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=(21)/(2(2))=5.25`

x=5

`y=(21)/(2(5))=2.1`

b)

c)

We locate for each case the points

d)

First we need to solve the equation given

`(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