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Textbooks are stored on 2 shelves. Each shelf is 0.72m long and each textbook is 30mm wide. Can 50 textbooks be stored on these 2 shelves?

First off, we better convert the 30mm into m. Now, we know that in 1cm there are 10mm. So in 2cm, there are going to 20mm and in 3cm there are going to be 30mm. So each textbook is really 3cm thick. Now, hop...
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Answered by Jack D. • Maths tutor
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What is the difference between differentiation and integration, and why do we need Calculus at all?

We need calculus to find out the properties complex curves that we cannot find with simple arithmetic as we would with linear graphs. Differentiation allows us to calculate the gradient of a curve at a speci...
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Answered by Samuel H. • Maths tutor
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The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0

This is a quadratic equation of the form ax^2 + bx +c, where (t-1)=a 4=b . (t-5)=0 Therefore if there are no real roots, you get that b^2-4ac<0. (using the quadratic formula) First plug in values for a b ...
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Answered by Rachel Y. • Maths tutor
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Question 3 on the OCR MEI C3 June 2015 paper. Find the exact value of Integral x^3 ln x dx between 1 and 2.

This is a good candidate for integration by parts because it is a product of two functions – ln(x) and x^3, and x^3 is easy to integrate. The definition for integration by parts is: integral(u dv/dx) dx = uv...
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Answered by Tom K. • Maths tutor
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Question 3 on the OCR MEI C1 June 2015 paper. Evaluate the following. (i) 200^0 (ii) (9/25)^(-1/2)

For both parts you have to remember some of the properties of powers. Rule 1: x^0 = 1. Rule 2: x^(-n) = 1/(x^n). Rule 3: x^(1/n) = n-th root of x. For part (i) we can use rule 1 to see that 200^0 = 0. For pa...
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Answered by Tom K. • Maths tutor
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