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Two points have coordinates (1,-6) and (-2,3). Find the equation of the line which joins them, and their midpoint.

To find the line's equation, you need the gradient and the y-intercept. The gradient is found using:

(y2-y1)/(x2-x1)

Or simply (change in y direction)/(change in x direction...

Answered by Kara V. • Maths tutor

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Differentiate 4x^2 + 2ln3x + e^x

To differentiate x² you bring the power of x down, then reduce the power of x by 1, so d/dx(x²) = 2x¹

ln3x differentiates to (d/dx(3x))/3x = 3/3x = 1/x

Answered by Thomas M. • Maths tutor

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Differentiate x^2+4x+9.

To differentiate you must look at each term separately. So for x^2 to differentiate we bring the two down to multiply in front of the x and then take one away from the power leaving 2x. For 4x, x is to...

Answered by Iman W. • Maths tutor

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How does the product rule for differentiation work

The chain rule works so that if you have y=f(x)g(x), where f(x) and g(x) are functions of x, dy/dx = f'(x)g(x) + f(x)g'(x)

Answered by Jesse P. • Maths tutor

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A is a function of P . It is known that A is the sum of two parts, one part varies as P and the other part varies as the square of P . When P = 24 , A = 36 and when P = 18 , A = 9. Express A in terms of P .

Let A = aP + bP2 , where a and b are constants.
Sub. P = 24 , A = 36 ,
24a + 576b = 36
2a + 48b = 3 ………… (1)
Sub. P = 18 , A = 9 ,
18a + 324b = 9
2a + 36b = 1 ………… (...

Answered by Chun Yin L. • Maths tutor

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