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Solve the simultaneous equations: 6x + 2y = -3, 4x - 3y = 11

(1) 6x + 2y = -3 (2) 4x - 3y = 11 Multiply by 3 so that the coefficients of y are the same 3 x (1) 18x + 6y = -9 3 x (2) 8x - 6y = 22 Add these 2 together to eliminate y 26x = 13 Divide by 26 to get x x = 1/...
DH
Answered by David H. • Maths tutor
6793 Views

Prove that sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)

We know that 1. sin(a+b) = sin(a)cos(b)+sin(b)cos(a) and 2. sin(a-b) = sin(a)cos(b)-sin(b)cos(a) Add equations 1. and 2. sin(a+b)+sin(a-b) = 2sin(a)cos(b)+sin(b)cos(a)-sin(b)cos(a) = 2sin(a)cos(b) Let x=a+b ...
AV
Answered by Anna V. • Maths tutor
37711 Views

The points A and B have coordinates (3, 4) and (7, 6) respectively. The straight line l passes through A and is perpendicular to AB. Find an equation for l, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

For the line passing through A and B: m = (y2-y1)/(x2-x1) = (-6-4)/(7-3) = -5/2 For the perpendicular line: m = -1/(-5/2) = 2/5 y - y1 = m*(x - x1) >> y - 4 = (2/5)*(x - 3) >> 5y - 20 = 2x - 6 &g...
DA
Answered by Deji A. • Maths tutor
12768 Views

Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where x = 3

y = (3x 4 - 18)/x The gradient of a tangent to a curve is equal to dy/dx However, we must simplify this equation before we can differentiate it; y = 3x 3 - 18/x = 3x 3 - 18x -1 dy/dx = 3(3x 2 ) - (-1)(18x -2...
RO
Answered by Rachel O. • Maths tutor
5157 Views

Find the difference between the areas of these 2 shapes to 2 decimal places. Rectangle (width 4cm length 2.5cm) Circle (diameter 2.4) use pi = 3.14

Rectangle: Area = width x length hence area = 4cm x 2.5cm area = 10cm 2 Circle: Area = pi x radius 2 Radius = 1/2 x diameter Radius = 1.2cm Area = 1.2 2 x 3.14 Area = 1.44 x 3.14 Area = 4.5216 Difference bet...
LH
Answered by Lyam H. • Maths tutor
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