(Solved): The dye dilution method is used to measure cardiac output with \( 6 \mathrm{mg} \) of dye, using th ...

The dye dilution method is used to measure cardiac output with \( 6 \mathrm{mg} \) of dye, using the following formula: Cardiac output \( =\frac{\text { Quantity of dye }}{\int_{0}^{10}(\text { Concentration of dye }) d t} \) The dye concentrations, in \( \mathrm{mg} / \mathrm{L} \), are modeled by \( c(t)=\frac{1}{5} t(10-t), 0 \leq t \leq 10 \), where \( t \) is measured in seconds. Find the cardiac output, accurate to at least 3 decimal places. L/sec