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Using standard formulae, derive an expression for the final speed of a falling object in terms of its change in height. Assume zero air resistance or other resistive forces.

E k = (1/2)mv 2 E p = mg(dh) Set these equal to each other, because of conservation of energy: (1/2)mv 2 = mg(dh) Cancel the mass: (1/2)v 2 = g(dh) v 2 = 2g(dh) v = (2g(dh)) 1/2
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Answered by Danny L. • Physics tutor
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Why do metals conduct electricity?

To answer this question we need to think about the bonding that occurs within metals. Metallic elements form strong lattices due to the metallic bonding. This consists of a lattice of positive metal atoms. T...
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Answered by Alex M. • Chemistry tutor
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Fully simplify (8a^2b * ab^4)/(2a^3b^2)

8a 3 b ab 4 2a 3 b 2 (can write this more clearly by hand using whiteboard) First go about seperating and collecting terms. Begin with the top line. 8 remains the same as there are no other known numbers. We...
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Answered by Archie I. • Maths tutor
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Given that x(a+bx)(a-bx)=25x-4x^3, what is the value of b^(-a)? a,b>0

It's a two part question. First Part Expand the equation the left hand side to get a^(2)*x-b^(2)*x^3 thus comparing co-efficients a^2=25 and b^2=4 thus a= 5 b=2 Second Part Therefore b^(-a) is equal to 2^(-5...
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Answered by Cameron P. • Maths tutor
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Solve the inequality 7x+3y-4 > 5y-19x for y in terms of x.

7x+3y-4 > 5y-19x Adding 19x to both sides: 26x+3y-4 > 5y Subtracting 3y from both sides: 26x-4 > 2y Divide both sides by 2 to put the expression in its simplest form: 13x-2 > y or (remembering to...
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Answered by Danny L. • Maths tutor
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