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A curve has equation y = x^3 - 48x. The point A on the curve has x coordinate -4. The point B on the curve has x coordinate - 4 + h. Show that that the gradient of the line AB is h^2 - 12h.

First, let's recall the gradient formula:grad = change in y / change in x = y2 -y1 / x2 - x1So let's label point A as x1, and point B as x2, and find the corresponding y1 and y2 using the equation of the cur...
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Answered by Oliver W. • Maths tutor
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Given the equation x^3-12x^2+ax-48=0 has roots p, 2p and 3p, find p and a.

QUESTION: Given the equation x 3 -12x 2 +ax-48 = 0 has roots p, 2p and 3p, find p and a. Roots mean x = p, x = 2p and x = 3p hence (x-p), (x-2p) and (x-3p) are factors of the equation. Expanding these three ...
MD
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How do you work out an electron configuration?

A full electron configuration shows the amount of electrons in each shell and subshell of an element or ion. Shells (also called energy levels) progress from 1 to 4, with 1 being the closest to the centre of...
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Answered by Lauren B. • Chemistry tutor
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Define light, critical and heavy damping in simple harmonic motion.

Damping reduces the amplitude of oscillation of a system over time. Critical damping reduces the amplitude of the oscillations to zero in the shortest possible time, returning the system to the equilibrium p...
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Answered by Oscar W. • Physics tutor
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Prove by contradiction that 2^(1/3) is an irrational number

Assume 2^(1/3) is rational, so can be written as p/q where p and q are integers with no common factors. p/q = 2^(1/3) (p^3)/(q^3) = 2 p^3 = 2q^3 Hence, p is even. Thus, p can be written as 2r, where r is an ...
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Answered by Oscar R. • Maths tutor
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