Asked by Frank
proportionality A〖∝ L〗^3
A 20-foot sailboat estimated cost is $10,000. So what would the estimated cost be for a similar 40-foot boat?
A 20-foot sailboat estimated cost is $10,000. So what would the estimated cost be for a similar 40-foot boat?
Answers
Answered by
Steve
If A is the cost, and is proportional to L^3, and L is the length of the boat, then
A = kL
Find k:
10000 = k*20^3 = 8000k
k = 1.25
Now we have the formula
A(L) = 1.25 L^3
A(40) = 1.25 * 40^3 = 1.25 * 64000 = 80,000
Makes sense. If the length scales by a factor of 2, the cost scales by a factor of 2^3 = 8.
A = kL
Find k:
10000 = k*20^3 = 8000k
k = 1.25
Now we have the formula
A(L) = 1.25 L^3
A(40) = 1.25 * 40^3 = 1.25 * 64000 = 80,000
Makes sense. If the length scales by a factor of 2, the cost scales by a factor of 2^3 = 8.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.