(a) Make m the subject of the relations (h = frac{mt}{d(m + p)}).
(b)
In the diagram, WY and WZ are straight lines, O is the centre of circle WXM and < XWM = 48°. Calculate the value of < WYZ.
(c) An operation (star) is defind on the set X = {1, 3, 5, 6} by (m star n = m + n + 2 (mod 7)) where (m, n in X).
(i) Draw a table for the operation.
(ii) Using the table, find the truth set of : (I) (3 star n = 3) ; (II) (n star n = 3).
Explanation
(a) (h = frac{mt}{d(m + p)})
(dh(m + p) = mt)
(dhm + dhp = mt implies dhp = mt – dhm)
(dhp = m(t – dh) implies m = frac{dhp}{t – dh})
(b)
In the diagram above, < WXM = 90° (angle in a semicircle)
< WMX = 180° – (90° + 48°)
= 42°
< XMZ = 180° – 42° (angles on a straight line)
= 138°
< WYZ = 180° – 138° (opp. angles of a cyclic quadrilateral)
= 42°
(c)
| (star) | 1 | 3 | 5 | 6 |
| 1 | 4 | 6 | 1 | 2 |
| 3 | 6 | 1 | 3 | 4 |
| 5 | 1 | 3 | 5 | 6 |
| 6 | 2 | 4 | 6 | 0 |
(ii) From the table, the truth set of :
(I) (3 star n = 3; n = {5})
(II) (n star n = 3; n = { })