SOLUTION: The mass Kg of a metal bar varies jointly as its length L meters and the square of its diameter d mm. If W = 140 when d = 4 and L = 54, find d in terms of W and L

Algebra ->  Proportions  -> Lessons -> SOLUTION: The mass Kg of a metal bar varies jointly as its length L meters and the square of its diameter d mm. If W = 140 when d = 4 and L = 54, find d in terms of W and L      Log On


   

Question 1137279: The mass Kg of a metal bar varies jointly as its length L meters and the square of its diameter d mm. If W = 140 when d = 4 and L = 54, find d in terms of W and L
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+W+ is the mass in kg
Let +k+ = constant
+W+=+k%2AL%2Ad%5E2+
+W+=+140+
+L+=+54+
+d+=+4+
+140+=+k%2A54%2A4%5E2+
+140+=+864k+
+k+=+.16204+
+d%5E2+=+W%2F%28+k%2AL+%29+
+d+=+sqrt%28+W%2F%28+k%2AL+%29%29+
+d+=+sqrt%28+W%2F%28+.16204L+%29%29+
check:
+d+=+sqrt%28+140%2F%28+.16204%2A54+%29%29+
+d+=+sqrt%28+140%2F8.75+%29+
+d+=+sqrt%28+16+%29+
+d+=+4+