Red light is 15.1cm
yellow is 16.3cm
purple is 19.3cm
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
Answer:
Step-by-step explanation:
Given that bottle was half full at 11.35 a.m. and full at 11.40 a.m.
This implies it takes 5 minutes for the liquid to double.
This is confirmed by the statement that before 5 minutes i.e. at 11.30 the bottle was only 1/4 full.
Hence true statements would be:
1) The bottle was 1/2 full at 11:35 a.m. and doubled again after 5 minutes.
2) The bottle was 1/4 full at 11:30 a.m. and doubled twice after 10 minutes. The bottle was 1/2 full at 11:35 a.m.
3) Exponential growth involves a constant multiplicative rate of change.
(The rate cannot be additional as we get 2 times every 5 minutes)
I believe the answer would be C. u subtract the 5 from both sides and divide by the -4 and flip the inequality. it has to be greater than than 13/4.
