Draw a circle and label the parts. Briefly explain the parts of the circle. Copy and complete the table below: A straight ladder 10 meters long is placed against a wall with its lower end 6 meters away from the wall. How high up the wall does it reach? Solve for n in the diagram below:

Here are the solutions to the questions.

1. (a) Briefly define communication in your own words

As an AI, I cannot draw. However, I can explain the parts of a circle: • Center: The point equidistant from all points on the circle. • Radius: A line segment connecting the center to any point on the circle. • Diameter: A line segment passing through the center and connecting two points on the circle. Its length is twice the radius. • Circumference: The total distance around the circle. • Chord: A line segment connecting any two points on the circle.

1. (b) Copy and complete the table below:

Step 1: Calculate the Class Boundaries. For a class interval $a-b$, the lower class boundary is $a - 0.5$ and the upper class boundary is $b + 0.5$.

Step 2: Calculate the Class Width. Class Width = Upper Class Boundary - Lower Class Boundary.

Step 3: Calculate the Class Midpoint. Class Midpoint = $\frac{Lower Class Limit + Upper Class Limit}{2}$.

Step 4: Complete the table with the calculated values.

| Mark | Frequency | Class Boundaries | Class Width | Class Midpoint | | :---- | :-------- | :--------------- | :---------- | :------------- | | 1-5 | 5 | 0.5 - 5.5 | 5 | 3 | | 6-10 | 7 | 5.5 - 10.5 | 5 | 8 | | 11-15 | 9 | 10.5 - 15.5 | 5 | 13 | | 16-20 | 3 | 15.5 - 20.5 | 5 | 18 | | 21-25 | 1 | 20.5 - 25.5 | 5 | 23 | | 26-30 | 6 | 25.5 - 30.5 | 5 | 28 | | 31-35 | 4 | 30.5 - 35.5 | 5 | 33 | | 36-40 | 2 | 35.5 - 40.5 | 5 | 38 |

2. A straight ladder 10 meters long is placed against a wall with its lower end 6 meters away from the wall. How high up the wall does it reach?

Step 1: Identify the given values. This problem forms a right-angled triangle. Length of the ladder (hypotenuse, $c$) $= 10$ m. Distance from the wall (base, $b$) $= 6$ m. Height up the wall (height, $a$) is unknown.

Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states $a^2 + b^2 = c^2$.

Step 3: Substitute the values and solve for $a$. $a^2 + 6^2 = 10^2$ $a^2 + 36 = 100$ $a^2 = 100 - 36$ $a^2 = 64$ $a = \sqrt{64}$ $a = 8$ The height the ladder reaches up the wall is 8 meters.

$\boxed{8 m}$

3. Solve for n in the diagram below:

Step 1: Set up the equation for angles on a straight line. Angles on a straight line sum to $180^\circ$. $(4n - 22)^\circ + (8n - 10)^\circ = 180^\circ$

Step 2: Simplify the equation. $4n - 22 + 8n - 10 = 180$ $12n - 32 = 180$

Step 3: Solve for $n$. $12n = 180 + 32$ $12n = 212$ $n = \frac{212}{12}$ $n = \frac{53}{3}$ $n = 17.67 \text{ (approximately)}$ The value of $n$ is $\frac{53}{3}$ or approximately 17.67.

$\boxed{n = \frac{53}{3} or n \approx 17.67}$

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