The length L in inches of a standard nail can be modeled by

[kingrotty]

The length L in inches of a standard nail can be modeled by L= 54d^3/2, where d is the diameter in inches of the nail. What is the diameter of a standard nail that is 3 inches long?

I did this

3=54d^3/2
divided both side by 54
3/54=d^3/2
reduced
1/18=d^3/2
mutilped both side by the recipricol exponent ^2/3
1/18^2/3=d
Not sure if I did this correctly. Any help greatly appreciated

 

[soroban]

Re: Algebra word problem

Hello, kingrotty!

The length \(\displaystyle L\) in inches of a standard nail can be modeled by: .\(\displaystyle L\:=\: 54d^{\frac{3}{2}}\)
where \(\displaystyle d\) is the diameter in inches of the nail.
What is the diameter of a standard nail that is 3 inches long?

\(\displaystyle \text{I did this: }\;3\;=\;54d^{\frac{3}{2}}\)

\(\displaystyle \text{Divided both side by 54: }\;\frac{3}{54} \:=\:d^{\frac{3}{2}}\)

\(\displaystyle \text{Reduced: }\;\frac{1}{18} \:=\:d^{\frac{3}{2}}\)

\(\displaystyle \text{Took the }\frac{2}{3}\text{ power of both sides: }\;\left(\frac{1}{18}\right)^{\frac{2}{3}} \:=\:d\)


Not sure if I did this correctly. . . . . You did great!

Just crank it through your calculator . . . you should get 0.145596744

 

[Denis]

Re: Algebra word problem

3=54d^3/2

3 = 54d^(3/2) : you NEED brackets here...else 54d^3/2 means 54d^3 divided by 2

 

[kingrotty]

Re: Algebra word problem

Thanks for the help