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Line AB, with equation: 3x + 2y - 1 = 0, intersects line CD, with equation 4x - 6y -10 = 0. Find the point, P, where the two lines intersect.

Let eqn. 1 be: 3x + 2y - 1 = 0 & Let eqn. 2 be: 4x - 6y -10 = 0 Multiply eqn. 1 by a factor of 3, and add the two eqautions together. (This eliminates y from the equation) This gives: 9x + 6y - 3 = 0 + 4...
KS
Answered by Kris S. • Maths tutor
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A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates of the points where this line intersects the axes

M=3 y1=1 x1=2 y-y1=m(x=x1) y-1=3(x-2) y-1=3(x-2) y-1=3x-6 y=3x-6 at the x axis, y=0. ‘Sub in to find the x co-rdinate: 0=3x-5 3x=5 x=5/3 (5/3, 0) at the y axis, x=0 y=(0X3)-5 y=-5 (0,-5)
AC
Answered by Anna C. • Maths tutor
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A football is kicked at 30 m/s at an angle of 20° to the horizontal. It travels towards the goal which is 25 m away. The crossbar of the goal is 2.44 m tall. (A) Does the ball go into the goal, hit the crossbar exactly, or go over the top?

With questions about projectiles, such as a ball travelling in the shape of a parabola through the air as in the above question, it is always good to split the problem into the horizontal and vertical compon...
ES
Answered by Ehsaan S. • Maths tutor
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Differentiate x^cos(x) and find the derivative of cosec^-1(x)

for part a) let y=x cos(X) , the ln(y)=ln (x cos(X) )=cos(x)ln(x), thus d/dx (ln(y(x)) = d/dx (cos(x)ln(x)), 1/y*dy/dx=cox(x)/x - sinxlnx => solve for dy/dx => y'(x)=x cos(X) (cox(x)/x - sinxlnx) b) d/...
HP
Answered by Hari P. • Maths tutor
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integrate 1+ln(x) with respect to x

Integrate ln(x) by parts with u=ln(x) and dv/dx=1 Gives x+xln(x)-x+c Therefore xln(x)+c
CM
Answered by Christopher M. • Maths tutor
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