a. Find the range of values of x which satisfy the following inequalities simultaneously: 5 - x > 1 and 9 + x \(\geq\) 8

In the diagram, O is the centre of the circle, IPQI = IQRI and < PSR = 56°. Find < QRS. 

a. A textbook company discovered that the profit made from selling its books is given by y = \(\frac{x^2}{8}\) + 5x, where x is the number of textbooks sold (in thousands) and y is the corresponding profit (in Ghana Cedis). If the company made a profit of GH₵ 20,000.00

i. form a quadratic equation in x;

ii. (using the quadratic formula, find, correct to the nearest whole number, the number of textbooks sold to make the profit.

b. The angle of elevation of the top T of a tree from a point P on the same ground level as the foot Q of a tree is 28\(^o\). A bird perched at a point R, halfway up the tree.

i. Represent the information in a diagram.

ii. Calculate, correct to the nearest degree, the angle of elevation of R from P.

(a) Evaluate: \(\int \limits_1^2 (2x^3 - 4x + 3) dx\)

(b) Given that P\(^{-1}\) = \(\begin{pmatrix} -1 & 1 \\ 4 & -3 \end{pmatrix}\), find the matrix P.

 

(a)
(i) Copy and complete the addition \(\oplus\) and multiplication \(\otimes\) tables in modulo 5 on the set {2, 3, 4}.

(ii) Use the tables to:

(a) solve the equation 4 \(\otimes\)e\(\oplus\) 2 \(\equiv\) 1 (mod 5):
(b) find the value of n, if 4 \(\oplus\)n\(\otimes\) 2 \(\equiv\) (mod 5).

(b) Consider the following statements:

p: Landi has cholera,

q: Landi is in the hospital.

If p = q, state whether or not the following statements are valid:

(i) If Landi is in the hospital, then he has cholera.

(ii) If Landi is not in the hospital, then he does not have cholera.

(iii) If Landi does not have cholera, then he is not in the hospital.

Using ruler and a pair of compasses only, construct:

(a) (i) quadrilateral PQRS with |PQ| = 6 cm, |PS| = 8 cm, < PSR = 90\(^o\), |SR| = 12 cm and |QR| = 11 cm;

(ii) perpendicular from Q to cut \(\over{SR}\) at K.

(b) Measure:

(i) IQRI;

(ii) < QRS.