A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the size of the object. Suppose a person has a windpipe with a 20-mm radius. If a foreign object has a radius r, in millimeters, then the coughing velocity V(r), in millimeters per second, needed to remove the object is given by V(r)= k(20r^2 - r^3), 0 <= r <= 20

where k is some positive constant. For what size object is the maximum velocity required to remove the object?

this is a very good question

step-by-step explanation:

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130.66 for edgedunity students

a and c

for infinitely many solutions we require both left and right sides to be equal

distribute and simplify

a

14 - 8x = 20 - 8x - 6 = 14 - 8x ← both sides equal so infinite solutions

b

6x - 54 = 6x - 54 + x = 7x - 54 ← not equal

c

4x + 16 = 4x + 10 + 6 = 4x + 16 ← both sides equal so infinite solutions

d

5x - 40 + 10 = 5x + 10

5x - 30 = 5x + 10 ← not equal