For positive variables: $$A\propto r^2,\qquad T\propto\frac1A$$ When $r=3$, $A=45$ and \(T=

Question

For positive variables: $$A\propto r^2,\qquad T\propto\frac1A$$ When $r=3$, $A=45$ and $T=8$. Find equations for $A$ in terms of $r$, and $T$ in terms of $A$. Hence express $T$ directly in terms of $r$. If $r$ increases by $50\%$, find the new value of $T$ and its percentage decrease. Explain why a $50\%$ increase in $r$ does not produce a $50\%$ decrease in $T$.

Accepted Answer

(a) $A=5r^2,\ T=\frac{360}{A}$; (b) $T=\frac{72}{r^2}$; (c) $T=\frac{32}{9}$, decrease $55\frac{5}{9}\%$; (d) Inverse-square scaling.

Direct and Inverse Proportion

Direct and Inverse Proportion

Solution:

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