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A ball, dropped vertically, falls d metres in t seconds. d is directly proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How many metres does the ball drop in the next 7 seconds?

d = kt². 45 = k x 3². 45 = k x 9 (/9). 5 = k.3+7 = 10 seconds total as we are investigating the NEXT 7 seconds. d = kt². d = 5 x 10². d = 5 x 100d = 500m in 10 ...

Answered by Emily N. • Maths tutor

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A curve is defined by the parametric equations x = 3^(-t) + 1, y = 2 x 2^(t). Show that dy\dx = -2 x 3^(2t).

Write 3^(t) as an expression involving x : We can rewrite x = 3^(-t) + 1 as x - 1 = 3^(-t) ; equivalently, 3^(t) = (x-1)^(-1). Substitute this expression into y, to write y in terms of x: y = 2 x 3^(t) = ...

Answered by Maleeha K. • Maths tutor

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expand and simplify (x+1)(x-1)

first begin by expanding the brackets using the CLAW method (shown using whiteboard diagram)multiply the first of each bracket together, we get x²multiply the first term of the first bracket an...

Answered by Adam T. • Maths tutor

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root3 (root6 + root12) can be written as Aroot2 + B

root3 (root6 + root12) (root3 * root6 ) + (root3 +root12) = root18 + root36= (root9 + root2) + 6= 3root2 +6a= 3 b = 6

Answered by Dorcus M. • Maths tutor

3266 Views

Write down the expansion of (cosx + isinx)^3. Hence, by using De Moivre's theorem, find cos3x in terms of powers of cosx.

First, we expand by using binomial expansion (it is always helpful to draw Pascal's triangle to find each term's coefficients): 1 1
1 2 1
1 3 3 1
Since the function is raised to the...

Answered by Hiro F. • Maths tutor

12090 Views