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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: 9...

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

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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 com...

f'(x)=( sqrt (x^2+1) - x * ( x / sqrt (x^2 +1) ) ) / (x^2+1) = (x^2 + 1 + x^2) / ( (x^2 + 1) * sqrt ( x^2 + 1) ) =  1 / ( (x^2 + 1) * sqrt (x^2 + 1) ). 

f'(x) > 0 for any x => f is increasing...

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 =>...