Answer:
- 8π radians/second
- 527.8 meters
Step-by-step explanation:
A) The angular velocity is the ratio of angular distance to time:
ω = 1 revolution / (0.25 s) = (2π radians)/(0.25 s)
ω = 8π radians/second
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B) The arc length is ...
s = rθ = rωt
s = (35 cm)(8π rad/s)(60 s) = 16,800π cm
s ≈ 52779 cm = 527.79 m
The wheel travels about 527.8 meters in one minute.
Whenever you get questions like these you can turn the percentage into a decimal by adding a point at the beginning of a number then multiply the decimal by the number you need to find a part of
Lines <em>a</em> and <em>b</em> are parallel, so lines <em>p</em>, <em>q</em>, and <em>t</em> are considered to be transversals. To solve this, you make use of the fact that alternate interior angles are equal, as are alternate exterior angles, as are corresponding angles. Of course any linear pair of angles is supplementary.
∠1 = 90° — corresponding angle to the right angle above it
∠2 = 68° — the sum of 22° and angles 1 and 2 is 180°
∠3 = 112° — supplementary to angle 2 (and the sum of 22° and 90°, opposite interior angles of the triangle)
∠4 = 112° — equal to angle 3
∠5 = 68° — equal to angle 2; supplementary to angle 4
∠6 = 56° — base angle of isosceles triangle with 68° at the apex; the complement of half that apex angle
∠7 = 124° — supplementary to the other base angle, which is equal to angle 6; also the sum of angles 5 and 6
∠8 = 124° — alternate interior angle with angle 7, hence its equal.
Answer:
price of 5 bags of popcorn = 3.75 x 5 = 18.75
price of 8 drinks = 5 x 8 = 40
price of p bags of popcorn = 3.75 x p
price of d drinks = 5 x d