High School Graphing a*b^0.3=constant: Which Variable Goes on the Y-Axis?

[mech-eng]

I would like to sketch the graph of equation a*b^0.3=constant for a and b are positive real numbers. How do I start?

Which one should be as y-axis, and which one be x-axis. This only affects the shape of the graph. The confusing part for me is that should I use b itself or b^03 as an axis?

Thank you.

 

[mech-eng]

I put b in the horizontal axis and give it values 10, 15, 20, 25, 30, 35, 40, 45 and calculated b^0.3 values. I choose constant=100 and then dividing 100/b^0.3 values I calculate a values. The graph is a curve with negative slope, nonlinear shape but it is like it behaves almost linear between b=20 and b=35 values.

Thank you.

 

[fresh_42]

Here's the graph $ab^{0.3}=a \cdot (b^{0.3})=100$ for control:
http://www.wolframalpha.com/input/?i=a*(b^0.3)=100
It's a hyperbola. The constants $100$ and $0.3$ are only a matter of scaling.

 

[mech-eng]

Here's the graph $ab^{0.3}=a \cdot (b^{0.3})=100$ for control:
http://www.wolframalpha.com/input/?i=a*(b^0.3)=100
It's a hyperbola. The constants $100$ and $0.3$ are only a matter of scaling.

What is the name/category of this kind of web service? An online calculator?

Thank you

 

[fresh_42]

What is the name/category of this kind of web service?

Thank you

I don't know, how it is named and by whom. Wolframalpha is a well-known company that provides solutions for simple equations. More detailed solutions and graphics have to be paid by a membership, but for a quick and dirty look-up, they are a good source. Here's another page with similar properties: https://www.desmos.com/calculator

 

[mech-eng]

Are there CAD versions and multiphysics versions of such programs?

Thank you.

 

[fresh_42]

Are there CAD versions and multiphysics versions of such programs?

Thank you.

I don't know. Perhaps you could search for them on Google. "free CAD software" of "physics simulations" could be a start.

 

[berkeman]

Are there CAD versions and multiphysics versions of such programs?

By the same people who bring you WolframAlpha...

http://www.wolfram.com/mathematica/online/?src=google&420

http://www.wolfram.com/

 

[Nidum]

I would like to sketch the graph of equation a*b^0.3=constant for a and b are positive real numbers

In experimental work where you might be needing to determine the actual values for the exponent and the constant from your graph it is often useful to use log axes .

Simple example :

The function y = k . xⁿ then it can be rewritten as log y = log k + n . log x

Plotted on log axes the graph curve now becomes a straight line with n and k being given by the slope and intercept .

 

[mech-eng]

Is this a linearization process? This is very confusing for me because shape of the original and converted one is different so what is same?

Thank you.