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(2 points) Bronze is an alloy, or mixture, of copper and tin. The alloy initiall

ID: 2878014 • Letter: #

Question

(2 points) Bronze is an alloy, or mixture, of copper and tin. The alloy initially contains 5 kg copper and 5 kg tin. Suppose you change the amount of copper by x kg (i.e., add copper if x is positive but remove copper if x is negative). The concentration of copper in the new alloy is a function of x: Total amount of copper x) Concentration of copper E Total amount of alloy (1) Find an explicit formula f(x) Recommended: graph this function, locate interesting features tems (2)--(6) ask you to compute a quantity and then select one of the following statements to interpret that value. A the amount of copper to remove in order for the alloy to become pure tin B initial concentration of copper in the alloy C the total amount of the alloy you have if its concentration of copper is 70%. D copper concentration of the alloy after adding 0.7 kg of copper E copper concentration of the alloy after removing 0.7 kg of copper. F the change in amount of copper which yields an alloy with copper concentration of 70% G copper concentration of the alloy after removing 3 kg of copper H not physically meaningful (2) f(0.7) which is (pick meaning) (3) f(0) which is (pick meaning) (4) f(-3) which is (pick meaning) (5) f (0.7) which is (pick meaning) (60 f (0) which is (pick meaning)

Explanation / Answer

1)amount of copper =5+x

concentration of copper =f(x)=(5+x)/((5+x)+5)

concentration of copper =f(x)=(5+x)/(10+x)

2)f(0.7)=(5+0.7)/(10+0.7)=57/107. option D

3)f(0)=5/10 =1/2. option B

4)f(-3)=(5-3)/(10-3)=2/7. option G

5)let f-1(0.7) =p

f(p)=0.7

(5+p)/(10+p)=0.7

5+p=7+0.7p

0.3p=2

p=2/0.3

p=20/3

f-1(0.7) =20/3

option F

6)

let f-1(0) =p

f(p)=0

(5+p)/(10+p)=0

5+p=0

p=-5

f-1(0) =-5

option A