50 liters of maple syrup to make the ratio 1:1. Since 90% or 9/10 of the amount of sap will evaporate, she can obtain those 50 liters of maple syrup from 50 × 10 = \(\boxed{500}\) liters of maple sap.

smileysmiley

tertre  May 20, 2018

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