The equations s1 = 18 + 0.4m and s2 = 11.2 + 0.54m give the lengths of two diffe

Question

The equations s1 = 18 + 0.4m and s2 = 11.2 + 0.54m give the lengths of two
different springs in centimeters, s1 and s2, as mass amounts in grams, m, are
separately added to each.

a. When are the springs the same length?
b. When is one spring at least 10 cm longer than the other?
c. Write a statement comparing the two springs.

Explanation / Answer

a) to find where they are the same length you just have to set them equal to each other and solve. 18 +.4m = 11.2 + .54 m 6.8 + .4 m = .54m 6.8 = .14m m = (6.8/.14) = 48.5714286 b) So we want the length of one to be at least 10 cm longer, so add 10 to one equation and set up an inequality: 18+.4m +10 >= 11.2 + .54m 28 +.4m >= 11.2 + .54m 16.8 +.4m >= .54m 16.8 >= .14m 120>=m I'm not sure what you mean by write a statement comparing the two springs. I would say that 18+.4m started out longer, but does not stretch as quickly as the other spring (since .4 < .54). Once m=48.57 is reached, the spring that started out shorter will surpass the other in length.

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