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Rearranging equations

Quesiton: Solve 10x - 7 = 5x + 3, to find the value of x Answer: x = 0.5 Solution: First you must rearrange the equation so that all the like terms are on the same side: 10x - 5x = 3 +7 5x = 10 Then to find ...
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Answered by Hamid S. • Maths tutor
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f(x) = (4x + 1)/(x - 2). Find f'(x)

Quotient rule: (vu' - uv')/v^2 u = 4x + 1 u' = 4 v = x - 2 v' = 1 Input into formula: [(x - 2)(4) - (4x + 1)(1)](x - 2)^2 Simplify: [4x - 8 -4x - 1]/(x - 2)^2 = -9/(x - 2)^2
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Answered by Salah S. • Maths tutor
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The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

Tangent is parallel, therefore (dy/dx)=0. Find y: y = r sin(x) = 3a(1 + cos(x))(sin(x)) Differentiate y with respect to x dy/dx = 3a[(2cos(x) - 1)(cos(x) + 1)] = 0 Solve equation 2cos(x)- 1 = 0 cos(x) = 1/2 ...
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What characteristics might a perfectly competitive market have? Choose 3 (6 marks)

The first characteristic is that the products are homogenous, meaning there is little difference between the quality of the goods being sold by the individual firms. The second characteristic is that all the...
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Answered by Salah S. • Economics tutor
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A sound wave has a frequency of 500 Hz. The sound wave has a wavelength of 0.34 m in air. Calculate the speed of the sound wave in air?

As we know so far, c = f / λ. This equation comes from a much simpler version of speed = distance/ time. As the λ (with units &quot;m&quot;) can be seen as distance and the frequency (with units &quot;1/s&qu...
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Answered by Reni A. • Physics tutor
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