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Points P and Q are situated at coordinates (5,2) and (-7,8) respectively. Find a) The coordinates of the midpoint M of the line PQ [2 marks] b) The equation of the normal of the line PQ passing through the midpoint M [3 marks]

a) For finding the midpoint M, the point M must be equidistant from P and Q in both the x and y axes. Hence, we consider the x and y axis separately. The midpoint of the x coordinates is essentially a mea...

Answered by Justin U. • Maths tutor

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The gradient of the curve at A is equal to the gradient of the curve at B. Given that point A has x coordinate 3, find the x coordinate of point B.

We are told f(x) = (2x-5)^2 (x+3).In part b) we are asked to show that f'(x) = 12x^2 -16x -35, so for part (c) we shall assume this definition for f'(x). We are told that the x coordinate for A is 3. Call...

Answered by Thomas F. • Maths tutor

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Solve x(5(3^0.5)+4(12^0.5))=(48^0.5) to the simplest form. (4 Marks)

The aim of the question is to equate x= into an expression.Step 1. Look to see if you can simplify the equation. On the left hand side of the equation you can see that 3 is a factor of 12. And also a fact...

Answered by Richard C. • Maths tutor

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If a ball is dropped from 6m above the ground, how long does it take to hit the floor and what is its speed at impact (assuming air resistance is negligible)?

Distance, s = 6m ; initial speed, u = 0 m/s ; final speed, v = v m/s ; acceleration, a = 9.8 m/s (g) ; time, t = t sTime:s = ut + 0.5at² , 6 = 0 + (0.5 x 9.8)t² , 6 = 4.9t²

Answered by Rebecca R. • Maths tutor

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Given ∫4x^3+4e^2x+k intergrated between the bounds of 3 and 0 equals 2(46+e^6). Find k.

Sorry I couldn't write the question properly in the question box. The question should read:Given ∫³₀4x³+4e^2x+k dx = 2(46+e⁶)Find K.Step 1- Intergrate...

Answered by Charlie M. • Maths tutor

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