A wire of length 8x is bent into the shape of a circle. A. Express the circumference of the circle as a function of x. B. Express the area of the circle as a function of x.

Explanation:

Given length is

Circumference of a circle is given as:

a.But the circumference is equal to length of the wire. Therefore circumference as a function of is:

b.Area as function of

Area is calculated as

Rewrite the circumference equation to make r the subject of the formula.

To express area as a function of :-

Therefore area of circle as a function of is

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.