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

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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