# fall 2013 – MTH 138 – final exam instructor

fall 2013 – MTH 138 – final

exam

instructor: M.Schmidtová

100 minutes, no notes, no books, only calculators are allowed

_________________________________________________________________________

NAME: score:

50 /

All calculations must be included,

if only results are written they will not be graded.

FORMULAS

ar.as=ar+s ar_as=ar-s .0/msohtmlclip1/01/clip_image002.gif”>

a-n=1/an (an)m=an.m .0/msohtmlclip1/01/clip_image004.gif”>

(ab)n=an.bn (a/b)n=an/bn .0/msohtmlclip1/01/clip_image006.gif”>

(a+b)(a-b)=a2-b2

(a+b)2=a2+2ab+b2 (a+b)3=a3+3a2b+3ab2

+b3

(a-b)2=a2

-2ab+b2

(a-b)3=a3-3a2b+3ab2+b3

x3+y3=(x+y)(x2-xy+y2)

x3-y3=(x-y)(x2+xy+y2)

.0/msohtmlclip1/01/clip_image008.gif”> a(x-x1)(x-x2)=ax2+bx+c

Vx=

-b/(2a)

COMBINATORICS/Counting

Pk(n)=n! : (n-k)!

P’k(n)= nk

Pn(n)=n!

P=n! : (n1!.n2!. … .

nr!)

.0/msohtmlclip1/01/clip_image010.gif”>

.0/msohtmlclip1/01/clip_image012.gif”>

STRAIGHT LINES

y-y1=m.(x-x1)

y=mx+b

ax+by+c=0

Only formulate both

linear programming problems. Do NOT solve them. Give the objective function and all

constraints. [4pts]

a) A company knows that they have to produce

at least 25000 gears and 14500 axles. They have two machines that they can use

to fill these orders. The first costs $2000 per hour to operate and can produce

1000 gears and 300 axles per hour. The second costs $2400 per hour to operate

and can produce 600 gears and 600 axles per hour. How many hours should each

machine operate and what is the minimum cost?

[NOTE: Use letters X

and Y to represent unknown variables]

b) A furniture manufacturer makes two types of

coffee tables. A circular table requires 3h of skilled labor and 6h of

unskilled labor and produces a profit of $50. A rectangular table requires 2h

of each type of labor and yields a profit of $30. If 90h of skilled labor and

120h of unskilled labor are available for a week, determine how many of each

type of table should be made in order to maximize the profit. [NOTE: Use letters X and Y to represent unknown variables] [4pts]

Solve the system of

linear inequalities graphically: [9pts]

.0/msohtmlclip1/01/clip_image014.gif”>

NOTE: Number each straight line with

corresponding number of inequality. The final solution set

must be highlighted/cross-hatched. Identify/calculate

all vertices of feasible set. Do not give too small figure, you have the entire

page for it. Use ruler if possible.

Twelve graduate students have applied for three available teaching

assistantships. In how many ways can the assistantships be awarded among

these applicants [2+2+3pts]

a) if no preference is given to any student?

b) if one particular student must be awarded

an assistantship?

c) if the group of applicants includes seven

men and five women and it is stipulated that exactly 2 men and one woman must

be awarded an assistantship?

____________________________________________________________________________________

A company car that has a seating capacity of five is to be used by

five employees. How many possible seating arrangements are there if:

[2+3pts]

a) all five can drive?

b) only three employees can drive?

_____________________________________________________________________________________

Find number of all 6-digits numbers

that can be formed using digits 1, 2, 3, 4, 5, 6,7 with conditions that

repetitions are not allowed and first and last digit has to be even. [4pts]

Graph 3x+2y-9=0.

[2+1pts]

a) Be sure values of x- and y-intercepts are

displayed in the graph.

b) What is the slope of line displayed in a)?

______________________________________________________________________________________

Solve the quadratic

equation by any method:2×2− 7x+ 3

= 0 [4pts]

____________________________________________________________________________________

Write the

slope-intercept form

of the equation of the line p that

passes through the point [-2;1] and is perpendicular to the line q: 6x+3y-5=0. [4pts]

**30%**with the discount code: ESSAYHELP