Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with...
Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with −?2<?≤?2−π2<θ≤π2 for the
following Cartesian coordinates:
(a) If (?,?)=(18,−10)(x,y)=(18,−10) then
(?,?)=((r,θ)=( , )),
(b) If (?,?)=(7,8)(x,y)=(7,8) then
(?,?)=((r,θ)=( , )),
(c) If (?,?)=(−10,6)(x,y)=(−10,6) then
(?,?)=((r,θ)=( , )),
(d) If (?,?)=(17,3)(x,y)=(17,3) then
(?,?)=((r,θ)=( , )),
(e) If (?,?)=(−7,−5)(x,y)=(−7,−5) then
(?,?)=((r,θ)=( , )),
(f) If (?,?)=(0,−1)(x,y)=(0,−1) then (?,?)=((r,θ)=( ,))
Consider the relation R defined on the set R as follows: ∀x, y ∈
R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈
R, (x, y) ∈ R if and only if x + 2 > y.
For example, (4, 3) is in R because 4 + 2 = 6, which is greater
than 3.
(a) Is the relation reflexive? Prove or disprove.
(b) Is the relation symmetric? Prove or disprove.
(c) Is the relation transitive? Prove or disprove.
(d) Is it an equivalence relation? Explain.
Let f(x, y) = x^3 − 4xy^2 , x, y ∈ R. Use the definition of...
Let f(x, y) = x^3 − 4xy^2 , x, y ∈ R. Use the definition of
differentiability to show that f(x, y) is differentiable at (2,
1).
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S =
{(y,x),(z,y),(x,z)} on {x, y, z}. a)...
1. Consider the relations R = {(x,y),(y,z),(z,x)} and S =
{(y,x),(z,y),(x,z)} on {x, y, z}. a) Explain why R is not an
equivalence relation. b) Explain why S is not an equivalence
relation. c) Find S ◦ R. d) Show that S ◦ R is an equivalence
relation. e) What are the equivalence classes of S ◦ R?
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 +
y^2= a^2...
Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 +
y^2= a^2 + b^2.
a) Prove S in an equivalence relation
b) compute [(0,0)], [(1,2)], and [(-3,4)].
c) Draw a picture in R^2 representing these three equivalence
classes.