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Show that the curves r^n=a^n cos(n theta) and r^n=b^n sin(n theta) intersect orthogonally. Question Question Show that the curves r^n=a^n cos(n theta) and r^n=b^n sin(n theta) intersect orthogonally. Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the…

Find the angle between the polar curves r=a(1-cos(theta)) and r=b(1+cos(theta)). Question Question Find the angle between the polar curves r=a(1-cos(theta)) and r=b(1+cos(theta)). Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar curves r=a(1-cos(theta))…

Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Question Question Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar…

Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)). Question Question Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)). Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar…

Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Question Question Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar curves r=a(1-cos(theta))…

Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)). Question Question Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)). Topic Angle between two polar curves Problems Find the angle between the pair of curves r=6cos(theta) & r=2(1+cos(theta)) Find angle between the curves r=a/ (1+cos(theta)) and r=b/ (1-cos(theta)) Find the angle of intersection of the curves r=a(1+sin(theta)) and r=a(1-sin(theta)) Find the angle between the curves r^2 sin(2theta)=4 and r^2=16 sin(2theta) Find the angle between the polar…

A voltage E e^ (-at) is applied at t=0 to a circuit of inductance L and resistance R. Show that the current at any time ‘t’ is E/(R-aL) [e^ (-at)-e^ (-Rt/L)] given that the current is initially zero when t=0. Question Question A voltage E e^ (-at) is applied at t=0 to a circuit of inductance L and resistance R. Show that the current at any time ‘t’ is E/(R-aL) [e^ (-at)-e^ (-Rt/L)] given that the current is initially zero…

The L-R series circuit differential equation acted on by an electromotive force E sin(omega)t satisfies the differential equation L di/dt+Ri = E sin(omega)t. If there is no current in the circuit initially, obtain the value of current at any time ‘t’. Question Question The L-R series circuit differential equation acted on by an electromotive force E sin(omega)t satisfies the differential equation L di/dt+Ri = E sin(omega)t. If there is no current in the circuit initially, obtain the value of current…

An inductance 2 henry (H) and a resistance 20 ohms (Ω) are connected in series with emf E volts (V). If the current is initially zero when t=0, find the current at the end of 0.01 seconds if E=100V. Question Question An inductance 2 henry (H) and a resistance 20 ohms (Ω) are connected in series with emf E volts (V). If the current is initially zero when t=0, find the current at the end of 0.01 seconds if E=100V.…

A series circuit with resistance R, Inductance L and electromotive force E is governed by the differential equation L di/dt+Ri=E, where L and R are constants and initially the current ‘i’ is zero. Find the current at any time t Question Question A series circuit with resistance R, Inductance L and electromotive force E is governed by the differential equation L di/dt+Ri=E, where L and R are constants and initially the current ‘i’ is zero. Find the current at any…

A metal ball is heated to a temperature of 100 degree Celsius and it is placed in water which is at 40 degree Celsius. If in 4 minutes the temperature of the ball is reduced to 60 degree Celsius. Find the time at which the temperature of the ball is 50 degree Celsius Question Question A metal ball is heated to a temperature of 100 degree Celsius and it is placed in water which is at 40 degree Celsius. If…

A body is originally at 80 degree Celsius cools down to 60 degree Celsius in 20 minutes. If the air temperature is 40 degree Celsius, what will be the temperature of the body after 40 minutes? Question Question A body is originally at 80 degree Celsius cools down to 60 degree Celsius in 20 minutes. If the air temperature is 40 degree Celsius, what will be the temperature of the body after 40 minutes? Topic Newton’s law of cooling Problems…

A bottle of mineral water at a room temperature of 72 degree Fahrenheit is kept in a refrigerator where the temperature is 44 degree Fahrenheit. After half an hour, water cooled to 61 degree Fahrenheit.  What is the temperature of the mineral water in another half an hour? How long will it take to cool to 50 degree Fahrenheit? A bottle of mineral water at a room temperature of 72F is kept in a refrigerator where the temperature is 44F.…

If the temperature of the air is 30 degree Celsius and a metal ball cools from 100 degree Celsius to 70 degree Celsius in 15 minutes, find how long will it take for the metal ball to reach a temperature of 40 degree Celsius Question Question If the temperature of the air is 30 degree Celsius and a metal ball cools from 100 degree Celsius to 70 degree Celsius in 15 minutes, find how long will it take for the…

A body in air at 25 C cools from 100 C to 75 C in 1 minute. Find the temperature of the body at the end of 3 minutes Question Question A body in air at 25 C cools from 100 C to 75 C in 1 minute. Find the temperature of the body at the end of 3 minutes Topic Newton’s law of cooling Problems A body in air at 25 C cools from 100 C to 75 C…

Find the Orthogonal trajectories of the family r^n cos(n.theta) = a^n Question Question Find the Orthogonal trajectories of the family r^n cos(n.theta) = a^n Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Using the…

Show that the family of parabolas y^2=4a (x+a) is self-orthogonal Question Question Show that the family of parabolas y^2=4a (x+a) is self-orthogonal Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find the orthogonal trajectories of the family 2a/r=1-cos(theta) Find the Orthogonal trajectories of the family of curves r^n=a^n cos(n.theta) Using the concept of…

Using the concept of orthogonal trajectories show that the family of curves r=a (sin(theta)+cos(theta)) and r=b (sin(theta)-cos(theta)) intersect each other orthogonally Question Question Using the concept of orthogonal trajectories show that the family of curves r=a (sin(theta)+cos(theta)) and r=b (sin(theta)-cos(theta)) intersect each other orthogonally Topic Applications of Differential Equations Problems of Differential Equations Find the orthogonal trajectories of the family of curves x^2/a^2 +y^2/ (b^2+λ) =1, where λ is the parameter Find the orthogonal trajectories of the family r=a(1+sin(theta)) Find…