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Using the diagram and your knowledge of vectors, show that BCD is a straight line

BC = BA - CA = (3a - b) - (a + 4b) = 2a - 5b BD = BA + AB = (3a - b) + (a - 9b) = 4a - 10b BC = 1/2 BD. Using basic vector rules, we know that if vectors are multiples, then they are parallel. Since BC and B...
JA
Answered by Jonathan A. • Maths tutor
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Given a spinner divided in 3 sections numbered 1, 2 and 3, and that the arc of section 2 is double that of section one (~57.6 cm), calculate pi to 2 decimal places. The radius of the spinner is 30cm and the angle sub-intended by section 3 is 30 degrees.

Use angle of section 3 to get ratios of arcs: Realise either one of the arcs 1 or 2 will do.Calculate 360-30 / 3 to get 110 degrees for section 1.Calculate ratio of arcs for section 1: 11/36 Find pi: Multipl...
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Answered by Filipe C. • Maths tutor
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Find the equation of the line L passing through (0, 3) and (5, 7). What would the gradient of a line perpendicular to this line be? What about a line parallel to it?

Since L is a straight line between two points, it has the form y=mx+c, where m is the gradient. To find m we use that it is the difference in y values of the points divided by the difference in x values, ie ...
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Answered by Victoria I. • Maths tutor
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A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.

Resolving perpendicular to the plane : R - mg cos30 = 0 . Therefore, R = m g cos30 , where R is the reaction force perpendicular to the plane. Resolving down the plane : ma = m g sin30 - 0.2 R = m g sin30 - ...
MB
Answered by Matthew B. • Maths tutor
6508 Views

Evaluate f'(1) for the function f(x) = (x^2 + 2)^5

First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5. T...
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Answered by Tahrim U. • Maths tutor
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