Tutor profile: Jugal V.

Solve the simultaneous equation 3x + 4y = 24 4x + 3y = 22

here multipy eq 1 by 4 we get ----> 12x + 16y = 96 multiply eq 2 by 3 we get ---> 12x + 9y = 66 now subtract ecq 2 from eq 1 7y = 30 y = 30/7 therefore x = 16/7

A 230V , 50 Hz supply is given to the RL circuit with R = 100 ohm and L = 1 H. Calculate the current through the circuit and the power consumed.

R = 100 ohm , $$X_{L}$$ = $$2\pi$$fL = 314.159 ohm The total impedance Z = 100 + 314.159 = 414.159 ohm $$\phi$$ = $$tan^-1(X_{L}$$/R) = 72.34 Current I = V/Z = 100/414.159 = 0.241 A P = VIcos$$\phi$$ = 230*0.241*0.3033 = 16.81 Watt

If $$x^3 + Y^3 = 9$$ and x + y = 3 , Find the value of $$x^4 + y^4$$.

We know that $$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$$ Therefore, 9 = 3$$(x^2 - xy + y^2 )$$ 3 = $$(x^2 + 2xy + y^2 - 3xy)$$ 3 = $$(x + y)^2 - 3xy$$ 3 = 9 - 3xy 2 = xy Therefore, substitute $$ x^4 + y^4 = (x^2 + y^2)^2 - 2(xy)^2$$ = $$((x + y)^2 - 2xy))^2 - 2(xy)^2$$ = $$(9 -(2*2))^2 - 2(4)$$ = 25 - 8 = 17