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BBR 23603 Essential Mathematics

UNIVERSITI TUN HUSSEIN ONN MALAYSIA

BBR 23603

MATEMATIK ASAS / ESSENTIAL MATHEMATICS

INDIVIDUAL ASSIGNMENT NO.2

SEMESTER I 2012/2013

KOHORT 1

NAME : MAZLINA BINTI ALI

NO. MATRIKS : DB 100 387

SECTION : MATHEMATICS SECTION 4

LECTURER’S : DR. LAI CHEE SERN

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UNIVERSITI TUN HUSSEIN ONN MALAYSIA

BBR 23603

MATEMATIK ASAS / ESSENTIAL MATHEMATICS

INDIVIDUAL ASSIGNMENT NO.2

SEMESTER I 2012/2013

KOHORT 1

Instructions to students:

1. This is an individual assignment that accounts for 10% of the total marks

for the course

2. This assignment contains FOUR (4) question only

3. You can answer in Malay or English

4. Write down your name, student’s card number, section and lecturer’s name

on the cover of your hardcopy assignment

4. Your assignment is to be submitted on the second meeting, 15 December 2012

(Saturday).

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Question 1 ( 6 marks )

Express the following as a single log term in its simplest form.

a) 2 log y + 3 log x

Answer

2 log y + 3 log x = log y ² + log x³

= log ( y² + x³ )

b) log 2x – 2 log x + x log 2

Answer

log 2x – 2 log x + x log 2 = log 2x – log x² + log 2˟

= log ( 2x X 2˟ ) x²

= log ( 2 (x + 1 ) ˟ ) x²

= log ( 2 (x + 1 ) ) x

3



The voltage gain of an amplifier is given by

gain = 20 log ( Vₒ ) V1

Where V , is the input voltage and Vₒ is the output voltage. Given that the output voltage from an amplifier is 250 mV. If the amplifier has a gain of 17 dB, calculate its input voltage.

gain = 20 log ( Vₒ ) V1

Answer

V 1 = InputVₒ = OutputOutput = 250 mVGain = 17 dB

17 dB = 20 log ( 250 mV ) V1

17 db = log ( 250 mV ) 20 V1

Gunakan prinsip log….

Contoh log10 x = a x = 10 6

17 db = log10 250 mV 20 V1

10 = 250 V1

V1 = 250 10

V1 = 35.31 mV

4

1720

1720



Find the exact value of each the five remaining trigonometric functions of the acute angle

where sin θ = 2 √ 13

X

x² = √ 13 – 2²

x² = 13 – 4

x² = 9

x = 3

1) cos θ =

2) tan θ = 2 3

3) csc θ = 1 sin θ

=

4) sec θ = 1 cos θ =

5) cot θ = 1 tan θ = 3 2

5

√ 13

2

θ

3√ 13

3√ 13

√13 2

√13 3



You can use right triangles to find distances, if you know an angle of elevation or an angle of depression. The figure below shows each of these kinds of angles.

Suppose that you are standing 20 feet away from a tree, and you measure the angle elevation to be 38 ? How tall is the tree, if your height is given as 5.50 feet ?

Answer

Tan 38 = r 20

r = tan 38 X 20= 0.78128 X 20= 15.626

Tall is the tree = 15.626 + 5.50= 21.126

6

20

r

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