Question 1186180
Write each fraction in terms of the LCM of the denominators.
{{{15/((16a^3b^3))}}}, {{{17/((30a^5b))}}}
LCM: {{{240a^5b^3}}} so we have
{{{((15a^2(15)))/((240a^5b^3))}}} = {{{((225a^2))/((240a^5b^3))}}}
and
{{{((8ab^2(17)))/((240a^5b^3))}}} = {{{((136b^2))/((240a^5b^3))}}}
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2.) The Water Cube was built in Beijing, China, to house the National Swimming Center for the 2008 Olympics.
 Although not actually a cube (its height is not equal to its length and width), the Water Cube is designed to look like a "cube" of water molecules.
The volume of the 31-meter-high Water Cube is 971,199 m3.
Find the length of a side of its square base.
Base is square and height 31,
therefore
31b^2 = 971199
b^2 = 971199/31
b = {{{sqrt(31329)}}}
b = 177 meters
the dimensions: 177 by 177 by 31
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3.) A square piece of cardboard is formed into a box by cutting 10-centimeter squares from each of the four corners and then folding up the sides, as shown in the figure below.
 If the volume V of the box is to be 81,000 cm3, what size square piece of cardboard is needed?
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let s = length and width of the cardboard, 
Removing the 10 cm squares reduces the cardboard dimension by 20
The height is give as 10
(s-20)^2 * 10 = 81000
simplify, divide by 10, then square the sides
s^2 - 40s + 400 = 8100
s^2 - 40 + 400 - 8100 = 0
s^2 - 40s - 7700 = 0
Use the quadratic formula a=1, b=-40,c=-7700, but this will factor
(s-110)(s+70) = 0
positive solution
s = 110 cm the length of the square base
Dimensions of piece of cardboard; 110 by 110
Box dimensions: 90 by 90 by 10
 Check
(110 - 20)^2 * 10 = 81000 cu/cm