Explanation

To find the inverse of 3 in modulo 7, we need to find a number x such that:

3x ≡ 1 (mod 7)

We can try multiplying 3 by each number from 1 to 6:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9 ≡ 2 (mod 7)

3 × 4 = 12 ≡ 5 (mod 7)

3 × 5 = 15 ≡ 1 (mod 7)

So, the inverse of 3 in modulo 7 is 5.

Explanation

Abstruse means غیر معمولی

Concealed means پوشیدہ

Explanation

Brawl means جھگڑا

Agree means متفق ہونا

Explanation

"Called off" means to cancel or stop something, which fits the context of a strike being canceled.

Example: "The strike was called off after negotiations."

مذاکرات کے بعد ہڑتال کو بلایا گیا۔

Explanation

Using Vieta's formulas, we know that α + β = 4/2 = 2 and αβ = 5/2.

Now, α^2β + αβ^2 = αβ(α + β) = (5/2)(2) = 5.

Explanation

Explanation

Copious means متعدد

Sparse means ویرل

Explanation

For matrices A × B ≠ B × A in general, so matrix multiplication is not commutative.

However, matrix addition is commutative and associative, and matrix multiplication is associative, but not commutative.

Explanation

Explanation

1. Pipe A fills the tank in 15 minutes (rate = $\frac{1}{15}$ per minute).

2. Pipe B fills the tank in 20 minutes (rate = $\frac{1}{20}$ per minute).

3. Combined rate: $\frac{1}{15}+\frac{1}{20}=\frac{7}{60}$ per minute.

4. Time taken together: $\frac{1}{\frac{7}{60}}=\frac{60}{7}$ minutes.