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Tom thinks of a number. He squares it, adds 3 times the original number and then subtracts 18. The result is 0. What two numbers could Tom have been thinking of?

Formulate the problem algebraically:x²+3x-18=0This is a factorisation problem. To find the solutions, factorise:-Factors of x² are 1 and 1, so answe...

Answered by George H. • Maths tutor

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Explain the role of the Loop of Henle in the absorption of water from the glomerular filtrate

After the filtrate in the nephron undergoes Selective Reabsorption in the Proximal Convoluted Tubule, it then travels to the Loop of Henle. The Loop of Henle is a ‘U’ shaped structure found in the Medulla...

Answered by Akshee A. • Biology tutor

17688 Views

Prove that the square of an odd number is always 1 more than a multiple of 4

This is a nice little question off the 2018 Edexcel Higher Maths paper! When we heard the word 'prove' in a question at this level, automatically we should be thinking about using algebra to help us out! ...

Answered by Thomas R. • Maths tutor

3327 Views

Describe how regulators maintain a constant body temperature?

Receptors in the skin send messages to the hypothalamus in the brain which then sends nerve impulses to effectors around the body. Examples of effectors include sweat glands, blood vessels and muscles. Th...

Answered by Katie S. • Biology tutor

1274 Views

Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.

We use the product rule with u=x and v=ln(x) (so u'=1 andv'=1/x) to differentiate xln(x) to ln(x)+1, and -x just differentiates to -1, hence we have. f'(x)=ln(x).
Now note that ln(x^3)=3ln(x) using p...

Answered by Matthew J. • Maths tutor

3027 Views