If you buy a computer directly from the manufacturer for $ 3 , 500 and agree to repay it in 60 equal installments at 1.75 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
If you buy a computer directly from the manufacturer for $ 3 , 500 and agree to repay it in 60 equal installments at 1.75 % interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
If you buy a computer directly from the manufacturer for
$
3
,
500
and agree to repay it in
60
equal installments at
1.75
%
interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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