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Prove algebraically that the square of any odd number is always also an odd number.

Firstly, an algebraic expression of an odd number should be identified, such as 2n+1 or 2n-1. Doing this would also indicate the knowledge that 2n is always an even number, which will be important further on...
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Answered by Matthew H. • Maths tutor
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A curve has equation y = x^2 - 7x. P is a point on the curve, and the tangent to the curve at P has gradient 1. Work out the coordinates of P.

The gradient of the tangent at P (=1) will be equal to the gradient of the curve at point P (=1). The gradient at a point on a curve is given by dy/dx (the differential). First, differentiate the equation of...
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Sketch the graph of y= (x^2) -2x -3 labelling the turning points and points of intersection

The gradient of the curve equals the first derivative.dy/dx = 2x - 2At the turning point the gradient equals zero.2x -2 = 02x = 2 x= 1to find the y co-ordinate to this point substitute x = 1 into the origina...
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Answered by Lavana C. • Maths tutor
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Order the following substances from highest to lowest boiling point stating hat type of bonds they have. Iron, Water, Sodium Chloride(5)

2 Mark for order 3 for correct bondIt is important to think about the bonds even if you are unsure about the order as you can still get 3 marks.Think about the bonds: Water, covalent bond (h 2 o) this is wea...
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Answered by Lavana C. • Chemistry tutor
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PHYSICS A LEVEL Explain why, when a red giant becomes a white dwarf, it moves towards the lower left of the Hertzsprung-Russell diagram [2]

The fusing red giant shell drifts away form the core forming planetary nebula. Leaving only very hot core (white dwarf) (1) The core is hotter than the shell , the star moves left on the diagram. (1) Luminos...
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Answered by Lavana C. • Physics tutor
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