Posted by Karen on Wednesday, October 9, 2013 at 8:30pm.
At the ruins of Caesarea, archaeologists discovered a huge hydraulic concrete block with a volume of 945 cubic meters. The block's dimensions are x meters high by 12x - 15 meters long by 12x - 21 meters wide. What is the height of the block?
I have no idea how to do this. Can someone please help me?
math - Reiny, Wednesday, October 9, 2013 at 9:17pm
remember , volume = lwh
x(12x-15)(12x-21) = 945
simplifying a bit
x(3)(4x - 5)(3)(4x-7) = 945
x(4x-5)(4x-7) = 105
16x^3 -48x^2 +35x - 105=0
by grouping ...
16x^2(x - 3) + 35(x-3) = 0
(x-3)(16x^2 + 35) = 0
x = 3 or x^2 = -35/16 , which is not real
so the only real solution is x = 3
so the block is 3 m high,
math - Karen, Wednesday, October 9, 2013 at 9:22pm
How do you get 105?
math - Reiny, Wednesday, October 9, 2013 at 9:23pm
I divided both sides by 9
notice the (3)(3) is gone on the left side
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