Answer:
B = 68° and C = 22°
Step-by-step explanation:
Let angle B's measure be B and angle C's measure be C.
Also note that complementary means that they sum to 90.
Now:
<u>The m∠B is two more than three times the measure of ∠C:</u>
we can write:
B = 3C + 2
<u>If ∠B and ∠C are complementary angles:</u>
B + C = 90
Putting 1st equation in 2nd, we get:
B + C = 90
3C + 2 + C = 90
4C = 90 - 2
4C = 88
C = 88/4 = 22
Now B = 3C + 2, so
B = 3(22) + 2 = 68
Hence, B = 68 degrees and C = 22 degrees
Answer:
a) The angular velocity is 0.4π radians/second ⇒1.25664 radians/second
b) The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters
Step-by-step explanation:
The angular velocity ω = 2 π n ÷ t, where
- n is the number of revolution
The distance that moving by the angular velocity is d = ω r t, where
- r is the radius of the circle in meter
a)
∵ A wheel completes 12 revolutions in 1 minute
∴ n = 12
∴ t = 1 minute
→ Change the minute to seconds
∵ 1 minute = 60 seconds
∴ t = 60 seconds
→ Substitute n and t in the rule above
∵ ω = 2 (π) (12) ÷ 60
∴ ω = 24π ÷ 60
∴ ω = 0.4π radians/second
∴ The angular velocity is 0.4π radians/second ⇒1.25664 radians/second
b)
→ To find the distance in 5 minutes multiply ω by the radius by the time
∵ The wheel has a radius of 33 cm
∴ r = 33 cm
→ Change it to meter
∵ 1 m = 100 cm
∴ r = 33 ÷ 100 = 0.33 m
∵ t = 5 minutes
→ Change it to seconds
∴ t = 5 × 60 = 300 seconds
→ Substitute them in the rule of the distance above
∵ d = 0.4π (0.33) (300)
∴ d = 39.6π meters ⇒ 124.407 meters
∴ The wheel travels 124.4071 meters in 5 minutes ⇒ 39.6π meters
P(H,H,H)=P(H,T,H)
This is classical probability, so the probability of an event is the number of "favorable" events over total events.
The total number of events, by the counting principle, is 2^3=8.
The total number of events remains the same for P(H,H,H) and P(H,T,H), as you're still flipping 3 coins with two sides.
For P(H,H,H) the favorable event is (H,H,H) so 1, for P(H,T,H) the favorable event is (H,T,H) also one.
Conclusion:
P(H,H,H)=P(H,T,H)=1/8
