The potential gradient is given as 0.6 V/m, which is the calibration value for the potentiometer.

The balancing length is calculated as L = V / (potential gradient) = 2V / 4 V/m = 0.5 m.

If the enthalpy of a system increases, the process is considered endothermic.

An increase in enthalpy indicates that the system is gaining heat.

A negative enthalpy change indicates that the reaction releases heat, making it exothermic.

An increase in entropy indicates that the process is spontaneous, as per the second law of thermodynamics.

If entropy increases, ΔG decreases, making the reaction more favorable.

To solve for x, subtract 3 from both sides to get 2x = 8, then divide by 2 to find x = 4.

Rearranging the equation to y = -2/3x + 2 shows that the slope is -2/3.

Substituting x = 1 gives 2(1)^2 + 3(1) + k = 0 => 2 + 3 + k = 0 => k = -5.

Using Vieta's formulas, k = 2*1*(-2) = -4.

Using Vieta's formulas, r1 + r2 = -b/a = -3/2.

To find the y-intercept, set x = 0. The equation becomes -3y + 6 = 0, leading to y = 2.

'm' represents the slope of the line in the slope-intercept form of a linear equation.

To find the x-intercept, set y = 0. The equation becomes 0 = -1/2x + 3, leading to x = 6.

Substituting x = 4 into the equation gives y = -1/2(4) + 3 = -2 + 3 = 1.

'm' in the equation of a line represents the slope, which indicates the steepness and direction of the line.

In the equation y^2 = 4px, p = 3, hence the value of 'p' is 3.

Rewriting the equation in standard form gives (x^2/16) + (y^2/9) = 1, so semi-major axis a = 4 and semi-minor axis b = 3.

Using Vieta's formulas, p = -(2 + 3) = -5.

For equal roots, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 => 25 - 4k = 0 => k = 25/4 = 6.25.

The equilibrium constant for the reverse reaction is the reciprocal of the forward reaction, so Kc' = 1/Kc = 0.1.

A Kc value greater than 1 indicates that the products are favored at equilibrium.

For the reverse reaction, Kc is the reciprocal of the forward reaction. Therefore, Kc (reverse) = 1/Kc (forward) = 1/10 = 0.1.

A Kc value less than 1 indicates that at equilibrium, the concentration of reactants is greater than that of products, thus reactants are favored.

The term is given by C(n, 3) * a^2 * x^3. Setting C(n, 3) * a^2 = 15 gives n = 6.

In the term x^4y^2, the sum of the exponents (4 + 2) must equal n, hence n = 6.

The sum of the exponents in the term x^4y^3 is 4 + 3 = 7, hence n must be 7.

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

The equation y = k/x represents a family of hyperbolas.