A 35-mm camera allows you to control the diameter d of the aperture by changing the f-stop, which varies inversely with the diameter according to the formula equals f=44 over d . a. if f =4, find the diameter. b. if the diameter is quadrupled, by what factor will the f dash stop change? c. the radius r is one-half of the diameter. describe the proportional relationship between the radius and the diameter. d. area a is proportional to the radius squared according to the equation a equals pi r^2. what is the equation that relates area and diameter? e. what is the equation that relates area and f-stop?

a) 11

b) Factor of 1/4

c) r = d/2

d)

e)

Step-by-step explanation:

Part a)

The relation between F dash stop and the diameter of the aperture is given by:

We have to find the value of diameter, if F = 4. Substituting F = 4 in above equation, we get:

This means, if f-stop is at F=4, the diameter of the aperture would be 11 mm.

Part b)

Let the new diameter be represented by d' and new F-stop by F'. Since, the diameter is quadrupled, the new diameter is 4 times the previous one. i.e.

d' = 4d

Now, the formula of F' with new diameter will be:

Using the value of d', we get:

This means, the dash stop will change by a factor fo 1/4 when the diameter is quadrupled.

Part c)

Radius is defined as one half of the diameter. If r represents the radius, the relation between radius r and diameter d can be expressed as:

Part d)

Area of lens (Circle) is given as:

Using the value of r from previous part, we get:

Part e)

In order to find the relation between Area and F-stop, we replace the value of d with its equivalent expression in terms of Area.

From the previous part:

Using this value of d, in formula of F, we get:

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680

a - base

b - exponent

so,