Project Addmath 2013
PART 1
a) Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620.
The objective of both men was to simplify mathematical calculations. This approach originally arose out of a desire to simplify multiplication and division to the level of addition and subtraction. Of course, in this era of the cheap hand calculator, this is not necessary anymore but it still serves as a useful way to introduce logarithms.
b) The first field of study: Chemistry
In chemistry, a solution’s pH is defined by the logarithmic equation:
p(h) = – log10 (h)
where h is the hydronium ion concentration in moles per liter. We usually round pH values to the nearest tenth.
Example:
Find the pH of a solution with hydronium ion concentration 4.5 x 10-5
Given h=4.5 x 10-5,
p(h) = – log10 (4.5 x 10-5)
= – ( log10 4.5 + log10 10-5 )
= – ( log10 4.5 + (–5)(log10 10) )
= – ( 0.6532 + (–5) )
= – ( 0.6532 – 5 )
= – (–4.3468)
= 4.3
The second field of study: Physics
The loudness of sound is measured in units called decibels. These units are measured by first assigning an intensity I0 to a very soft sound (which is called the threshold sound). The sound we wish to measure is assigned an intensity I, and we measure the decibel rating d of this sound with the equation.
Example:
Find the decibel rating of a sound with intensity 5000I0.
5000Io
Io
d = 10 log10
= 10 log10 5000
= 36.99 decibels
PART 2
a) i) By using a pair of vernier calipers, the diameter of six (6) different spheres is taken.
ii) The volume of spheres is obtained by using water displacement method.
iii) The values of the diameter, D, in cm, and its corresponding volume, V, cm3 are tabulated as below:
Diameter (cm) | Volume (cm3) | 2 | 4.19 | 3 | 14.14 | 4 | 33.52 | 5 | 65.48 | 6 | 113.14 | 7 | 179.67 |
a) Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620.
The objective of both men was to simplify mathematical calculations. This approach originally arose out of a desire to simplify multiplication and division to the level of addition and subtraction. Of course, in this era of the cheap hand calculator, this is not necessary anymore but it still serves as a useful way to introduce logarithms.
b) The first field of study: Chemistry
In chemistry, a solution’s pH is defined by the logarithmic equation:
p(h) = – log10 (h)
where h is the hydronium ion concentration in moles per liter. We usually round pH values to the nearest tenth.
Example:
Find the pH of a solution with hydronium ion concentration 4.5 x 10-5
Given h=4.5 x 10-5,
p(h) = – log10 (4.5 x 10-5)
= – ( log10 4.5 + log10 10-5 )
= – ( log10 4.5 + (–5)(log10 10) )
= – ( 0.6532 + (–5) )
= – ( 0.6532 – 5 )
= – (–4.3468)
= 4.3
The second field of study: Physics
The loudness of sound is measured in units called decibels. These units are measured by first assigning an intensity I0 to a very soft sound (which is called the threshold sound). The sound we wish to measure is assigned an intensity I, and we measure the decibel rating d of this sound with the equation.
Example:
Find the decibel rating of a sound with intensity 5000I0.
5000Io
Io
d = 10 log10
= 10 log10 5000
= 36.99 decibels
PART 2
a) i) By using a pair of vernier calipers, the diameter of six (6) different spheres is taken.
ii) The volume of spheres is obtained by using water displacement method.
iii) The values of the diameter, D, in cm, and its corresponding volume, V, cm3 are tabulated as below:
Diameter (cm) | Volume (cm3) | 2 | 4.19 | 3 | 14.14 | 4 | 33.52 | 5 | 65.48 | 6 | 113.14 | 7 | 179.67 |