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A function is defined as f(x) = x / sqrt(2x-2). Use the quotient rule to show that f'(x) = (x-2)/(2x-2)^(3/2)

u = x v = (2x-2)^(0.5)u' = 1 v' = (2x-2)^(-0.5)f'(x) = (vu' - uv') / v^2Therefore, f'(x) = (((2x-2)^(0.5) * 1) - (x * (2x-2)^(-0.5))) / ((2x-2)^(0.5))^2f'(x) = (2x - 2 - x) / (2x-2)^(3/2) = (x-2) / (2x-2)^(3...
IF
Answered by Isaac F. • Maths tutor
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Jay, Shelia & Harry share £7200 in the ratio 1:2:5. How much does Harry receive?

Explain how the ratio shows everyone's share of the £7200: 1:2:5 (Jay's share:Sheila's Share:Harry's Share)Add up the terms of the ratio to find out many equal parts the £7200 is split into: 1+2+5=8 (parts)W...
PB
Answered by Philip B. • Maths tutor
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A complex number z has argument θ and modulus 1. Show that (z^n)-(z^-n)=2iSin(nθ).

This problem wants you to use De Moivre's theorem to prove a trigonometric identity.We will tackle this problem by taking the left hand side and using theorems and manipulation to show it is equivalent to th...
GC
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¿Cómo juegan un papel los temas de la muerte y la fatalidad en Crónica de una muerte anunciada en la dirección de la trama del libro?

Los temas de muerte y fatalidad están muy vinculados en esta novela, y parece que siguen mutuamente. Esto se debe principalmente a que el destino del protagonista principal es la muerte, tal como lo determin...
LW
Answered by Lauren W. • Spanish tutor
3961 Views

A ladder of length 6.5m is leaning against a vertical wall. The foot of the ladder is 1.5m from the wall. Calculate the distance the ladder reaches up the wall to 3 significant figures.

(using Pythagoras' theorem) 6.5 2 = x 2 + 1.5 2 x 2 = 6.5 2 - 1.5 2 x 2 = 42.25 - 2.25 x 2 = 40 x = sqrt(40) x = 6.32 (to 3sf) = 6.32m
PB
Answered by Pollyanna B. • Maths tutor
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