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4 years ago

The town of Manchester (population 50,000) has the shape of a rectangle that is 5 miles wide and 7 miles long.

Mathematics

1 answer:

topjm [15]4 years ago

5 0

Answer:

Step-by-step explanation:

Population density is expressed as the ratio of the total number of people, N living in or occupying an area or space to the total area or space. Therefore

Population density = number of people/area

A) The town of Manchester (population 50,000) has the shape of a rectangle that is 5 miles wide and 7 miles long. The area would be

5 × 7 = 35 square miles

Population density = 50000/35

= 1429 people/square mile

B) The business area has radius of 1 mile. Its area would be

πr² = 3.14 × 1² = 3.14 square miles.

The area where people reside outside the business area is

35 - 3.14 = 31.86 square miles

Population density = 50000/31.86

= 1569 people per square mile

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The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

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Answer:

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Step-by-step explanation:

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Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

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$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

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$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

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