Question

a) complete the table in the answer space for the equation y=21/2x when x=2 and x=5b) using a scale of 2cm to 1 unit on the x-axis and 2cm to 2 unit on the y-axis, draw the graph of y= 21/2x for 0.5 ≤ x ≤ 7c) from the graph in (b) ,find:i. the value of y when x=4.5ii. the value of x when y= 7.6d) draw a suitable straight line on the graph in (b) to find the value of x which satisfy the equation 21/2x=15-2x for 0.5 ≤ x ≤ 7.State the values of x

Answer 1

For a)

x=2

$y=\frac{21}{2(2)}=5.25$

x=5

$y=\frac{21}{2(5)}=2.1$

b)

c)

We locate for each case the points

d)

First we need to solve the equation given

$\frac{21}{2x}=15-2x$

We isolate the x

$21=2x(15-2x)$

we simplify

$21=30x-4x^2$

Then we make zero the equation

$4x^2-30x+21=0$

Then we solve the second-degree equation.

The solutions are

$\begin{gathered} x=0.781 \\ x=6.719 \end{gathered}$

Both solutions are inside the given interval

Therefore the lines are