Explanation

To find g(3), substitute t = 3 into the equation:

g(3) = (3)³ + (3)² - 9(3) - 9

= 27 + 9 - 27 - 9

= 0

Explanation

Explanation

Given the object's speed is 8 m/s after 1 second, we can determine the acceleration due to gravity on this planet is 8 m/s², since it starts from rest (0 m/s).

To find the speed after 3 seconds, we use the formula: speed = initial speed + acceleration × time

Initial speed = 0 m/s (since it's dropped)

Acceleration = 8 m/s²

Time = 3 seconds

Speed after 3 seconds = 0 + 8 × 3 = 24 m/s

Explanation

Surprised and Astonished are synonyms — both mean being amazed.

Likewise, Generosity and Magnanimity are synonyms — both mean kindness and nobility of spirit.

Explanation

The sentence is in the past tense, so the correct verb form is "spoke".

"Spoke" is the simple past tense of "speak," matching the context.

Explanation

The center of gravity is the point where the entire weight of an object appears to act.

It can lie inside or outside the object, depending on its shape (e.g., outside for a ring or hollow sphere).

Explanation

Given f(x) = 6x/(3x - 2)

The denominator cannot be zero:

3x - 2 ≠ 0

3x ≠ 2

x ≠ 2/3

So, the domain of f(x) is all real numbers except x = 2/3.

The answer is R - {2/3}.

Explanation

Step-by-step Solution:

Given numbers:

17, 13, 18, 17, 14, 18, 19, 17, 13, 16, 18, 20

1. Arrange in ascending order:

13, 13, 14, 16, 17, 17, 17, 18, 18, 18, 19, 20

2. Count the numbers:

Total = 12 (even number)

3. Median = average of the 6th and 7th terms:

6th term = 17, 7th term = 17

Median = (17 + 17) / 2 = 17

Explanation

An electric generator converts mechanical energy (like rotation from a turbine) into electrical energy using electromagnetic induction.

The mechanical movement causes a conductor to cut magnetic field lines, generating electric current.

Explanation

Since ΔU = 0 for a cyclic process, Q = W.

The gas absorbs 50 J of energy as heat and does 50 J of work, where Q = W = 50 J.

The best answer is The gas absorbs 50 J of energy as heat and does 50 J of work.