The equation can be factored as (x + 1)^2 = 0, giving a double root at x = -1.

The equation can be factored as (x + 2)^2 = 0, giving a double root at x = -2.

Factoring gives (x-1)(x-2) = 0, so the roots are 1 and 2.

If the scalar product is 0, the vectors are orthogonal.

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.

A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12. Solving gives b + c = 6.

A soap bubble adopts a spherical shape because it minimizes the surface area for a given volume, which is energetically favorable due to surface tension.

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Rearranging gives y = (3/4)x + 3. Slope = 3/4.

The derivative f'(x) = cos(x). At x = π/4, f'(π/4) = cos(π/4) = √2/2.

The derivative f'(x) = 3x^2 - 3. At x = 1, f'(1) = 3(1)^2 - 3 = 0, so the slope is 0.

The slopes can be found by solving the quadratic equation derived from the given equation.

Using the quadratic formula, the slopes are found to be -3/5 and -2/5.

The slopes can be calculated using the quadratic formula, yielding -3/5 and -2/5.

The Stefan-Boltzmann Law relates to radiation, stating that the total energy radiated per unit surface area is proportional to the fourth power of the black body's temperature.

The sum of the first n natural numbers is given by the formula n(n+1)/2.

The nth term a_n = S_n - S_(n-1) = (3n^2 + 2n) - (3(n-1)^2 + 2(n-1)). For n=10, a_10 = 32.

Using Vieta's formulas, the sum of the roots is -(-3)/2 = 3/2.

The sum of the roots is given by -b/a = 4/2 = 2. Setting this equal to 3 gives k = 1.

The sum of the roots is given by -b/a = 12/3 = 4.

The sum of the roots is given by -b/a = 7/1 = 7.

Using the sum of roots formula -b/a, we have 4/2 = 2, thus 2 + 1 = 3, so k = 1.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, the sum of the roots is -(-12)/3 = 4.

Using Vieta's formulas, sum of roots = -b/a = 12/3 = 4, hence k = 8.

The sum of the roots is given by -b/a = 7/1 = 7.

The capillary rise method is commonly used to measure surface tension by observing the height to which a liquid rises in a capillary tube.

True value can be in the range of (Measured value - Error) to (Measured value + Error) = 25°C ± 1°C = 24°C to 26°C.

The time period of a satellite in a low Earth orbit is approximately 90 minutes due to its close proximity to the Earth.

If the mass is doubled, the new time period T' = 2π√(2m/k) = √2 * (2π√(m/k)) = √2 * T. Thus, the time period increases.