serafimharmane4944
14.07.2019 •
Mathematics
Write the appropriate rotation formulas so that in a rotated system the equation has no x'y'-term. 10x2 - 4xy + 6y2 - 8x + 8y = 0
Solved
Show answers
More tips
- G Goods and services How to Choose a Video Camera: Tips from Professionals...
- F Family and Home How to Remove Tar Stains: Tips and Recommendations from Experts...
- H Health and Medicine Novomin: What is it and how to use it?...
- P Philosophy Unbelievable stories of encounters with otherworldly forces...
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- H Health and Medicine How to Treat Whooping Cough in Children?...
- H Health and Medicine Simple Ways to Lower Cholesterol in the Blood: Tips and Tricks...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
Answers on questions: Mathematics
- M Mathematics Pls hel Add the mixed numbers 9 3/5 + 10 3/5, write the answer as a mixed number....
- M Mathematics Triangle DEF is shown on the coordinate grid below triangle DEF is reflected across the Y axis which role best describes this transformation...
- M Mathematics Look at dis in 4K like 4K HD...
- M Mathematics In order, range, median, mode and mean. Round the mean to the nearest tenth. PLS HELP ASAP...
- M Mathematics Donavan records his height each month for a year. The equation of the line that models the data is y= 0.212 + 61.4, where y represents Donavan s height, in inches, after 3 months....
- M Mathematics Which characteristic(s) doesn t belong for Absolute Value Functions. -Straight lines -Always has a Maximum or Minimum -Horizontal Symmetry -Increases and decrease -Continuous...
- M Mathematics 1. In a vacuum, the wavelength of light from a laser is 630 nm (630 x 10 m). What is the frequency of the light?...
- M Mathematics Elaine is 28 years older than Carly. Elaine is x years old. Carly is y years old. Which set of equations shows this situation? * O x = y + 28, y = x + 28 x = y + 28, y = x - 28 x =...
- M Mathematics Toni wants Max to paint one side of the fence the same color of the house. The paint covers 200 square feet per gallon. The stockade fence has a height of 6 feet, each panel has a...
- M Mathematics Is the motion rigid or nonrigid...
Ответ:
x = x' cos (π/8) + y' sin (π/8)
y = -x' sin (π/8) + y' cos (π/8)
Step-by-step explanation:
Canonical form of conics section:
A*x^2 + B*x + C*y^2 + D*y + E*x*y + F = 0
We want that in the rotated system the equation has no x'y'-term. To do this the rotated angle has to satisfy:
tan(2 θ) = E/(C - A)
The rotation formula when the coordinates system rotates an angle θ are:
x = x' cos θ + y' sin θ
y = -x' sin θ + y' cos θ
The conic section is: 10*x^2 - 4*x*y + 6*y^2 - 8*x + 8*y = 0, then:
A = 10
B = -8
C = 6
D = 8
E = -4
F = 0
So,
tan(2 θ) = -4/(6 - 10)
2 θ = tan^-1 (1)
θ = (π/4)*(1/2) = π/8
Finally,
x = x' cos (π/8) + y' sin (π/8)
y = -x' sin (π/8) + y' cos (π/8)
Ответ:
the answer is 250.
by: nicholas