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kvasek [131]
2 years ago
5

SOMEONE HELP ME WITH THIS MATH PLS

Mathematics
1 answer:
cluponka [151]2 years ago
6 0

Answer: add

Step-by-step explanation:

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A school district had four elementary schools to start the year. North Elementary School had 1,200 students, East Elementary Sch
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If θ=0rad at t=0s, what is the blade's angular position at t=20s
babunello [35]
The attached figure represents the relation between ω (rpm) and t (seconds)
To find the blade's angular position in radians ⇒ ω will be converted from (rpm) to (rad/s)
              ω = 250 (rpm) = 250 * (2π/60) = (25/3)π    rad/s
              ω = 100 (rpm) = 100 * (2π/60) = (10/3)π    rad/s

and from the figure it is clear that the operation is at constant speed but with variable levels
            ⇒   ω = dθ/dt   ⇒   dθ = ω dt

            ∴    θ = ∫₀²⁰  ω dt  
 
while ω is not fixed from (t = 0) to (t =20)
the integral will divided to 3 integrals as follow;
       ω = 0                                          from t = 0  to t = 5
       ω = 250 (rpm) = (25/3)π            from t = 5   to t = 15
       ω = 100 (rpm) = (10/3)π            from t = 15 to t = 20

∴ θ = ∫₀⁵  (0) dt   + ∫₅¹⁵  (25/3)π dt + ∫₁₅²⁰  (10/3)π dt
     
the first integral = 0
the second integral = (25/3)π t = (25/3)π (15-5) = (250/3)π
the third integral = (10/3)π t = (25/3)π (20-15) = (50/3)π

∴ θ = 0 + (250/3)π + (50/3)π = 100 π

while the complete revolution = 2π
so instantaneously at t = 20
∴ θ = 100 π - 50 * 2 π = 0 rad

Which mean:
the blade will be at zero position making no of revolution = (100π)/(2π) = 50
















3 0
3 years ago
Inequality Match Up Lab
Artist 52 [7]
1. 2x+3<-3 = x<-3
You get this by subtracting 3 from both sides, which gives you -6. Then divide 2 from both sides.

2. -3x<-6 = x>2
You divide -3 from both sides. You must switch the sign because any time you multiply or divide a negative integer from both sides of an inequality the sign is switched.

3. -5x<5 = x>1
See number 2

4. 5-2x<11 = x>-3
Subtract 5 from both sides to get -2x<6. Then, divide both sides by -2 and switch the sign.

5. x+2<5 = x<3
Subtract 2 from both sides

6. 2-3x<5 = x>-1
Subtract 2 from both sides to get -3x<3. Then, divide -3 from both sides and switch the sign.
5 0
3 years ago
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