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A sequence increases by 5 each time and the first term is x. The sum of the first four terms is 54. Set up and solve an equation to work out the value of x.

The first term is x, and if it increases by 5 each time then the second term is x+5, third is x+10, and the fourth is x+15. Adding these values together we get 4x+5+10+15, and this equals 54. Therefore; 4x+3...
TP
Answered by Tom P. • Maths tutor
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The work in an office takes 200 hours to complete every week. Each person in the office works 35 hours a week. What is the smallest number of people needed to complete the work?

To answer this question we need to divide the hours needed to complete work (200) by how much a person works a week (35). The key aspect of this question that catches people out is that when dividing 200 by ...
TP
Answered by Tom P. • Maths tutor
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What is Homeostasis?

Homeostasis is the maintenance of a constant internal environment within the body . This sounds quite confusing but don’t panic – in simpler terms, homeostasis is the process which works to keep the conditio...
YW
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Prove that the function f:ZxZ -> ZxZ defined by f(x,y) = (2x+y,x+y) is a bijetion.

Here, we must remember the definition of a bijection. To be bijective, a function must be both injective and surjective. For a function to be injective, we must have that f(a) = f(b) implies that a = b. For ...
FS
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Use l’Hôpital’s rule to find lim(csc(x) - cot(x)) as x -> 0.

This question relies partially on remembering the trigonometric identities, csc(x) = 1/(sin(x)) and cot(x) = 1/(tan(x)) = cos(x)/sin(x). Plugging these values into the equation, we want to find Lim((1-cos(x)...
FS
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