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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
36020 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]
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Answered by Tom F. • Physics tutor
7567 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...
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Answered by Tom F. • Music tutor
19083 Views

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

2x 2 (x 2 + 2 - 16x)
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Answered by Tom F. • Maths tutor
3510 Views

Can two shelves of 0.72 meters long each store 50 30mm wide textbooks?

First, convert the units so you can compare more easily. 0.72m = 72cm = 720mm So 1 shelf is 720mm and 1 textbook is 30mm wide. To find the maximum number of books that can be stored on a shelf, you divide th...
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Answered by Valerie L. • Maths tutor
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