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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.)

 May 31, 2023
 #1
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We can solve this problem by using the second equation to solve for a in terms of b, and then substituting that expression for a into the first equation.

From the equation ab = 72, we can solve for a by dividing both sides by b:

a = 72/b

Now we can substitute this expression for a into the first equation:

ab^4 = 48

(72/b) * b^4 = 48

Simplifying, we get:

72b^3 = 48

Dividing both sides by 72, we get:

b^3 = 2/3

Taking the cube root of both sides, we get:

b = (2/3)^(1/3)

This is the exact value of b in the ordered pair (a, b). If you need a numerical approximation, you can use a calculator to evaluate the cube root of 2/3, which is approximately 0.892. Therefore, b is approximately 0.892 in this ordered pair. 

 May 31, 2023

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