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# help plz

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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.)

Jun 5, 2023

#1
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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)

🐺🐺🐺

Jun 5, 2023
#2
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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)

.

Jun 6, 2023