Working with formulas

Working with formulas > Formulas and the Graphic Calculator

Overview

1234Formulas and the Graphic Calculator

Exercises

Exercise 1

Plot the graphs of the following formulas. Remember to use brackets and appropriate window settings!

$s = 250 t - 4.9 t^{2}$

$k = 0.04 + \frac{200}{a}$

$4 \cdot x \cdot h + 2 \cdot x^{2} = 100$

$N = \frac{60}{30 + 0.5 d^{2}}$

Exercise 2

The volume of a cone is given by: $V = \frac{1}{3} G h$ , where $G$ is the area of the base and $h$ the height. The base is a circle with radius $r$ .

What formula describes the relation between $V$ , $r$ and $h$ ?

Give the formula describing the relation between $r$ and $h$ for a cone with a volume of $1$ liter from the given formula.

Write the relation in such a way that $r$ is a function of $h$ .

Determine the value of $h$ for $r = 10$ cm. Round the answer to two decimals.

Determine the value of $r$ for $h = 10$ cm. Approximate with a value rounded to two decimals.

Exercise 3

The monthly lease for a copying machine is € 200 to which an amount of $4$ cent per copy is added. $K$ represents the total cost and $a$ is the (average) number of copies made in a month.

Write down the formula for $K$ as a function of $a$ .

Somebody using the copying machine pays $10$ cent per copy. Write down the formula for the revenue $I$ as a function of $a$ .

How many copies should be made in a month if you want the $10$ cents per copy to cover the costs?

Exercise 4

Imagine a company that sells posters. In order to stand out the area of such a poster should be $1$ m². The poster will be printed in such a manner that there is a white border of $10$ cm on both sides and on the top. At the bottom that border is $15$ cm. The management wonders what dimensions the poster can have now. They find the formula: $(l + 25) (b + 20) = 10000$ .

Show how they got this formula and what $l$ and $b$ mean.

Plot the graph belonging to this formula.

Check if all dimensions shown are feasible.

In retrospect the management wants the printed part to be square. What poster size would you recommend now?

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