Explanation

During the migration from Makkah to Medina, the Holy Prophet (PBUH) and Hazrat Abu Bakar Siddique (R.A) took shelter in the Cave of Soor

On September 24, 622, the prophet Muhammad completes his Hegira, or “flight,” from Mecca to Medina to escape persecution.

Explanation

The equation z = a + 2by + 2bxy will be true when the terms containing b are zero, which happens when b = 0.

Explanation

• The vector ax(bxc) is the cross product of vector a and the cross product of vectors b and c.
• This resulting vector is perpendicular to vector a and vector (bxc), which is parallel to vector c.
• Therefore, ax(bxc) lies in the plane containing vectors a and c.

Explanation

The action of wearing socks and shoes commute.

Explanation

• In a group (G, *), the binary operation * is defined such that for all a, b ∈ G, a * b ∈ G.
• This means that the result of combining any two elements of the group using the group operation is always an element of the group.

Explanation

The set of integers, Z, forms a group under addition.

Explanation

Square root is a unary operation because it takes only one argument or input, whereas addition and multiplication are binary operations that require two inputs.

Explanation

The p-series is a series of the form:

1 + 1/2^p + 1/3^p + 1/4^p + ...

The p-series is convergent if p > 1. If p ≤ 1, the series is divergent.

Explanation

The formula for the volume of a solid of revolution around the x-axis is π ∫[a, b] (f(x))^2 dx, where f(x) is the function being rotated, and a and b are the limits of integration.

Explanation

• A convergent sequence in a metric space is bounded.
• This means that the sequence has a finite limit, and all terms of the sequence are within a finite distance from this limit.
• As a result, the sequence is bounded, meaning it has a finite upper and lower bound.