Fitzpatrick 15 (e) (1 Viewer)

[edu89]

Would anyone enlighten me in this question...What is proportional... anyway please explain in steps ^^

The running cost (cost of fuel) for a certain ship is $3 per hour when the ship is not moving, and this cost increases by an amount that is proportional to the cube of its speed, Vkmh^-1. If fthe running cost per hour is $6.75 when the speed is 15kmh^-1, obtain a formula for the running cost per hour at speed V, and calculate the value of V for which the total running cost for a journey of 450km is a minimum.

 

[Drongoski]

Would anyone enlighten me in this question...What is proportional... anyway please explain in steps ^^

The running cost (cost of fuel) for a certain ship is $3 per hour when the ship is not moving, and this cost increases by an amount that is proportional to the cube of its speed, Vkmh^-1. If fthe running cost per hour is $6.75 when the speed is 15kmh^-1, obtain a formula for the running cost per hour at speed V, and calculate the value of V for which the total running cost for a journey of 450km is a minimum.

Good question: There are many who do not understand this very simple concept. When we say one variable y is proportional to x (usually written " y followed by the infinity-like symbol for 'proportional to' followed by x" . . . ugh! I wish I knew how to use LaTeX) means y = kx where k is a constant, called the constant of proportionality. Thus let's say it costs $5 to buy an apple, then the cost of the purchase of apples, P, is proportional to the n, the number of apples purchased. Thus P = $5n; here 5 is the constant of proportionality.

Thus we can have Q being proportional to the square of another quantity z say; then Q = kz^2. In Physics, we have many phenomena that follow the inverse square law; e.g. the force of gravitation between 2 objects is inversely proportional to the distance 'r' between them, ie proportional to 1/r^2

Much more familiar examples: The surface area of a sphere radius 'r'is given by S = 4 x pi x r^2; here S is proportional to the square of the radius and 4pi is the constant of proportionality.

In the case of your example, the hourly running cost, say, C = $3 + $6.75 v^3 ; 6.75 is the constant of proportionality.

Sorry to explain it in such child-like manner.

 

[edu89]

Thanks mate. I got it

 

[Iruka]

Good question: There are many who do not understand this very simple concept. When we say one variable y is proportional to x (usually written " y followed by the infinity-like symbol for 'proportional to' followed by x" . . . ugh! I wish I knew how to use LaTeX) means y = kx where k is a constant, called the constant of proportionality.

The command you are looking for is \propto