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12345Using formulas

Exercises

Exercise 1

The volume of a cylindrical tin can is given by: $V = π \cdot r^{2} \cdot h$ . Here $V$ is the volume, $r$ the radius in centimetres and $h$ the height in centimetres.

In what unit should $V$ be expressed?

What is the volume of a tin can with a diameter of $80$ millimetres and a height of $16$ centimetres?

What formula describes the relation between $V$ and $r$ for those tin cans that have a height of $16$ centimetres?

Plot the corresponding graph of the formula you found in question c.

Of a different set of tin cans the volume is fixed: $V = 1$ L. What is the relation between $r$ and $h$ ? Plot the corresponding graph.

Exercise 2

Which of the formulas below describes the relation between two variables? Plot the corresponding graphs.

`volume` (cube)= $r^{3}$

$s = 400 - 5 t^{2}$

$a^{2} + b^{2} = c^{2}$

Exercise 3

Re-write the formulas below so that $y$ is a function of $x$ .

$2 x + 4 y = 10$

$2 x - 3 y + 6 = 0$

$0.5 y^{2} = 8 x$

$x^{2} \cdot y = 6$

Exercise 4

Remove the brackets:

$- 2 x (x^{2} + 6 x)$

$- 2 x - (x^{2} + 6 x)$

$(t + 20) (t - 5)$

$(x^{2} + 1) (3 x - 2)$

$(a - 3) (a + 3)$

${(6 x - 3)}^{2}$

Exercise 5

An entrepeneur sells a product. There is a relation between the number of products $q$ sold (per month) and the price $p$ of the product (in €, per sold item). This relation can be described by the formula: $q = 4000 - 20 p$ .

How many units of the product does he sell when he prices the product at € 50 per unit?

The entrepeneur buys this product at € 30 per unit. If he does not want to make a loss he must sell at the same price. What is the maximum number of units he can sell each month?

Negative values for $q$ are impossible. What is, therefore, the maximum selling price?

The profit per month can be calculated by multiplying the price $p$ by the number of units sold. Show that the profit $R = 4000 p - 20 p^{2}$ .

Make a table for the profit, where $p = 30, 40, 50, 60, ..., 200$ . Use your graphic calculator to make the table.

For which price does the entrepeneur receive the highest monthly profit?

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