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It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.

(i) Let f(x) = A/(x-1) + B/(x 2 +9). Multiplying through by (x-1)(x 2 +9) we get x 2 +9x = A(x 2 +9) + B(x-1). By substituting x=1 in to eliminate B, we find that A=1 , and by equating coefficients, B=9. Hen...
AC
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Find the square roots of 2 + isqrt(5)

Since we’re finding the square roots of 2 + isqrt(5) then (x+iy)^2 = 2 + isqrt(5)Thereforex^2 + 2ixy - y^2 = 2 + isqrt(5)Take real and imaginary parts it followsx^2 - y^2 = 2 and 2ixy = isqrt(5)solving this ...
SL
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How to multiply and divide by complex numbers

Multiplying and dividing by complex numbers is very similar to how you have learned how to multiply and divide surds (numbers with a rational and irrational part) in GCSE and early A-Level. Take two complex ...
LC
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Work out the gradient of the curve y=x^3(x-3) at the point (3,17)

First simplify the equation of the curve y= x^4 - 3x^3 .The gradient is the differential.To differentiate, bring down the power and take one from it.x^4 becomes 4x^3-3x^3 becomes (-3x3)= -9x^2dy/dx= 4x^3 - 9...
SM
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A particle is projected from the top of a cliff, 20m above the sea level at an angle of 30 degrees above the horizontal at 20m/s. At what vertical speed does it hit the water?

Using SUVAT equations:s = -20mu = 20sin(30) = 10m/sv = ?a = -9.8m/s^2t = ?v^2 = u^2 + 2asv = sqrt(100 + 40x9.8)= 22.2m/s
AR
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