Please help!!!!!! + lots of points
2 answers:
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Answer:
The length of each side of the polyhedron, s is 4.142 or
=
Step-by-step explanation:
If we take the distance of the length of the side of the cube where Donatello make the cut to the corner of the cube as x we get the side of length each polyhedron as
x·√2 because we have an hy
Therefore, the original cube had sides of length
10 = 2·x + x·√2
Solving for x we get
Therefore the length of s is x·√2 which gives
The length of each side of the polyhedron, s = 4.142.
Step-by-step explanation:
The quadratic formula is honestly the most straightforward way of solving here.
Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:
1) a=1, b=0, c=8
This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)
2) a=-9, b=4, c=-10
This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.
3) a=1, b=8, c=17
This reduces to x=(-4+i), (-4-i)
So those are the answers for each.