Top answers

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
4507 Views

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
4245 Views

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
3868 Views

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
3037 Views

A child weighing 50kg is pushed down a 2m long slide (u=0.1), angled at 45 degrees from the horizontal, at 5m/s. At what speed does the child reach the bottom of the slide?

Change in GPE=Change in KE + ResistanceResistance = ForcexDistnaceForce=Friction= R u = mass cos45 g 2 * 0.1Change in KE = 0.5 m*(v 2 -25)Change in GPE = m g 2Sin 45Can cancel down by m (both sides in all pa...
MW
2669 Views