Fine the mean, median, and mode/s of the data. 2, 8, 10, 12, 56, 9, 5, 2, 4.
Anna35 [415]
Mean: 12, Median: 5, Mode: 54
The velocity of an object in free fall increases downwards with time
- Please find attached the correct graph showing velocity as a function time, with the positive direction to be upwards.
Reason:
The known parameters are;
Location where the rocks are released; Earth
The time at which rock Y is released = A few seconds after rock X is released.
Required:
To select the graph that shows the vertical velocity of rock, <em>x</em>, as a function of time.
Solution:
Let <em>t </em>represent the time after which rock x are released, with the positive direction being upwards, we have;
- The equation for the velocity of x is v = -9.81·t
With the above equation, the graph of the vertical velocity of rock x is plotted with MS Excel.
Learn more about the graphs of velocity of object in free fall here:
brainly.com/question/11363021
Answer:
7) x = 9°
8) x = 5°
9) x = 10°
10) x = 12°
Explanation:
7) By the angle subtended at the center is twice the angle subtended at the circumference, we have;
∠JLM = ∠JKV = 55°/2 = 27.5°
Similarly;
∠JML = ∠JVK = (18·x + 13)/2 = 9·x + 6.5
By exterior angle theory, we have;
13·x - 2 = 27.5 + 9·x + 6.5 = 9·x + 34
13·x - 9·x = 34 + 2 = 36
4·x = 36
x = 36/4 = 9
x = 9°
8) By the theorem angle formed on the outside of the circle by a tangent and a secant is equal to the difference of the arcs formed in between by the intercept of the tangent and the secant and the circle multiplied by half
Therefore;
8·x + 8 = (1/2) × (170° - (15·x - 1))
8·x + 8 = 85° - 7.5·x + 1/2
8·x +7.5·x = 85° - 8 + 1/2 = 77.5°
15.5·x = 77.5
x = 77.5°/15.5 = 5°
x = 5°
9) ∠TEU = ∠TWV = 175°/2 = 87.5°
∠TUU = ∠TYV = (5·x - 5)/2 = 2.5·x - 2.5
115° = 87.5° + 2.5·x - 2.5 = 90° + 2.5·x
2.5·x = 115° - 90° = 25°
x = 25°/2.5 = 10°
x = 10°
10) The measure of the intercepted arc formed by a chord is equal to twice the measure of the angle the chord forms with a tangent it intersects at the tangent point;
21·x + 18 = 2 × (The supplementary angle to ∠STU)
The supplementary angle to ∠STU = 180° - 45° = 135°
∴ 21·x + 18 = 2 × 135° = 270°
21·x = 270 - 18 = 252
x = 252/21 = 12
x = 12°.
