Write an equation that relates the variables. g varies inversely as the sixth ext { sixth } sixth root of zA) g = k z 6 g = \sqrt [ 6 ] { k z } g = 6 k z B) g = 1 z 6 g = \frac { 1 } { \sqrt [ 6 ] { z } } g = 6 z 1 C) g = 1 k + z 6 g = \frac { 1 } { k + \sqrt [ 6 ] { z } } g = k + 6 z 1 D) g = k z 6 g = k \sqrt [ 6 ] { z } g = k 6 z E) g = k z 6 g = \frac { k } { \sqrt [ 6 ] { z } } g = 6 z k

Question

Write an equation that relates the variables. g varies inversely as the    sixth  	ext { sixth }  sixth    root of zA)    g = k z 6 g = \sqrt [ 6 ] { k z } g = 6 k z ​ B)    g = 1 z 6 g = \frac { 1 } { \sqrt [ 6 ] { z } } g = 6 z ​ 1 ​ C)    g = 1 k + z 6 g = \frac { 1 } { k + \sqrt [ 6 ] { z } } g = k + 6 z ​ 1 ​ D)    g = k z 6 g = k \sqrt [ 6 ] { z } g = k 6 z ​ E)    g = k z 6 g = \frac { k } { \sqrt [ 6 ] { z } } g = 6 z ​ k ​

Marisol Pedroza · Accepted Answer

Final Answer : E, Explanation :  When a variable is said to vary inversely, it means that as one variable increases, the other decreases, and vice versa. In this case, we are told that g varies inversely as the sixth root of z. The mathematical expression for this relationship is: g=k/z^(1/6), where k is a constant of proportionality. Solving for g, we get: g=k/(z^(1/6)), which is the same as g=k/(6th root of z). Thus, the best choice is E, which is equivalent to the equation we derived.

Write an equation that relates the variables. g varies inversely as the $\text { sixth }$ root of z

A) $\sqrt [ 6 ] { k z }$
B) $\frac { 1 } { \sqrt [ 6 ] { z } }$
C) $\frac { 1 } { k + \sqrt [ 6 ] { z } }$
D) $\sqrt [ 6 ] { z }$
E) $\frac { k } { \sqrt [ 6 ] { z } }$

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