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Show that the area bounded by the curve, (x/2)^2 /3 + (y/4)^2/3 = 1 is 3π.


  • Find the area of the surface of the solid formed by the revolution the curve, x=a(θ - sinθ) and Y=a(1- cosθ) about x-axis (y=0).

Find the volume of the solid formed by revolving the curve, r=a(1+cosθ), about the initial line.


Find the volume of the solid generated by revolving about the x-axis by the curve, y2 = 9x and the line y = 3x


A voltage source 𝑣(𝑡)=240 sin(314.16𝑡−20v°)𝑉 is connected to a load having an toa load having an impedance of Z. The resulting current through the load is 𝑖(𝑡)=15 sin(314.16𝑡+22.5°)A. Determine the circuit power factor and identify the elements that constitute the load, given that Z comprises of only two elements connected in series.


An electrical load operates at 120 Vrms The load absorbs an average of 8 kW at .lagging power factor of 0.8 The effective current I rms is:


select one:

a. 43.48 A 

b. 41.67 A 

c. 90.91 A 

d. 83.33 A 

e. 45.45 A


The current in a series circuit of R = 50 and L= 50 mH lags the applied voltage by 80 °,the angular frequency w is:


 Select one:

 a. 945 rad/s

 b. 473 rad/s

 c. 709 rad/s

 d. 405 rad/s

 e. 567 rad/s


An electrical load operates at 240 V rms. The load absorbs an average of 8 KW at lagging power factor of 0.6 The reactive power Q is:


 Select one:

а. 6.48L25.84°Ω

b. 5.04L45.57°Ω

с. 4.32L53.13°Ω

d. 5.76L36.87°Ω

е. З.бL60°Ω


A voltage V, =220L 30° Volt in a 3 phase ABC sequence system .Find VB:

A. 220 L-90° V

B. none of these

C. 220L -120° V

D. 220 L150° V


A 2000V, 100KW, 9000 rpm series connected DC motor has an armature resistance of 6Ω and a negligible field resistance.


(a) Determine the armature current at the rated load.


(b) Determine the copper loss at the rated load.


(c) Determine the mechanical loss knowing that the no-load armature current is 7 A at a speed of 9000 rpm.


(d) Determine the full load mechanical torque delivered to the load at a speed of 9000 rpm.


(e) Determine the efficiency of the motor.


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