The product of the slopes of the lines can be found from the equation. Here, the product of the slopes is given by -c/a, where c is the coefficient of xy and a is the coefficient of x^2.

For the lines to be perpendicular, the condition 4 - 4(3)(2) = 0 must hold, leading to k = 0.

The product of the slopes of the lines represented by ax^2 + bxy + cy^2 = 0 is given by c/a. Here, c = 2 and a = 3, so the product is 2/3.

The lines are coincident when the determinant of the coefficients is zero, leading to k = 0.

The nature of the intersection can be determined by the slopes, which indicate that the angle is obtuse.

The angle can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes derived from the equation.

The sum of the slopes of the lines is given by -b/a, which is 0 in this case.

The nature of the roots can be determined by the discriminant of the quadratic equation.

The lines are not perpendicular as the condition for perpendicularity is not satisfied.

The condition for the lines to be real and distinct is that the discriminant D must be greater than 0.

For the lines to be perpendicular, the condition a + b = 0 must hold.

For the lines to be coincident, the constant term must be zero.

If the magnetic field around a closed loop is constant, the current through the loop must also be constant according to Ampere's Law.

In a uniform magnetic field, the magnetic field lines are straight and parallel.

The force on a charged particle is directly proportional to the magnetic field strength, so if the magnetic field strength is doubled, the force also doubles.

According to Faraday's law, the induced EMF is directly proportional to the rate of change of magnetic flux, which depends on the magnetic field strength.

The magnetic force on a charged particle is given by F = qvB sin(θ). If the magnetic field strength B is doubled, the force F also doubles, assuming charge q and velocity v remain constant.

Magnetic flux is given by the product of magnetic field strength and area. If the magnetic field is doubled, the magnetic flux also doubles.

According to Lenz's law, the induced current will flow in the opposite direction to oppose the increase in magnetic flux.

If the magnetic field is increasing at a constant rate, the induced EMF is also increasing, which means the induced current is increasing.

The gravitational force acting on the satellite will double if its mass is doubled, as gravitational force is directly proportional to mass.

The period T = 2π√(m/k). If m is doubled, T increases.

Gravitational potential energy U = m * V = 10 * (-30) = -300 J.

Gravitational potential energy U = mgh = 5 * 10 * 10 = 500 J.

The gravitational potential energy U = mgh will double if the mass m is doubled at constant height h.

Gravitational potential energy is directly proportional to mass and inversely proportional to distance, so it halves.

The gravitational potential energy U = mgh is directly proportional to the mass, so if the mass is halved, the potential energy also halves.

Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.

Percentage error = (absolute error / measured value) * 100 = (0.2 / 10.0) * 100 = 2%.

Percentage error = (absolute error / measured value) * 100 = (0.5 / 50) * 100 = 1%.