<span>The limitation of
algebra that leads development of calculus is that it can make a complex number
of variables present it as a single variable and then apply the necessary
formula needed to find the answer. After manipulation, the presented single
variable can be changed back to a complex variable by substitution</span>
Now the aim of the above discussion is to internalize the mathematical relationships for open-end air columns in order to perform calculations predicting the length of air column required to produce a given natural frequency. And conversely, calculations can be performed to predict the natural frequencies produced by a known length of air column. Each of these calculations requires knowledge of the speed of a wave in air (which is approximately 340 m/s at room temperatures). The graphic below depicts the relationships between the key variables in such calculations. These relationships will be used to assist in the solution to problems involving standing waves in musical instruments.
The examples and solutions to the functions are illustrated below based on the information given.
<h3>How to illustrate the functions?</h3>
1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.
The function will be:
C = 100 + (95 × p)
C = 100 + 95p
<u>2nd example:</u><u> </u>The cost of a pen is $5. Find the cost of s pens.
The function will be:
C = 5 × p
C = 5p
<u>3rd example</u>: Calculate the total amount for m tickets if each ticket is $20.
The function will be;
C = 20 × m
C = 20m
<u>4th example:</u> Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.
C = (2 × g) + (3.40 × d)
C = 2g + 3.4d
<u>5</u><u>t</u><u>h</u><u> </u><u>example</u><u>:</u><u> </u>The average age of k number of boys is 7. Find their total age.
The function will be:
a = (7 × k)
a = 7k
Learn more about functions on:
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<u>Answer</u>
2nd diagram
<u>Explanation.</u>
When contraction a parallel line from a point say N, outside the line, the first thing is to draw a line from point N to the that line.
The point where this line from N intersect with line, name it say P. From this point you can use the properties of angles in a parallel lines to construct the parallel line.
The line NP can act like a transverse of the two parallel lines. The diagram 2 shows first step.
