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.

Explanation

To find acceleration, we use the formula:

a = (v - u) / t

where:

v = final velocity = 15 m/s

u = initial velocity = 10 m/s

t = time = 4 seconds

a = (15 - 10) / 4

= 5 / 4

= 1.25 m/s²

Explanation

In SHM, total energy (kinetic + potential) remains constant if no external force or damping is present.

Though kinetic and potential energy change with time, their sum stays the same throughout the motion.

Explanation

When a nitrogen nucleus is hit by an alpha particle, it can produce oxygen and a proton.

This was observed in early nuclear reactions, such as Rutherford's experiment.

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

Imperative sentences change to indirect speech using verbs like "ordered" or "told" (depending on tone).

Since it's a command to a servant, "ordered" is the most appropriate verb.

Explanation

Commutative property means the order doesn’t matter: 𝐴 ∗ 𝐵 = 𝐵 ∗ 𝐴.

Union ∪ is commutative, so 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴.

Explanation

In ax² + bx + c = 0, if > 0, b > 0, and c > 0, the parabola opens upward and lies entirely above the x-axis unless discriminant D = b² - 4ac ≥ 0.

If real roots exist, they are negative because both b and c are positive.

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 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.