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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

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