Why is [tex]$\sqrt[3]{4}$[/tex] equal to [tex]$4^{\frac{1}{3}}$[/tex] ?
[tex]$\left(4^{\frac{1}{3}}\right)^3=4^{\left(\frac{1}{3}+3\right)}=4^1=4$[/tex]
[tex]$\left(4^{\frac{1}{3}}\right)^3=4^{\left(\frac{1}{3}\right)^{(3)}}=4^1=4$[/tex]
[tex]$\left(4^{\frac{1}{3}}\right)^3=4^{\left(\frac{1}{3}+3\right)}=4^1=4$[/tex]
d [tex]$\quad\left(4^{\frac{1}{3}}\right)^3=4^{\left(\frac{1}{3}-3\right)}=4^1=4$[/tex]
Answer (2)
Answer: The equation is y=k(x). So 12=k(5), divide by 5 on both sides coming up with k=2.4. Plug 2.4 in as k in the original equation, making it 30=2.4(x), divide both sides by 2.4, 30 divided by 2.4 is 12.5, making x=12.5
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To find x when y = 30 with direct variation, we first determine the constant of variation k from the values y = 12 when x = 5, which gives k = 2.4. Then, we use this constant in the equation y = kx to find x when y = 30, resulting in x = 12.5.
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