Explanation

Chaotic means افراتفری

Disorderly means بے چین

Explanation

In an arithmetic progression, the sum of n terms between a and b is given by: Sum = n(a+b)/2

This formula uses the first and last terms to find the total of evenly spaced values.

Explanation

To find the sum, we need to calculate each term:

i^101 = i (since i^1 = i and the powers repeat every 4 terms)

i^102 = i^2 = -1

i^103 = i^3 = -i

i^104 = i^4 = 1

Now, let's add them up:

i + (-1) + (-i) + 1 = 0

Explanation

The square root of any prime number is not a perfect square.

Therefore, √𝑝 is irrational, meaning it cannot be expressed as a fraction of two integers.

Explanation

The phrase “went on” followed by a gerund (-ing form) means to continue doing something.

So, the correct structure is: He went on explaining the benefits.

Explanation

The painting was stolen last month by them.

The sentence is in simple past tense (stole).

Passive voice of simple past is formed as:

was/were + past participle, hence:

was stolen.

Explanation

Conduct management refers specifically to the strategies teachers use to prevent and respond to misbehavior and discipline issues.

It is a subset of classroom management focused on student behavior.

Explanation

The Trapezoidal Rule is a numerical method to approximate the definite integral of a function.

It works by dividing the area under a curve into trapezoids instead of rectangles for better accuracy.

Explanation

- f tan xdx = ln[cos x] + C.

This is a standard result from integral calculus involving trigonometric functions.

Explanation

A function is concave down on an interval if its second derivative is negative over that interval.

Graphically, this means the curve bends downward like an upside-down bowl.