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If n is an integer prove (n+3)^(2)-n^(2) is never even.

Let us begin by simplifying the expression:(n+3) 2 - n 2 = (n+3)(n+3) - n 2 = n 2 + 6n + 9 - n 2 (expanded brackets)= 6n + 9 (collected like terms)= 3(2n+3) (taken out a factor of 3)Now we can consider this ...
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Answered by Hugh K. • Maths tutor
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For what values of k does the graph y=x^(2)+2kx+5 not intersect the x-axis

Where the graph intersects the x-axis, x 2 +2kx+5 must be equal to zero. Thus we can answer the equivalent question: For what k does x 2 +2kx+5 = 0 not have a solution?This is now a simpler problem (roots of...
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Answered by Hugh K. • Maths tutor
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Why can metal conduct electricity and heat?

Conduction is possible as delocalised (free) electrons are able to carry a charge and move through the metal.
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Answered by Bertie H. • Chemistry tutor
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What does an organism use energy from respiration for?

In all organisms, allows creation of bigger molecules from smaller ones In animals, enables muscle contraction In some animals (mammals and birds), provides heat to maintain a constant body temperature In pl...
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Answered by Bertie H. • Biology tutor
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Find all positive integers n such that 12n-119 and 75n-539 are both perfect squares. Let N be the sum of all possible values of n. Find N.

Let 75n - 539 = l^2 and 12n - 119 = k^2 . where n is a natural number. Multiply 75n - 539 = l^2 by 4 to give 300n - 2156 =4l^2 and 12n - 119 = k^2 by 25 to give 300n - 2975 = 25k^2. Subtract the two new expr...
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Answered by Soham K. • STEP tutor
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