## Related Rates

### 1. Suppose \( x^2+4y^2=17\), where \(x\) and \(y\) are functions
of \(t\). Find \(\frac{dy}{dt}\) if given that \(\frac{dx}{dt}= 1.5\), \(x=3\) and
\(y=2\). solution

### 2. Suppose the quantity demanded weekly of the SuperTitan radial tire is
related to its unit price by the equation \(p + x^2 = 144\) where \(p\) is
measured in dollars and \(x\) is measured in units of 1000. How fast is the
quantity demanded weekly changing when \(x=8, p = \$80\) and
the price per tire is increasing at a rate of $4
per week? solution

### 3. The demand equation for a certain brand of earbuds is \(100x^2 + 8p^2 =
2358\) where \(x\) represents the number (in thousands) of earbuds demanded each
week that the unit price is $p. How is the quantity demanded changing when the
unit price per set of earbuds is $13.50 and the price is dropping at a rate of
$0.12 per earbud set per week?
solution