Mr. Garcia needs at least 60 paintbrushes for his art classes. He has 22 paintbrushes already and will buy more paintbrushes of
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a) C(0.5) = 39, C(2) = 39, C(4) = 69
b) Answers in part (a) represents the values of C at x = x₀
c) C(x) is continuous at x = 2
C (x) = 39 for 0 ⩽ x ⩽ 2
Since x = 0.5 is in the range 0 ⩽ x ⩽ 2:
C(0.5) = 39
Since x = 2 is in the range 0 ⩽ x ⩽ 2
C(2) = 39
Since x = 4 is in the range x > 2
C(4) = 39 + 15(x - 2)
C(4) = 39 + 15 (4 - 2)
C(4) = 39 + 15(2)
C(4) = 39 + 30
C(4) = 69
b) The answers in part A represents C(x). That is, the values of C at x = x₀
c) Is C(x) continuous at x = 2
C(2) = 39
Since , the function C(x) is continuous at x = 2
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