Im having trouble with this
One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)
+180 Hi there! If ab^4 = 48, and ab= 72 then we know that a = 72/b, so we can subsitute a into the first equation and we get 72/b * b^4 = 48, we simplify to get 72b^3 = 48. Now we divide 72 by both sides and we get b^3 = 3/4, so b = (cube root of 3/4)
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Vockey did a good job, and his method was fine, but
sometimes it's helpful to see a similar, but alternative,
approach. The following is how I answered this same
problem a while back:
One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72.
What is the value of b in this ordered pair?
To find b, consider ab4 = 48
We will divide both sides by ab.
Since ab=72, we will divide the left side
by "ab" and the right side by its equal 72.
ab4 48
—— = ——
ab 72
Note that ab4 = (ab) * (b3)
Cancel ab out of the left side.
Reduce 48/72 on the right side.
b3 2
—— = ——
1 3
b = cube root of (2 / 3)
.
