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What are the solutions of (x^3)+6 = 2(x^2)+5x given x = 3 is a solution?

Firstly we will put this into a form equal to zero, by rearranging to get x 3 -2x 2 -5x+6 = 0. This is because in order to solve a polynomial we first need to set it equal to zero. We now know that the value...
WB
Answered by William B. • Maths tutor
6823 Views

When using the trapezium rule to approximate area underneath a curve between 2 limits, what is the effect of increasing the number of strips used?

Ideally to find the exact area under the curve, we would integrate the function and substitute in the bounds given. However, using the trapezium rule gives an approximation whereby using more trapezia increa...
MM
Answered by Manan M. • Maths tutor
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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
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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
37470 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
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