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
Hopes this helps:
Answer: x = 6
Answer:
(n-5)^2 - (6n-35)=(n-10)(n-6)
-----------
- n²-10n+25-6n+35 =
- n²-16+60 = n²- 10n - 6n + 60 =
- n(n-10) - 6(n-10) =
- (n-10)(n-6)
Answer:
Step-by-step explanation:
Cross multiply and get:
L = 5w
L = 5w/
W = L/5
Answer:
4/6 is more than 5/12
Step-by-step explanation:
First, set the denominators of the fractions equal to eachother to make it easier to compare. mulitiply 6 and 4 by 2 so that the denominator now equals 12, and you have the new fractions 5/12 and 8/12. Since 8/12 is more than 5/12, 4/6 is more than 5/12.
