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Find an expression for the nth term of this sequence: 3 - 11 - 19 - 27 - 35 . The nth term of a different sequence is 2n^3 + 3. Write down the first 3 terms of this sequence.

First, the sequence is 3 - 11 - 19 - 27 - 35. Looking at it, we can observe that each element of the sequence is created by adding 8 to the previous. The first term is 3. The second term is 3 + 8...

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The equation of a curve is y = x^2 + ax + b where a and b are integers. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.

In the equation for our line we have 2 unknowns: a and b. However, we know that the line passes through two known points with x and y coordinates. Therefore, we can begin by substituting in our known x an...

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Describe the shape of, and bonding in, a molecule of benzene and explain why benzene does not readily undergo addition reactions.

Benzene is a planar, cyclical, hexagonal molecule, with the molecular formula C₆H₆. It consists of a ring of 6 carbon atoms with alternating single bonds and double bonds. The length...

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Show that (2x^2 + x -15)/(2x^3 +6x^2) * 6x^3/(2x^2 - 11x + 15) simplifies to ax/(x + b) where a and b are integers

As you begin the question, it is important to note that immediately multiplying the two fractions, while would eventually get you to the correct answer would take far too long in an exam scenario. Instead...

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