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 y' = 2x. At x = 2, y' = 2(2) = 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.

Rousseau's social contract theory argued for the importance of individual freedom and the idea that legitimate political authority comes from the collective will of the people.

The percentage of silt is given as 30%.

The percentage of silt in the soil is given as 30%.

The active voice focuses on the doer of the action. Here, 'the choir' is the doer, so it becomes 'The choir sang the song.'

The Speaker of the Lok Sabha is elected by the members of the Lok Sabha.

The word 'optimism' suggests a positive outlook, which aligns with the context of a captivating speech.

An engaging presentation typically requires an enthusiastic and dynamic tone, making option 1 the best fit.

The combination of humor and sadness suggests a 'bittersweet' tone.

Frustration typically aligns with sarcasm, making 'sarcastic' the most fitting option.

The word 'enthusiastic' describes a lively and engaging tone, which would indeed captivate an audience.

The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C.

The specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1 degree Celsius.

Standard deviation is unaffected by adding a constant. Therefore, new SD = 5.

Variance is the square of the standard deviation. Therefore, variance = 5² = 25.

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 context suggests a holistic benefit of exercise, making option 1 the most logical completion.

The conclusion drawn from the study suggests a positive relationship between physical activity and academic performance, supporting option 1.

The word 'resistance' indicates that the employees opposed the change, which fits the context of feeling blindsided.

The word 'unforeseen' suggests that the factors were unexpected, which aligns with the context of the price increase.

An increase in technology use typically transforms perceptions rather than regresses or stagnates them.

The sum of the angles in any triangle is always 180 degrees.