Working with formulas

Working with formulas > Equations

Overview

1234Equations

Exercises

Exercise 1

Solve the following equations algebraically.

$4 t + 50 = 200$

$4 t^{2} + 50 = 200$

$\sqrt{x + 4} = 20$

${(2 x - 5)}^{3} = 125$

$\sqrt{a^{2} + 4} - 20 = 0$

$\frac{12}{v} = 400$

$2 x^{2} - 2 = 12 x + 30$

Exercise 2

Use iteration to solve the following equations with the help of your graphical calculator. Find all solutions.

$\sqrt{x} = 6 - x$

$x^{4} = 2 + x$

Exercise 3

The Empire State Building is a high sky scraper in New York. Imagine somebody dropping a small stone from the $381$ m high building!
Under the influence of gravity the stone drops uniformly accelerated (neglect the air resistance). Physicists have devised a mathematical model for this. In this model the distance travelled is called $s$ (in meters) and the velocity $v$ (in m/s). Both depend on time $t$ (in seconds) according to the formulas $s = 4.9 t^{2}$ and $v = 9.8 t$ .

Give a formula for the height $h$ of the stone above the ground as a function of $t$ .

Calculate the time at which the stone hits the ground.

Calculate the velocity with which the stone hits the ground.

Give your answer in m/s and in km/h.

Exercise 4

For each of these formulas calculate the value of one variable if the other one is $0$ .

$2 p - 3 q = 650$

$W = -0.25 q (0.5 q - 100)$

$k^{2} + {(l + 2)}^{2} = 100$

$a = \frac{1200}{600 + 0.2 d^{2}} - 1$

$(x^{2} - 4) (y^{2} - 9) = -36$

$y^{4} + 1 = \frac{4}{1 + x^{2}}$

Exercise 5

The township asks a farmer to surround a piece of land with a woodstrip of $4$ m wide.

The piece of land is an exact square. At one side it already borders the woods.

"I get to keep only half of my land" , the farmer complains.

If this is true, what is the surface area of the piece of land?

Solve this problem using an equation.

Exercise 6

Some candles have an almost perfect cylindrical shape. Imagine you want to make such a candle with a height of $20$ cm. You take a wick with a $3$ mm diameter and repeatedly dip it in a bath of molten wax. With each dip the diameter of the candle increases with $1$ mm. The total volume of candle wax $V$ in the candle depends on the number of dips $a$ made.

Give a formula for $V$ as a function of $a$ .

Plot the graph of this function on your graphical calculator.

How many dips do you need to make to give the candle an approximate volume of $106$ cm³? First use your calculator to read out the answer from the graph, then find the solution algebraically by solving the corresponding equation.

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