SOLUTION: Use the given information to answer the question. The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the c

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Use the given information to answer the question. The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the c      Log On


   

Question 1128292: Use the given information to answer the question.
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 40 hp at 110rpm, what must the diameter, d, be in order to transmit 60 hp at 150 rpm? (Round your answer to two decimal places.)

My work so far have been:
hp = k*rpm*d^3
40= k*110*27
k = 40/2970= 0.01
60= 0.01*150*d^3 = 1.5d^3
d^3 = 60/1.5
* here I don’t know how exactly to divide ^3 into 60/15. My answer keep being 13.3333333.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+d%5E3+=+60%2F1.5+
You can take the log of both sides
+3%2Alog%28d%29+=+log%28+60+%29+-+log%28+1.5+%29+
+3%2Alog%28+d+%29+=+1.78+-+.18+
+3%2Alog%28d%29+=+1.6+
+log%28+d+%29+=+.5333+
+d+=+3.41+ in
---------------------------
You still need a calculator, though.
Check math & get a 2nd opinion if needed