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Why is the derivative of inverse tan(x) 1/(1+x^2)?

This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first princ...
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Answered by Neel G. • Maths tutor
7015 Views

Simplify x^2 - 9x + 20

Firstly write out the equation x 2 - 9x + 20 = 0. The aim is to find two numbers that multiply to make 20 and add up to make -9. Look at the constant without any x's , in this case it is 20. We need to work ...
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Answered by Amrit M. • Maths tutor
6812 Views

Mike has 4 blue balls, 6 green balls and 10 yellow balls what is the probability that he will pick a yellow ball.

It would be worked out by adding 4+6+10 to get 20 and then it would be number of yellow balls over total number of balls which would be 10/20. Depending on ability this may then be simplified down to 1/2.
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Answered by Georgia E. • Maths tutor
2639 Views

The diagram shows a garden in the shape of a rectangle. All measurements are in metres. The length of the rectangle: 4+3x and the width of the rectangle: x+6. The perimeter of the garden is 32 metres. Work out the value of x

Perimeter of a rectangle is the sum of all the sides. Therefore: 2(4+3x) + 2(x+6) = 32. Then, you expand: 8+6x+2x+12=32. Then, 8x+20=32. Finally, 8x=12, meaning that x=3/2.
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Answered by Sayakki P. • Maths tutor
15987 Views

How do you solve an equation like x^2+3x-4=0

There are many ways of solving this equation, which is called a second order polynomial (where the order describes the highest power of x), let's focus on the most general for now: the quadratic formula. For...
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Answered by Victor L. • Maths tutor
3640 Views