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Express 2 cos x – sin x in the form Rcos( x + a ), where R and a are constants, R > 0 and a is between 0 and 90 ° Give the exact value of R and give the value of to 2 decimal places.

2cosx - sinx = Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a) Implying 2cos(x)=Rcos(x)cos(a) Rcosa = 2 Similarly: Rsin(a) = 1 Therefore tan(a) = 1/2 Meaning a=26.57 Degrees R 2 (sin 2 a+cos 2 a)=5 Implying, given s...
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Answered by Thomas O. • Maths tutor
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Write a function that checks whether a number is prime or not.

Depending on the student level I would accept a simple answer such as: (cannot format code) or expect a more complex answer with optimization such as sieve of Eratosthenes
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Answered by Aimilios C. • Python tutor
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Explain the main criticisms that have been made of the World Trade Organization. (15 marks)

WTO (originally the GATT), is an organisation, set up during the Bretton Woods Conference of August 1944, that attempts to liberalise world trade and prevent a slide to protectionism that was seen during the...
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A particle is moving along a straight line. The fixed point O lies on this line. The displacement of the particle from O at time t seconds is s metres where s = 2t3 – 12t2 + 7t(a) Find an expression for the velocity, v m/s, of the particle at time t.

To find velocity you differentiate displacement with respect to time Therefore ds/dt = v = (3x2)t 2 -(12x2)t 2 +7 Implying v = 6t 2 -24t+7
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Answered by Thomas O. • Maths tutor
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Give the prime factorisation of 630

630 = 5 x 126 126 = 2 x 63 63 = 7 x 9 9 = 3 x 3 so 630 = 2 x 3 2 x 5 x 7
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Answered by Annie D. • Maths tutor
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