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Suppose a varies jointly with #b# and #c# and inversely with #d# and #a = 400# when #b = 16#, #c=5#, and #d = 2#. What's the equation that models the relationship?

Answer 1

#ad = 10bc#

If #a# varies inversely with #d# and jointly with #b# and #c# then #color(white)("XXX")ad = k * bc# for some constant #k#

Substituting #color(white)("XXX")a=400# #color(white)("XXX")d=2# #color(white)("XXX")b=16# and #color(white)("XXX")c=5#

#400 xx 2 = k * 16 xx 5#

#rarr 800 = k * 80#

#rarr k=10#

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Answer 2

Genesis Allen

The equation that models the relationship described is ( a = \frac{k \cdot b \cdot c}{d} ), where k is the constant of variation. To find k, substitute the given values: ( 400 = \frac{k \cdot 16 \cdot 5}{2} ). Once you find k, you can use it to represent the relationship between a, b, c, and d.

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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.