A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.
Answers
Answer:
9.856 m
x³ - 36x² + 433x - 1728 = 0
Step-by-step explanation:
A 12 metre tall tree was broken into two parts. It was found that the height of the part which was left standing was the cube root of the length of the part that was cut away. Formulate this into a mathematical problem to find the height of the part which was cut away.
Let sat Cut away Part was x m
Height of tree Standing = 12 - x m
Height of tree Standing = ∛x
=> ∛x = 12 - x
Cubing both sides
=> x = 1728 - x³ - 36x(12-x)
=> x = 1728 - x³ - 432x + 36x²
=> x³ - 36x² + 433x - 1728 = 0
x ≈ 9.856
Or
Let sat Height of tree Standing = x m
Height of Cut away Part = 12 - x m
Height of tree Standing = ∛(12 - x)
=> ∛(12 - x) = x
Cubing both sides
=> 12 -x = x³
=> x³ + x - 12 = 0
Here 12 -x will give Height of tree Standing
x ≈ 2.144
12 -x = 9.856