Question

Please help me with these questions!! Thank you!!

Answer 1

Answer:

Step-by-step explanation:

Left Frame

Formula

Area of Hexagon = 3*sqrt(3)*a^2 / 2

Area of a Square = a^2

In both cases a is a side length

Givens

A = 384*sqrt(3)

Solution

384*sqrt(3) = 3*sqrt(3)*a^2 / 2     Divide by sqrt(3) on both sides.

384 = 3 * a^2 / 2                           Multiply by 2

768 = 3 * a^2                                Divide by 3

256 = a^2                                     Take the square root of both sides

a = 16

Each side of the square will be = a

The area of the square = a^2

a^2 = 16^2 = 256

Center Frame

I don't know how to expand the question so that I'm doing some sort of step-by-step explanation. The question just means what does a equal when t = 0

The answer is 15.

Right Frame

The tangents meet the circumference of the circle at a 90o angle when the radius is connected by the point of  contact. Call the central angle (LON) = x

The two tangents and the two radii form a kite which is a quadrilateral.

All quadrilaterals have 4 angles that add up to 360.

x + 90 + 90 + 60 = 360           Combine the like terms on the left

x + 240 = 360                           Subtract 240 from both sides

x = 360 - 240

x = 120

The length of the arc is given by (Central angle / 360) * Circumference

x is the central angle so the central angle = 120

Length = (120 / 360) * 96

Length = 1/3 * 96

Length = 32