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Solve the simultaneous equations, make sure to show clear algebraic working: 3x + 5y = 14, 4x + 3y = 4

3x + 5y = 14 (times this entire equation by 3) --> 9x + 15y = 42 4x + 3y = 4 (times this entire equation by 5) --> 20x + 15y = 20Now both of the simultaneous equations have 15y, so you can subtract the...
AT
Answered by Alexander T. • Maths tutor
5801 Views

Express cos(2x) in the form acos^2(x) + b, where a and b are constants.

we first remember the double angle formula, a really important formula. cos(2x) = cos 2 (x) - sin 2 (x).We know that sin 2 (x) + cos 2 (x) = 1, therefore, cos(2x) = cos 2 (x) + cos 2 (x) - 1. Giving our fina...
JP
Answered by Jack P. • Maths tutor
7150 Views

Find the values of x and y for which dy/dx = 0 in y= x^3 - 4x^2 - 3x +2

dy/dx = 3x 2 - 8x - 3 when dy/dx = 0 , 0 = 3x 2 - 8x - 3 Factorise : 0= (3x + 1)(x - 3) when 3x+1 =0 , x = -1/3when x-3=0 , x =3 so x = -1/3 , 3co-ordinates are : (-1/3, 68/27), (3, -16)
MC
Answered by Mahir C. • Maths tutor
6463 Views

Gemma has the same number of sweets as Betty. Gemma gives 24 of her sweets to Betty. Betty now has 5 times as many sweets as Gemma. Workout the total number of sweets that Gemma and Betty have.

Number of sweets = xG=B Gemma and Betty have the same number of sweetsx=x 5(x-24) = x +24 Gemma gives 24 of her sweets to Betty. Betty now has 5 times as many sweets as Gemma.5x - 120 = x + 245x -x = 24 + 12...
KB
Answered by Kate B. • Maths tutor
14253 Views

Simplify 23/5 into a mixed number fraction

23/5 = 4 and 3/5 5 goes into 23, 4 times with a remainder of 3. Therefore, 23/5 is equivalent to 4 and 3/5.
JL
Answered by Jessica L. • Maths tutor
10223 Views