The demand equation for soccer tournament T-shirts is xy - 5,000 = y where y is the number of T-shirts the Enormous State University soccer team can sell at a price of $x per shirt. Find dy dx x = 6. dy/dx x = 6 = T-shirts per dollar Interpret the result. When the price is set at $6, the demand is by T-shirts per $1 increase in price.

Question

Molly Clayton

Mathematics

9 April, 15:47

The demand equation for soccer tournament T-shirts is xy - 5,000 = y where y is the number of T-shirts the Enormous State University soccer team can sell at a price of $x per shirt. Find dy dx x = 6. dy/dx x = 6 = T-shirts per dollar Interpret the result. When the price is set at $6, the demand is by T-shirts per $1 increase in price.

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Jaidyn Barr · Answer 1

The given equation is:

x y - 5000 = y

Rewrite this to create an explicit equation:

x y - y = 5000

y (x - 1) = 5000

y = 5000 / (x - 1)

Derive to get dy / dx:

dy = - 5000 dx / (x - 1) ^2

dy / dx = - 5000 / (x - 1) ^2

So plugging in x = 6,

dy / dx = - 5000 / (6 - 1) ^2

dy / dx = - 200