11 (Combinatorics] Prove by mathematical induction that every n-member set has 2" subsets. (Hint: In step B, when a new member is added to a k-member set, every subset of the resulting (k 1member set either contains the new member, or does not contain it.)

Q: Sx9'de 1. Integrate:

A: Given :

Q: Sinvy dy 3.

A: 3 Given integral is ∫lnydy. We have to evaluate the given integral. Use integration by part formula,…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.