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S= 0.5n(n+1) ( formula for the sum of the first n natural numbers) 0.5K(K+1)= 300 ( sub in K and make the formula equal to the total sum given) 0.5K(K+1)-300= 0 ( take away 300 from both sides) ...

First step is to take away 12 from both sides of the equation:5a + 12 = 37 (-12) 5a = 25 Second step is to then divide both sides by 5:5a = 25(÷5) Which gives you the final answer:a = 5

dy/dx = 2x - 2 -12x^-1/2dy/dx = 02x - 2 - 12x^-1/2 = 0x = 4 (stationary point)d²y/dx²= 2 + 6x^-3/2when x=4, d²y/dx²= 11/411/4 >...

Student will need to understand that the turning point will be a minimum as the curve is positiveStudent should complete the square:1) factorise out the 2: 2(x² + 7/2 x) - 82) complete the squa...

The second derivative is just two derivatives carried out back to back. In this case we just have to differentiate this function once, and then differentiate the result. The derivative of 2e^(2x) can then...