Question 72 – 1.4 A: Proof - AQA A Level Maths Questions

Detailed reasoning must be shown in this question.

A researcher studying fluid dynamics determines that for any two positive flow rates $u$ and $v$ in a bifurcated pipe, the 'effective velocity' $V_e$ and the 'total sum' $S$ are defined as:

V_e = \frac{u^3 + v^3}{u^2 + v^2} \quad \text{and} \quad S = u + v

Use proof by contradiction to show that $V_e < S$ for all positive real numbers $u$ and $v$ .

By providing a counter-example, show that the statement in part (a) is not true for all real numbers $u$ and $v$ where $u2+v2≠0u^2 + v^2 \neq 0$ .

Detailed reasoning must be shown in this question.

A researcher studying fluid dynamics determines that for any two positive flow rates $u$ and $v$ in a bifurcated pipe, the 'effective velocity' $V_e$ and the 'total sum' $S$ are defined as:

V_e = \frac{u^3 + v^3}{u^2 + v^2} \quad \text{and} \quad S = u + v

Use proof by contradiction to show that $V_e < S$ for all positive real numbers $u$ and $v$ .

By providing a counter-example, show that the statement in part (a) is not true for all real numbers $u$ and $v$ where $u2+v2≠0u^2 + v^2 \neq 0$ .

1.4 A: Proof

Question 60

1.4 A: Proof

Question 60

1.4 A: Proof

Question 60

1.4 A: Proof Questions

1.4 A: Proof

Question 60

1.4 A: Proof Questions