Explanation

The perimeter of a rectangle is given by:

P = 2(length + width)

= 2(4 + 3)

= 2 × 7

= 14

Explanation

An infinite geometric series converges (has a finite sum) only if the absolute value of the common ratio, |r|, is less than 1. If |r| ≥ 1, the series diverges, meaning it does not approach a finite sum. 

Explanation

limₓ→0 (sin(ax) / sin(bx))

Divide the numerator and the denominator by x:

= limₓ→0 [(sin(ax)/x) ÷ (sin(bx)/x)]  

= (a/b) × limₓ→0 [sin(ax)/(ax)] ÷ [sin(bx)/(bx)]

As x → 0, sin(kx)/(kx) → 1, so:

Answer: a / b

Explanation

The notation 7 ∈ Sr (5) indicates that point 7 belongs to the circle Sr (5), which means it is on the circle.

Since point 7 is on the circle, the distance between the center (point 5) and point 7 is equal to the radius r.

The correct answer is d(5,7) < r.

Explanation

The area  𝐴 of an equilateral triangle with side length 𝑎 is calculated using the formula  𝐴 = 3/4 𝑎^2.

This formula derives from the general area formula for triangles and takes into account the properties of equilateral triangles.

Explanation

• The trigonometric identity for cos(3a) is: cos(3a) = 4cos^3(a) - 3cos(a)
• This can be proved using the angle sum and difference formulas for cosine.

Explanation

The sine function, f(x) = sin(x), is an odd function because it has the property: f(-x) = -f(x).

Explanation

formula Area = s x s
It is not correct. 3×4=12 square ft

Explanation

cosecθ − cotθ = (1 - cosθ) / sinθ

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.