Note that we are trying to minimze this sum for some value of r
S = 9 / (1 - r)
If r = -1/2 the sum is 6
If r = -4/5 the sum is 5
If r = -5/4 the sum is 4
But l r l must be < 1 ......so r = -5/4 isn't allowed
So.....it appears that the sum is minimized to an integer whenever r = -4/5 and the minimized sum is 5
Menards has a 90 yard roll of chain for sale. A tow truck driver needs to purchase 60 feet to pull cars that are disabled. A dog breeder needs 5 chains that are 16 feet each. Then an artist comes in and buys some chain. After his purchase, 1/3 of the original roll is left. How much did the artist purchase, in yards, to the nearest tenth?
90 yards x 3 feet = 270 feet.
270 x 1/3 = 90 feet left
270 - 90 = 180 feet sold
60 feet are sold to tow truck driver.
5 x 16 = 80 feet sold to the dog breeder
60 + 80 = 140 feet sold to dog breeder and tow truck driver.
180 - 140 =40 feet sold to the artist
40/3 =13.3 yards sold to the artist.
Simplify: sqrt( 4x2 / 3y )
sqrt( 4x2 / 3y ) = sqrt( 4x2 ) / sqrt( 3y )
But sqrt( 4x2 ) = 2·| x | Technically, you need to use absolute value bars.
sqrt( 4x2 / 3y ) = 2·| x | / sqrt( 3y )
Now, multiply both the numerator and the denominator by sqrt( 3y )
sqrt( 4x2 / 3y ) = [ 2·| x | · sqrt( 3y) ] / [ sqrt( 3y ) · sqrt( 3y) ]
Since [ sqrt( 3y ) · sqrt( 3y) ] = 3y
sqrt( 4x2 / 3y ) = [ 2·| x | · sqrt( 3y) ] / ( 3y )
Jon has 3 boards that are each 8 feet long. First he makes 3 identical shelves. Then he uses 18 inches to make a bird house. When finished, he has 25% of the original amount left. How much wood was used for each shelf, in feet?
3 x 8 =24 feet - That Jon started with.
25% x 24 = 6 feet left.
24 - 6 = 18 feet used to make 3 shelves and a bird house
18 inches / 12 = 1.5 feet used for the bird house.
18 - 1.5 = 16.5 feet used for the 3 shelves
16.5 / 3 = 5.5 feet used for each of the 3 shelves.