What would the differential be called for $A = \pi r^2$??
$$ \frac{dA}{dr} $$
$$A = \pi r^2 \ \frac{dA}{dr}$$ How would you describe the differential??
The rate of change of area with respect to radius.
Can you differentiate $V = \frac{4}{3} \pi r^3$??
$$ \frac{dV}{dr} = 4\pi r^2 $$
$$V = \frac{4}{3} \pi r^3 \ \frac{dV}{dr} = 4\pi r^2$$ How could you explain “the rate of change of volume with respect to radius”??
How much additional volume you gain for a small change in the radius.
2021-01-29
This cubiod represents a tank with no top and area $54m^2$. What’s the formula for the surface area??
$$ 54m^2 = 2x^2 + 3xy $$
What’s the formula the volume of this cubiod??
$$ x^2y $$
You have the two equations $$A = 2x^2 + 3xy = 54m^2 \ V = x^2y$$ How would you find the actual volume of the cubiod??
Rearrange the first formula in terms of $y$ and then substitue back into the volume formula.
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date: 2021-01-27 09:37
tags:
- '@?maths'
- '@?differentiation'
- '@?public'
title: Maths - Modelling with Differentiation
