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How do you write the equation if A varies inversely as the cube of b and b is 1/3 when a is 27?

Answer 1

The equation can be written as A = k/b^3, where k is a constant. To find the value of k, substitute the given values of A and b into the equation. When a is 27 and b is 1/3, we have 27 = k/(1/3)^3. Simplifying, we get 27 = k/(1/27), which gives k = 27 * 27. Therefore, the equation is A = (27 * 27)/b^3.

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Answer 2

Eli Assouline

If #a# varies inversely as the cube of #b# then #color(white)("XXXX")##a*b^3 = c# for some constant #c#

Given #(a,b) = (27, 1/3)# is a solution for this equation #color(white)("XXXX")##27*(1/3)^3 = c#

#rArr##color(white)("XXXX")##c=1#

The equation is: #color(white)("XXXX")#a*b^3 = 1#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.