Firstly, we have to realize that we cannot solve this problem without knowing the radius of the iris. because from the information given, the radius of the iris could well be the size of the galaxy and contract from width of 4mm to 2mm and we wouldn't know!

The average radius of the iris is 6mm, so we take this value.

Now, initially the width of the iris is 4mm, that means the radius of the pupil is:

$6mm-4mm=2mm$

Therefore it's area $A$ is:

$A=\pi r^2=\pi (2)^2=4\pi$

When the iris contracts to 2mm, the radius of the pupil becomes:

$6mm-2mm=4mm$

Then it's area is $A$ :

$A=\pi r^2=\pi (4)^2=16\pi$

To find how many times greater this final area is than the initial area, we just divide it by the initial area:

$\frac{16\pi }{4\pi } =4$

This is 4 times greater than the initial area.

3 0

3 years ago

Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin?

Alex777 [14]

Answer:

$\frac{1}{2}x + 16 = 36$

40 comic books

Step-by-step explanation:

Let x be the Jill comic books.

Given:

Jill sold half of her comic books and then bought sixteen more. She now has 36.

$\frac{1}{2}\ (Jill\ books) + 16\ more\ books = 36$

$\frac{1}{2}\ (x) + 16 = 36$

$\frac{1}{2}x + 16 = 36$

Therefore the algebraic equation of the given statement.

$\frac{1}{2}x + 16 = 36$ --------(1)

Now we solve above equation for x.

Subtract by 16 both side of the equation 1.

$\frac{1}{2}x + 16 -16 = 36 -16$

$\frac{1}{2}x = 20$

Multiply by 2 both side of the above equation.

$2\times \frac{1}{2}x =2\times 20$

$x = 40$

Therefore, Jill had 40 comic books.

8 0

3 years ago

Help please? It’s math.

Umnica [9.8K]

Answer:
X = 7/5
when the value of x is 7/5 the equation will be true
Step-by-step explanation:
To fine the value of x that makes the equation true, we equate the expression to zero to find the value of x.
Check attachment for processes
Therefore when the value of x is 7/5 the equation will be true

8 0

3 years ago

A vehicle uses 1 7/8 gallons of gasoline to travel 56 1/4 miles. At this rate, how many miles can the vehicle travel per gallon

sweet [91]

Answer:

30 miles

Step-by-step explanation:

In this context, "per" means "divided by", so to find miles per gallon, divide miles by gallons:

(56 1/4 mi)/(1 7/8 gal) = 30 mi/gal

The vehicle can travel 30 miles per gallon of gas.

_____

My calculator divides mixed numbers directly, as many graphing calculators do. If you're working this out by hand, you can convert to improper fractions, then multiply the numerator by the inverse of the denominator.

(56 1/4)/(1 7/8) = (225/4)/(15/8)

= (225/4)·(8/15) = (225/15)·(8/4)

= 15·2 = 30

4 0

3 years ago