(A) Graph y = 1.2 x − 4.2 in a rectangular coordinate system . (B) Find the x and y intercepts algebraically to one decimal place. (C) Graph y = 1.2 x − 4.2 in a graphing calculator. (D) Find the x and y intercepts to one decimal place using TRACE and the ZERO command.
(A) Graph y = 1.2 x − 4.2 in a rectangular coordinate system . (B) Find the x and y intercepts algebraically to one decimal place. (C) Graph y = 1.2 x − 4.2 in a graphing calculator. (D) Find the x and y intercepts to one decimal place using TRACE and the ZERO command.
(A) Graph
y
=
1.2
x
−
4.2
in a rectangular coordinate system.
(B) Find the
x
and
y
intercepts algebraically to one decimal place.
(C) Graph
y
=
1.2
x
−
4.2
in a graphing calculator.
(D) Find the
x
and
y
intercepts to one decimal place using TRACE and the ZERO command.
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.
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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