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Solve the equation 3sin^2(x) + sin(x) + 8 = 9cos^2(x), -180<X<180. Then find smallest positive solution of 3sin^2(2O-30) + sin(2O-30) + 8 = 9cos^2(2O-30).

Cos^2(x) + sin^2(x) = 1. Therefore Cos^2(x) = 1 - sin^2(x). So equation becomes 3Sin^2(x) + sin(x) + 8 = 9(1 - sin^2(x)). Then becomes 12sin^2(x) + sin(x) - 1This is quadratic equation, solved to (4sin(x)...

JR
Answered by Joshua R. Maths tutor
13462 Views

Solve the simultaneous equations: 4x+5y=13 and 3x-2y=27


Equation 1 is 4x+5y=13 - multiply it by 3, Equation 2 is 3x-2y=27 - multiply it by 4, New equation 1 is 12x+15y=39, New eq...

TD
Answered by Thea D. Maths tutor
3888 Views

Solve the simultaneous equations: (1) x^2 + y^2 = 25 and (2) y - 3x = 13

Sub (2) y = 13 + 3x into (1)x^2 + (13 + 3x)^2 = 25x^2 + 169 + 39x + 39x + 9x^2 = 2510x^2 + 78x + 144 = 05x^2 + 39x + 72 = 0 (/2)572 = 360 - need ab=360 such that a+b=39a = 24 b = 155x^2 + 24x + 1...

MM
Answered by Meghna M. Maths tutor
2671 Views

differentiate 3x^56

=(3x56)x55

MG
Answered by Madalina G. Maths tutor
3490 Views

Square ABCD has length (x+3)cm and area 10cm^2. Show x^2 + 6x = 1

First sketch square ABCD. Split length into 3cm and then xcm for side AB and the same for side AD. Split the area of this square into 4 segments (a, b, c and d) such that a is a 3cm by 3cm square, b and c...

MM
Answered by Meghna M. Maths tutor
4132 Views

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