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The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2 passes through the origin and has gradient -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.

First, find equations for the 2 lines in the standard cartesian form y=mx+c:L1: To find gradient = dy/dx = change in y/change in x = (y2-y1)/(x2-x1) = (2-6)/(12-4) = -4/8 = -0.5 = m To find intercept use gra...
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Answered by Hugo F. • Maths tutor
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Differentiate y=3x^4 with respect to x

First we "bring the power down", that is, multiply by the power. Secondly, we subtract 1 from the power.Our answer is then dy/dx = 4*3x^(4-1) = 12x^3
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Answered by Ella B. • Maths tutor
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(x+2)/(x-3) - (x-1)/(x+3) can be written in the form (ax+b)/(x^2-9). Work out the value of a and the value of b.

Recall that in order to add and subtract fractions, they must have the same denominator. Therefore, we multiply the first fraction by (x+3)/(x+3) and the second fraction by (x-3)/(x-3) to create a common den...
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Answered by Hannah P. • Maths tutor
5657 Views

Solve the simultaneous equations 5x + y = 21, x - 3y = 9

Method 1 - By Elimination: Firstly, understand that in order to eliminate a variable, the coefficient needs to be the same for the variable in both equations. We can eliminate the x variable by multiplying t...
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Answered by Rahil V. • Maths tutor
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Simplify (2sin45 - tan45)/(4tan60) and leave your answer in the form of (sqrt(a)-sqrt(b))/c

To answer this question we need to remember the exact trig values.A trick I use for remembering these is the hand rule .For this you label any one of your hands with the set angles starting at your pinky fin...
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Answered by Isabella K. • Maths tutor
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