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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 ...
RY
Answered by Rachel Y. • Maths tutor
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What is negative feedback in terms of homeostasis?

To regulate a number of processes in the body, there needs to first be recognition of current levels in order to respond in the appropriate way. For example there is a temperature "norm" (~36.9°C),...
CD
Answered by Charlotte D. • Biology tutor
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What is homeostasis?

This is the way that the body maintains a stable internal environment, which is vital for correct functioning of the cells in the body. For a stable environment there are several things which need to be regu...
CD
Answered by Charlotte D. • Biology 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...
TK
Answered by Tom K. • Maths tutor
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Describe how restriction enzymes are used to cut out DNA fragments

Restriction enzymes cut at specific sequences named palindromic sequences. These are unique as they read the same in opposite directions. A specific palindromic sequence is complementary to a specific restri...
AC
Answered by Abigail C. • Biology tutor
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