kountryboye25
03.09.2020 •
Mathematics
1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a plane.b) a line.c) a circle.d) a point.2) What does the equation y + 3x = 2 represent in R^3? a) a plane.b) a circle.c) a line.d) a point.What does z - 4y = 8 represent? a) a line.b) a circle.c) a point.d) a plane.What does the pair of equations y = 2, z = 8 represent? In other words, describe the set or points (x, y, z) such that y = 2 and z = 8. a) a line.b) a circle.c) a plane.d) a point.
Solved
Show answers
More tips
- A Auto and Moto What to expect from the new VW Golf 7?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- S Style and Beauty How to Get Rid of Peeling Nails: Natural Remedies...
- S Science and Technology Understanding Magnetic Storms: A Guide to This Natural Phenomenon...
- F Family and Home What is Most Important in Men s Lives?...
- G Goods and services Which TV is better - LCD or Plasma?...
- C Computers and Internet Are there special gaming mice?...
- G Goods and services LED-подсветка в LCD-телевизорах: 5 причин, почему она лучше других технологий...
- C Computers and Internet Keep Your Mouse Pad Clean: The Right Way to Clean It?...
Answers on questions: Mathematics
- M Mathematics Forty minus two times a number....
- M Mathematics According to a 2012 report, 68.5 % of all US adults still have a landline telephone service for which they pay. Given the rise of cell phone use, an employee for a local telephone...
- M Mathematics I need a answer please...
- H History Why the issue of slavery wasn’t constitution...
- B Biology What field of science are homologous structures used as evidence for? ?...
- C Chemistry A sample of solid NH 4HS is placed in a closed vessel and allowed to equilibrate. Calculate the equilibrium partial pressure (atm) of ammonia, assuming that some solid NH 4HS remains....
- M Mathematics What is the binary number for 23...
- C Chemistry The eye is connected to the brain by nerves. A. True B. False...
Ответ:
The equation represents in R^2 c) a line
The equation represents in R^3 a) a plane
The equation represents in R^3 a) a plane
The equation represents d) a plane
The pair of equations represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , with ∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set we will have only one free variable in R^2 (which is a line in R^2). Therefore, represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set we will have only two free variables (y and z) and will represent a plane (which have two dimensions) in R^3.
2) The equation in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
Ответ: