3. In 1535, the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: a tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left standing is the cube root of the length of the part cut away. This problem can be represented by the following system of equations: (x+y = 12 x = ³√y where x is the height of the part left standing and y is the length of the part cut away. a. Use the given system of equations to write one equation that, if solved, gives the height of the part left standing. b. Show that the exact solution is in the interval [2,3]. c. Use Newton's Method to estimate the solution. (I highly suggest you let Desmos do your computations...) d. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact solution: height √2919+54-√√√√2919-54
3. In 1535, the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: a tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left standing is the cube root of the length of the part cut away. This problem can be represented by the following system of equations: (x+y = 12 x = ³√y where x is the height of the part left standing and y is the length of the part cut away. a. Use the given system of equations to write one equation that, if solved, gives the height of the part left standing. b. Show that the exact solution is in the interval [2,3]. c. Use Newton's Method to estimate the solution. (I highly suggest you let Desmos do your computations...) d. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact solution: height √2919+54-√√√√2919-54
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.5: Multiplication With The Addition-or-subtraction Method
Problem 31P
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![3. In 1535, the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: a
tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left
standing is the cube root of the length of the part cut away.
This problem can be represented by the following system of equations:
(x + y = 12
x = ³√y
where x is the height of the part left standing and y is the length of the part cut away.
a. Use the given system of equations to write one equation that, if solved, gives the height of the
part left standing.
b. Show that the exact solution is in the interval [2,3].
c. Use Newton's Method to estimate the solution. (I highly suggest you let Desmos do your
computations...)
d. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact
solution:
√2919 +54 − √√√√2919 – 54
3√9
Find the error and percentage error of your estimate from part (c) using this exact solution.
height:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F263edd0f-32ef-44d4-a9f5-bdc5d66df7b1%2F444e87e8-23bc-468c-9e7e-77faec77d875%2Foja4ocx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. In 1535, the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: a
tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left
standing is the cube root of the length of the part cut away.
This problem can be represented by the following system of equations:
(x + y = 12
x = ³√y
where x is the height of the part left standing and y is the length of the part cut away.
a. Use the given system of equations to write one equation that, if solved, gives the height of the
part left standing.
b. Show that the exact solution is in the interval [2,3].
c. Use Newton's Method to estimate the solution. (I highly suggest you let Desmos do your
computations...)
d. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact
solution:
√2919 +54 − √√√√2919 – 54
3√9
Find the error and percentage error of your estimate from part (c) using this exact solution.
height:
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