Tutorial 1 – Introduction to Calculus and Linear Algebra
Page 1 of 2
Tutorial 1
Introduction to Calculus and Linear Algebra
Solve Exercises 1 to 6
1.
1
3
2
7
3
=
+
=

y
x
y
x
2.
7
11
3
26
3
4

=

=
+
y
x
y
x
3.
7
3
5
1
12
7
=


=
+
n
m
n
m
4.
x
y
x
y
04
.
0
100
08
.
0
+
=
=
5.
79
.
0
3
.
0
8
.
0
07
.
0
5
.
0
2
.
0
=

=

v
u
v
u
6.
5
4
5
3
7
2
2
3
5
2

=
+
=

y
x
y
x
7.
A chemist has two solutions of hydrochloric acid in stock: a 50% solution and an 80%
solution.
How much of each should be used to obtain 100 milliliters of a 68% solution?
8.
Animals in an experiment are to be kept on a strict diet.
Each animal is to receive,
among other things, 20 grams of protein and 6 grams of fat.
The laboratory technician is
able to purchase two food mixes of the following compositions: Mix A has 10% protein
and 6% fat, mix B has 20% protein and 2% fat.
How many grams of each mix should be
used to obtain the right diet for a single animal?
9.
Suppose you have $12,000 to invest.
If part is invested at 10% and the rest at 15%, how
much should be invested at each rate to yield 12% on the total amount invested?
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 Spring '97
 KEITHCHAN
 Linear Algebra, Personal computer, desktop computer, Mower

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