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The supply function for the production of good A is P=50+45Q. The demand function is P= 100-5Q. Find the equilibrium price and quantity.

At P Qe supply equals demand so we set equations equal to each other and solve as symoltaneous equations: 50+45Q=100-5Q then 50Q=50 so Q e =1. By plugging Q=1 into our supply function we get P Qe =95.
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Answered by Peter K. • Economics tutor
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Find two values of k, such that the line y = kx + 2 is tangent to the curve y = x^2 + 4x + 3

There will be intersection when x^2 + 4x + 3 = kx + 2. Our goal is to find the values of k which would only give one solution to this quadratic equation, which would make the lines 'tangent' to each other. F...
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Answered by Andrew N. • Maths tutor
35841 Views

Calculate the kinetic energy of a proton moving at 95% of the speed of light. (c = 3x10^8 m/s, m_p = 1.67x10^-27 kg) [4 marks]

KE = 0.5mv 2 [1] v = 3x10 8 * 0.95 = 2.85x10 8 [1] KE = 0.5 * 1.67x10 -27 * (2.85x10 8 ) 2 [1] KE = 6.782 x10 -11 J [1]
TF
Answered by Tom F. • Physics tutor
7411 Views

Describe what is meant by the following musical textures: 1) homophonic, 2) polyphonic, 3) call and response.

Homophonic texture is when the music sounds 'as one', such as block chords, where all instruments change notes at the same time. Polyphonic means 'many sounds'. The instruments playing may all have different...
TF
Answered by Tom F. • Music tutor
18845 Views

Factorise the following expression: 2(x^4) + 4(x^2) - 32(x^3)

2x 2 (x 2 + 2 - 16x)
TF
Answered by Tom F. • Maths tutor
3425 Views