91Ó°ÊÓ

Find the equilibrium point for each pair of demand and supply functions. Demand: \(q=\frac{5}{x} ; \quad\) Supply: \(q=\frac{x}{5}\)

A function \(f\) takes a number \(x\), multiplies it by \(3,\) and then adds \(6,\) while a function \(g\) takes a number \(x\), adds \(a\) to it, and then multiplies the result by \(3 .\) Find \(a\) if \(f\) and \(g\) are the same function.

Suppose \((2,5),(4,13),\) and \((7, y)\) all lie on the same line. Find \(y .\)

Find the equilibrium point for each pair of demand and supply functions. Demand: \(q=\frac{4}{x} ; \quad\) Supply: \(q=\frac{x}{4}\)

A function \(h\) takes a number \(x,\) adds \(3,\) and then squares the result, while a function \(k\) takes a number \(x\), squares it, adds 6 times \(x,\) and then adds \(a\) to the result. Find \(a\) if \(h\) and \(k\) are the same function.

Find the equilibrium point for each pair of demand and supply functions. Demand: \(q=(x-3)^{2} ; \quad\) Supply: \(q=x^{2}+2 x+1\) (assume \(x \leq 3)\)

Find the equilibrium point for each pair of demand and supply functions. Demand: \(q=(x-4)^{2} ; \quad\) Supply: \(q=x^{2}+2 x+6\) (assume \(x \leq 4)\)

A large crane is being depreciated according to the model \(V(t)=900-60 t,\) where \(V(t)\) is in thousands of dollars and \(t\) is the number of years since \(2005 .\) If the crane is to be depreciated until its value is \(\$ 0,\) what is the domain of this model?

Find the equilibrium point for each pair of demand and supply functions. Demand: \(q=7-x ; \quad\) Supply: \(q=2 \sqrt{x+1}\)

The number of tickets sold for a fund-raiser is inversely proportional to the price of a ticket, \(p\). If 175 tickets can be sold for \(\$ 20\) each, how many tickets will be sold if the price is \(\$ 25\) each?