In the following exercises, plot each point in a rectangular coordinate system.
391.
(a)
(
−
1
,
−
5
)
(b)
(
−
3
,
4
)
(c)
(
2
,
−
3
)
(d)
(
1
,
5
2
)
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Expert Solution
To determine
(a)
Plot given point in the rectangular coordinate system.
Answer to Problem 391RE
Explanation of Solution
Given information:
Ordered pair (−2,0)
Calculation:
Given an ordered pair (−2,0). We must plot this point in a rectangular coordinate system.
The first number of the coordinate pair is x− coordinate, and the second number is the y− coordinate.
Since y=0, The point (−2,0) is on the x− axis.
Now let’s draw this point in a rectangular coordinate system using desmos graph calculator.
Expert Solution
To determine
(b)
Plot given point in the rectangular coordinate system.
Answer to Problem 391RE
Explanation of Solution
Given information:
Ordered pair (0,−4)
Calculation:
Given an ordered pair (0,−4). We must plot this point in a rectangular coordinate system.
The first number of the coordinate pair is x− coordinate, and the second number is the y− coordinate.
Since x=0, The point (0,−4) is on the y− axis.
Now let’s draw this point in a rectangular coordinate system using desmos graph calculator.
Expert Solution
To determine
(c)
Plot given point in the rectangular coordinate system.
Answer to Problem 391RE
Explanation of Solution
Given information:
Ordered pair (0,5)
Calculation:
Given an ordered pair (0,5). We must plot this point in a rectangular coordinate system. The first number of the coordinate pair is x− coordinate, and the second number is the y− coordinate.
Since x=0, The point (0,5) is on the y− axis.
Now let’s draw this point in a rectangular coordinate system using desmos graph calculator.
Expert Solution
To determine
(d)
Plot given point in the rectangular coordinate system.
Answer to Problem 391RE
Explanation of Solution
Given information:
Ordered pair (3,0)
Calculation:
Given an ordered pair (3,0). We must plot this point in a rectangular coordinate system.
The first number of the coordinate pair is x− coordinate, and the second number is the y− coordinate.
Since y=0, The point (3,0) is on the x− axis.
Now let’s draw this point in a rectangular coordinate system using desmos graph calculator.
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Q₁/(a) Let S and T be subsets of a vector space X over a field F such that SCT,show
that whether (1) if S generate X then T generate X or not. (2) if T generate X
then S generate X or not.
(b) Let X be a vector space over a field F and A,B are subsets of X such that A is
convex set and B is affine set, show that whether AnB is convex set or not,
and if f be a function from X into a space Y then f(B) is an affine set or not.
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MUN is a hyperspace of X and condition to get that MUN is not hyperspace of X.
Write with prove
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