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What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?

cos( AOB ) = a.b /(| a | x | b |) a.b = (6i - j + 3k) . (-4i + 2j + 10k) = (6 x -4) + (-1 x 2) + (3 x 10) = -24 + -2 + 30 = 4 (| a |)^2 = 6^2 + (-1)^2 + 3^2 = 36 + 1 + 9 = 46 -> | a | = 46^(1/2) (| b |)^2...
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Answered by David H. • Maths tutor
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Solve the simultaneous equations 3x + 4y = 17 and 4x + y = 14

Eq1: 3x + 4y = 17 Eq2: 4x + y = 14 Eq2 x 4: 16x + 4y = 56 Subtract Eq1 from this to isolate x: 16x + 4y - 3x - 4y = 56 - 17 Simplify: 13x = 39 Solve for x: x = 3 Substitute x into Eq1: 3(3) + 4y = 17 9 + 4y ...
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Answered by David H. • Maths tutor
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What is the median, upper quartile and lower quatile. How do we find them?

The easiest way to explain this would be to use an examplar question. For example: Ben is given a sequence of numbers and is told to find the median, lower quartile and upper quartile. 1,4,5,6,8,9,11,12,14,1...
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Answered by Daniella B. • Maths tutor
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What is the fraction of blue beads?

A tin contains red, white and blue beads in the ratio red:white:blue = x:2x:x^2 First we should find the total number of beads in the tin: x + 2x + x^2 = 3x + x^2 The number of blue beads is x^2 So the fract...
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Answered by Rheanne B. • Maths tutor
7673 Views

How many people chose A?

In a survey people had to choose either A, B, C or D. The percentage of people that chose B, C and D are shown here: B- 25% C- 35% D- 30% You are also told that 150 people chose B. How many chose A? So first...
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Answered by Rheanne B. • Maths tutor
6594 Views