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Solve the simultaneous equations: 3x+2y = 11, 2x-5y=20

Firstly, solving simultaneous equations finds the point(s) where two lines on a graph meet. They can either be two linear equations (finding one point of intersection), a linear and a quadratic (can have two...
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Answered by Olivia C. • Maths tutor
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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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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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Find the equation of the straight line which passes through the points (3,1) and (-1,3)?

The equation of a line is y=mx+c. The first step is to find m, which is the gradient. This is found by dividing the change in the y values, by the change in x values. So in this case, the gradient would be (...
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Answered by Joel P. • Maths tutor
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