geno3141

V  =  pi · r² · h

V  =  pi · 2² · 60

V  =  753.6 cu cm  for each rod

192 rods  =  192 · 753.6  =  144,691.2 cu cm

In factored form:  3774  =  2 · 3 · 17 · 37

Creating two two-digit numbers:  3 · 17  =  51  and 2 · 37  =  74.

So, the two numbers are:  51  and  74.

The smaller is ...

If the glass holds  x  ounces of water and if it is  3/4s  full, then  (3/4)·x  =  6

Multiply both sides by 4:    3x  =  24.

Divide both sides by 3:        x  =  8.

If it sells at the rate of 14 gal in 3 hrs, it is selling at the rate of 14/3 gal per hour

In 3 8-hour days, there are 24 hours.

Selling at the rate of 14/3 cal per hour:  (24 hr) x (14/3 gal/hr)  =  112 gal.

The volume of the original aquarium is 9" x 13" x 14'  =  1638 cu in.

It is filled in 3 minutes:  1638 cu in / 3 min  =  546 cu in per min.

An aquarium that is 21" x 25" x 35" contains 18 375 cu in.

Filling at the rate of 546 cu in per min  (18,375 cu in) / (546 cu in / min)  =  33.65 min (approximately)

Multiply by the common denominator, multiplying and simplifying throughout, and taking all terms to one side:

x⁶ - 28x⁴ - 14x³ + 147x² + 14x - 120  =  0

Checking possible solutions, these become the solutions:  -4, -3, -1, 1, 2, 5.

The number of degrees in the interior angles of a hexagon is 720°.

Since the hexagon is equiangular, each interior angle is 120°.

Therefore, each exterior angle of the hexagon is 60°.

This means that each one of the exterior triangles created on the hexagon is an equilateral triangle.

The sum of the two exterior sides of each triangle is equal to twice the length of the side of the hexagon.

Since the perimeter of the hexagon is 15, the sum of the sides created on the exterior of the hexagon is twice this, or 30.

The areas of two similar polygons (and all regular pentagons are similar polygons) has the same ratio as the squares of the corresponding sides.

One-fifth of 250  =  (1/5) x 250  =  50.