M L Aggarwal Solutions for Chapter: Appendix Mathematical Modelling, Exercise 4: QUADRATIC EQUATIONS

India is one of the largest importers of crude oil. Oil companies produce crude oil in barrels. Suppose the maximum oil produced by a company is $300$ barrels and profit made from sale of these barrels is given by the function $P\left(x\right)=-10x^2+ 3500x-66000$, where $P\left(x\right)$ is profit in rupees and $x$ is the number of barrels produced and sold.

If $100$ barrels are produced, then the profit or loss is

India is one of the largest importers of crude oil. Oil companies produce crude oil in barrels. Suppose the maximum oil produced by a company is $300$ barrels and profit made from sale of these barrels is given by the function $P\left(x\right)=-10x^2+ 3500x-66000$, where $P\left(x\right)$ is profit in rupees and $x$ is the number of barrels produced and sold.

If $400$ barrels are produced, then the profit or loss is

India is one of the largest importers of crude oil. Oil companies produce crude oil in barrels. Suppose the maximum oil produced by a company is $300$ barrels and profit made from sale of these barrels is given by the function $P\left(x\right)=-10x^2+ 3500x-66000$, where $P\left(x\right)$ is profit in rupees and $x$ is the number of barrels produced and sold.

What will be the shape of the graph represented by the polynomial $P\left(x\right)$?

A flight got delayed by $40$ minutes due to bad weather conditions. In order to reach its destination on time, which is $1600 \mathrm{km}$ away, the aeroplane had to increase the speed by 400 km/h of its original speed, which is $x \mathrm{km}/\mathrm{h}$.

What is the expression for the time taken (in hours) by the plane to cover $1600 \mathrm{km}$ with its increased speed?

A flight got delayed by $40$ minutes due to bad weather conditions. In order to reach its destination on time, which is $1600 \mathrm{km}$ away, the aeroplane had to increase the speed by 400 km/h of its original speed, which is $x \mathrm{km}/\mathrm{h}$.

Using which of the following equations, the original speed of the plane can be calculated?

A flight got delayed by $40$ minutes due to bad weather conditions. In order to reach its destination on time, which is $1600 \mathrm{km}$ away, the aeroplane had to increase the speed by 400 km/h of its original speed, which is $x \mathrm{km}/\mathrm{h}$.

The original speed of the plane is$?$

A flight got delayed by $40$ minutes due to bad weather conditions. In order to reach its destination on time, which is $1600 \mathrm{km}$ away, the aeroplane had to increase the speed by $400 \mathrm{km}/\mathrm{h}$ of its original speed, which is $x \mathrm{km}/\mathrm{h}$.

If the original speed of the plane is $750 \mathrm{km}/\mathrm{h}$, then find the time taken by the plane to cover a distance of $2250 \mathrm{km}$.

A flight got delayed by $40$ minutes due to bad weather conditions. In order to reach its destination on time, which is $1600 \mathrm{km}$ away, the aeroplane had to increase the speed by $400 \mathrm{km}/\mathrm{h}$ of its original speed, which is $x \mathrm{km}/\mathrm{h}$.

If the speed of the plane is decreased due to some technical reasons, then what will be the effect on the time taken if the distance remains the same?