SOLUTION: A particular breed of tilapia has its weight W in kg. related to its length L in cm. modeled by the function: W=(3.24 x 10^-3)L^2. Explain why the function is one to one even i

Algebra ->  Functions -> SOLUTION: A particular breed of tilapia has its weight W in kg. related to its length L in cm. modeled by the function: W=(3.24 x 10^-3)L^2. Explain why the function is one to one even i      Log On


   

Question 1043582: A particular breed of tilapia has its weight W in kg. related to its length L in cm. modeled by the function: W=(3.24 x 10^-3)L^2.
Explain why the function is one to one even if it is a quadratic function. Find the inverse of this function and approximate the length of a single fish if its weight is 400 grams.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The test for being an even funtion is:
+f%28L%29+=+f%28-L%29+
This function is even because:
+%283.24%2A10%5E%28-3%29%29%2AL%5E2+=+%283.24%2A10%5E%28-3%29%29%2A%28-L%29%5E2+
---------------------------------------
+W+=+%28+3.24%2A10%5E%28-3%29%29%2AL%5E2+
+L%5E2+=+W%2A%28+1%2F%28+3.24%2A10%5E%28-3%29%29%29+
+L%5E2+=+W%2A%28+10%5E3+%2F+3.24+%29+
+L%5E2+=+W%2A%28+.30864%2A10%5E3+%29+
+L%5E2+=+308.64W+
+L+=+sqrt%28+308.64+%29%2Asqrt%28W%29+
+L+=+17.568%2Asqrt%28W%29+
----------------------
+W+=+.4+ kg
+L+=+17.568%2Asqrt%28.4%29+
+L+=+17.568%2A.6325+
+L+=+11.111+
The approximate length of a fish is 11 cm
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check:
+.4+=+%28+3.24%2A10%5E%28-3%29%29%2A11.111%5E2+
+.4+=+.00324%2A123.454+
+.4+=+.39999+
OK