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How do you complete the square to answer quadratic equations?

x²+6x-2 = 0

We use completing the square when the equation cannot be factorised. Begin by placing x²in the brackets and halving the number in front of the x...

Answered by Mikhailia M. • Maths tutor

4219 Views

y is inversely proportion to the square of x. y=10 when x=5. Express y in terms of x.

y is proportion to 1/x². This can be written as y=k/x² where k is a constant of proportionality. Given that y=10 when x=5, k can...

Answered by Evan H. • Maths tutor

35014 Views

The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x²-2ax+8. At point B, <...

Answered by Evan H. • Maths tutor

8352 Views

A heater uses energy from a laptop computer to keep a mug of coffee hot. Energy is transferred to the coffee at the bottom of the mug. Explain how a convection current is set up in the coffee.

The molecules at the bottom of the mug gain energy and spread out as a result. This means that these molecules are less dense than the ones above them so they rise upwards. As they do so, they lose energy...

Answered by Evan H. • Physics tutor

4345 Views

The mercury atoms in a fluorescent tube are excited and then emit photons in the ultraviolet region of the electromagnetic spectrum. Explain (i) how the mercury atoms become excited and (ii) how the excited atoms emit photons.

(i) As they pass through the fluorescent tube, they collide with the mercury atoms within it and this collision transfers energy to the atom. This energy transfer allows the atom's orbiti...

Answered by Evan H. • Physics tutor

26354 Views