Your iris controls the amount of light that enters your eye by changing the size of your pupil. An eye is shown resembling a large circle. The pupil of the eye is marked resembling a smaller circle inside the large circle. The iris of the eye surrounding the pupil is also marked. The radius of the large circle is labeled 6 millimeters. The distance between the large circle and the small circle is labeled x. a. Write a polynomial in standard form that represents the area of your pupil. Write your answer in terms of $\pi$ . Area = mm $^2$ b. The width $x$ of your iris decreases from 4 millimeters to 2 millimeters when you enter a dark room. How many times greater is the area of your pupil after entering the room than before entering the room?

(b) 4 times

Step-by-step explanation:

The question is illustrated with the attached figure

Solving (a): The area of the pupil

First, we need to calculate the radius (r) of the pupil.

Since the smaller circle is the pupil, then

Area is then calculated as:

Solving (a): The area of the pupil

First, we need to calculate the radius (r) of the pupil.

Since the smaller circle is the pupil, then

Area is then calculated as:

Solving (b): How many times greater is the area of the pupil, if x decreases from 4 to 2

Initially,

So, the area of the pupil is:

When x reduces to 2, the area of the pupil is:

Calculate the ratio (r) of both areas:

Hence, it is 4 times greater

345

step-by-step explanation:

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.