Gegee: $f(x) = x^2 - 3x - 10$ Los op vir $x$: 1.1.1 $f(x) = 0$ 1.1.2 $f(x) < 0$ en stel die oplossing op $n$ getallen voor Los op vir $x$: $2x^2 - 11x = -7x$ (korrekt tot TWEE desimale plekke) Los op vir $x$ en $y$: $y - x + 1 = 0$ en $y + 7 = x^2 + 2x$ Die formule wat gebruik word om die weerstand in die diagram hieronder te bereken, in 'n stroombaan waar resistors in parallel gekoppel is, word gegee deur: $$rac{1}{R_p} = rac{1}{R_1} + rac{1}{R_2}$$ - $R_p$ = totale weerstand in ohm $( ext{Ω})$ - $R_1$ = weerstand van resistor 1 in ohm $( ext{Ω})$ - $R_2$ = weerstand van resistor 2 in ohm $( ext{Ω})$ 1.4.1 Maak $R_p$ die onderwerp van die formule - NSC Technical Mathematics - Question 1 - 2022 - Paper 1

We need to find the critical points where the function is less than zero. We know the roots are $x = -2$ and $x = 5$. The intervals to test are:

1. $(-\infty, -2)$
2. $(-2, 5)$
3. $(5, \infty)$

Testing these intervals using a test point from each interval:

• For $x = -3$: $f(-3) = 9 + 9 - 10 = 8 > 0$
• For $x = 0$: $f(0) = -10 < 0$
• For $x = 6$: $f(6) = 36 - 18 - 10 = 8 > 0$

Thus, the solution for $f(x) < 0$ occurs in the interval: $\text{Answer: } (-2, 5)$

Rearranging gives: $2x^2 - 4x = 0$ Factoring out $2x$: $2x(x - 2) = 0$ Thus, the solutions are: $x = 0 \quad \text{or} \quad x = 2$

First, solve the linear equation for $y$: $y = x - 1$ Substituting $y$ into the quadratic equation: $x - 1 + 7 = x^2 + 2x$ This simplifies to: $x^2 + 2x - x + 8 = 0 \implies x^2 + x + 8 = 0$ Using the quadratic formula: $x = \frac{-1 \pm \sqrt{1 - 4(1)(8)}}{2(1)}$ This results in complex roots: $x = \frac{-1 \pm \sqrt{-31}}{2}$ Thus, $y = \frac{-1 \pm \sqrt{-31}}{2} - 1$

Starting with the formula: $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$ We can rewrite this as: $R_p = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}$

Using the formula derived: $R_p = \frac{1}{\frac{1}{40} + \frac{1}{45}}$ Calculating: $\frac{1}{R_p} = \frac{1}{40} + \frac{1}{45} = \frac{45 + 40}{1800} = \frac{85}{1800}$ Therefore, $R_p = \frac{1800}{85} \approx 21.18 \text{ Ω}$

To add these binary numbers:

Align and add:

  1101100
+   1100

Starting from the right:

  1101100
+  001100
-----------
11000100 (carry over included)

Thus, $1101100_2 + 1100_2 = 11000100_2$.