I. \( 10 \frac{1}{\sqrt{m}+\sqrt{m+1}}=\sqrt{m+1}-\sqrt{m} \), determine, without the use of a calculator, the exact value of: \( \frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\ldots+\frac{1}{\sqrt{1680}+\sqrt{1681}} \)

A solid rectangular block has a square base. Find its maximum youme and the sides if the sum of its height and any one side of the base is 12 cm .

إذا كانت الدالة \( f(x) = \sqrt{x - 1} \)، فما هو مجال الدالة المعكوسة؟

UESTION 4 ketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). learly indicate all intercepts with the axes, turning point(s) and asymptote(s).

UESTION 3 he equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Srite down the equation of the new function that is formed when \( f \) is transformed as follows: \( 1 \quad \) Shift two units to the left \( 2 \quad \) Shift 3 units up

Exercises 1. In each of the following, two open statements \( P(x, y) \) and \( Q(x, y) \) are given, where the domain of both \( x \) and \( y \) is \( Z \). Determine the truth value of \( P(x, y) \Rightarrow Q(x, y) \) for the given values of \( x \) and \( y \). a. \( P(x, y): x^{2}-y^{2}=0 \). and \( Q(x, y): x=y .(x, y) \in\{(1,-1),(3,4),(5,5)\} \). b. \( P(x, y):|x|=|y| \). and \( Q(x, y): x=y .(x, y) \in\{(1,2),(2,-2),(6,6)\} \). c. \( P(x, y): x^{2}+y^{2}=1 \). and \( Q(x, y): x+y=1 \). \( (x, y) \in\{(1,-1),(-3,4),(0,-1),(1,0)\} \). 2. Let \( O \) denote the set of odd integers and let \( P(x): x^{2}+1 \) is even, and \( Q(x): x^{2} \) is even. be open statements over the domain \( O \). State \( (\forall x \in O) P(x) \) and \( (3 y \in O) Q(x) \) in words. 3. State the negation of the following quantified statements.