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-qbkr21
Hi guys!
We had to solve 15 problems for Hw in my math class, but I wasn't able to get these problems... Please help, I have a vague idea how to solve them, but I don't trust my answers. I need this by 9am on the 18th.
1) Find the edge of a cube if an increase of 3cm,, in one dimensione and 6cm in another, and a dec. of 2cm in the third, doubles the volume.
2) How long is the edhge of a wooden cube if, after a slice of 1cm thick is cut from one side, the volume of the remaining solid is 100 cubic cm?
3) The dimensions of a blovk of metal are 3cmby 4cm by 5cm. if each dimension is incresed by the same number of inches, the colume of the block becomes 3.5 times its original volume. How many centimeters were added to each dimensions??
4) A box has dimensions 12cm by 4cm by 4cm. If the first 2 dimnsions are decreased and the other dimension is increased by the same amount.. a second box is formed and its volumje is 5/8 the volume of the first box. Determine the dims of the second box
Thank you so much for all the help!!
Let x be the length of a side of the original cube. Then the original volume of the cube is V = x^3. Now we know that
2V = (x + 3)(x + 6)(x - 2)
2x^3 = (x + 3)(x^2 + 4x - 12) <-- Multiplying the last two factors
2x^3 = x^3 + 7x^2 - 36
x^3 - 7x^2 + 36 = 0
There is evidently a way to factor this beast, but not knowing how we can only do this numerically (disregarding the Cardano method) and I get:
x = -2, 3, 6
We may disregard the negative solution immediately. So we have TWO solutions:
x = 3 cm gives a rectangular prism l = 6 cm, w = 9 cm, h = 1 cm
and
x = 6 cm gives a rectangular prism l = 9 cm, w = 12 cm, h = 4 cm
-Dan
Let x be a side of the original cube. We cut a 1 cm by x by x slice of the cube off and the new volume is 100 cm^3. So:
(x - 1)x^2 = 100
x^3 - x^2 - 100 = 0
Again, I don't know how to factor this, so we are left with numerical methods. I get x = 5 cm as the only real solution.
-Dan