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How do radians work? Why can't we just keep working with degrees in school?

Degrees are a made up unit; mathematicians simply decided that a complete revolution of a circle has 360 degrees, without that number actually meaning anything. Tecnically any number could have been picke...

HD
Answered by Hans D. Maths tutor
1808 Views

Given f(x) = 3 - 5x + x^3, how can I show that f(x) = 0 has a root (x=a) in the interval 1<a<2?

In plain english, we need to show that there is a value of x, which we call "a", in the interval 1 < a < 2 where f(a)=0. To prove this we start by letting x = 1: f(1) = 3 - 5(1) + 13<...

GP
Answered by Giorgos P. Maths tutor
7224 Views

When given an equation with both letters and numbers on each side of the equals sign, for instance 4x +3 = 5x - 3, how do you know what to do first?

With equations like this the most important thing is that you end up with all the numbers on one hand side and all the letters on the other side. People often think there is a 'right' and 'wrong' order to...

SK
Answered by Sophie K. Maths tutor
2874 Views

Solve these simultaneous equations: 2x + y = 7, and 3x - y = 8. Do so by 1) Eliminating an Unknown and 2) Substitution.

  1. The number 'in front of' an unknown is called the Coefficient. When eliminating an unknown, look to see whether the coefficients of x are the same in both equations, or if the coefficients of y are ...
EH
Answered by Ellie H. Maths tutor
3094 Views

(1.) f(x)=x^3+3x^2-2x+15. (a.) find the differential of f(x) (b.) hence find the gradient of f(x) when x=6 (c.) is f(x) increasing or decreasing at this point?

(1.) (a.) f’(x)=3x^2+6x-2

(b.) x=6 gradient=142

(c.) since f’(x)>0 at x=6, the function is increasing.

JE
Answered by Joel E. Maths tutor
3411 Views

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