Explanation

This is an example of the associative property of multiplication:

  a × (b × c) = (a × b) × c

So, 8 × (6 × 7) = (8 × 6) × 7

Explanation

If the original cable breaks at a stretch of 2 mm, each half will have half the length and thus half the maximum stretch:

Maximum stretch for half = 2 mm / 2 = 1 mm.

Explanation

a^2 (-2b)^2 = a^2 × 4b^2 = 4a^2b^2

Explanation

After 3 half-lives, the mass remaining is calculated as:

Mass remaining = Initial mass / 2³

= 160 μg / 8

= 20 μg

Explanation

Dull means سست

Brilliant means شاندار

Interesting means دلچسپ

Explanation

The X-axis and Y-axis intersect at the point (0, 0), known as the origin.

It is the central reference point in the coordinate plane.

Explanation

Restoring force 𝐹 = −𝑘𝑥 depends on displacement 𝑥.

At the mid position, x = 0, so restoring force is minimum (zero).

Explanation

Step 1: Convert binary numbers to decimal for easier calculation

(101)2 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0 = 4 + 0 + 1 = 5

(110)2 = 1 × 2^2 + 1 × 2^1 + 0 × 2^0 = 4 + 2 + 0 = 6

Step 2: Add the decimal values

5 + 6 = 11

Step 3: Convert the sum back to binary

11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0 = (1011)2

Explanation

LCM of two prime numbers is their product, since they have no common factors other than 1.

So, LCM(a, b) = a × b when both a and b are prime.

Explanation

The energy density (u) in a capacitor is given by:

u = ½ε₀E²

Where:

- ε₀ is the permittivity of free space

- E is the electric field intensity between the plates

This shows that the energy density is proportional to the square of the electric field intensity (E²).