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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:

Mathematics

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Step-by-step solution

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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:

  1. Calculate the Class Boundaries.

    For a class interval a−ba-b, the lower class boundary is a−0.5a - 0.5 and the upper class boundary is b+0.5b + 0.5.

  2. Calculate the Class Width.

    Class Width = Upper Class Boundary - Lower Class Boundary.

  3. Calculate the Class Midpoint.

    Class Midpoint = Lower Class Limit+Upper Class Limit2\frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}.

  4. Complete the table with the calculated values.

    MarkFrequencyClass BoundariesClass WidthClass Midpoint
    1-550.5 - 5.553
    6-1075.5 - 10.558
    11-15910.5 - 15.5513
    16-20315.5 - 20.5518
    21-25120.5 - 25.5523
    26-30625.5 - 30.5528
    31-35430.5 - 35.5533
    36-40235.5 - 40.5538

    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?

  5. Identify the given values.

    This problem forms a right-angled triangle.
    Length of the ladder (hypotenuse, cc) =10= 10 m.
    Distance from the wall (base, bb) =6= 6 m.
    Height up the wall (height, aa) is unknown.

  6. Apply the Pythagorean theorem.

    The Pythagorean theorem states a2+b2=c2a^2 + b^2 = c^2.

  7. Substitute the values and solve for aa.

    a2+62=102a^2 + 6^2 = 10^2 a2+36=100a^2 + 36 = 100 a2=100−36a^2 = 100 - 36 a2=64a^2 = 64 a=64a = \sqrt{64} a=8a = 8

    The height the ladder reaches up the wall is 8 meters.

    8 m\boxed{\text{8 m}}

    3. Solve for n in the diagram below:

  8. Set up the equation for angles on a straight line.

    Angles on a straight line sum to 180∘180^\circ.

    (4n−22)∘+(8n−10)∘=180∘(4n - 22)^\circ + (8n - 10)^\circ = 180^\circ
  9. Simplify the equation.

    4n−22+8n−10=1804n - 22 + 8n - 10 = 180 12n−32=18012n - 32 = 180
  10. Solve for nn.

    12n=180+3212n = 180 + 32 12n=21212n = 212 n=21212n = \frac{212}{12} n=533n = \frac{53}{3} n=17.67 (approximately)n = 17.67 \text{ (approximately)}

    The value of nn is 533\frac{53}{3} or approximately 17.67.

    n=533 or n≈17.67\boxed{n = \frac{53}{3} \text{ or } n \approx 17.67}
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