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:
y = 5
Step-by-step explanation:
The y-axis and any lines that are parallel to it are vertical. Therefore, a line that would be perpendicular to the y-axis would need to be horizontal. All horizontal lines have a slope equal to 0 and are represented by the equation y = a constant, or a single number with no variables.
The only option that follows that format is y = 5, thus that is the answer.
Answer:
Step-by-step explanation:
Given that,
Length = 
Width = 
Depth = 9 yards
We need to find the volume of the swimming pool. The formula for the volume of a cuboid shape is given by :
So, the volume of the swimming pool is equal to 
.
The y-intercept is the point where the graph crosses the y-axis. It is found by setting x=0. For your equation, that makes the x-term vanish and only the constant remains. The ordered pair is ...
(x, y) = (0, -9)
Fraction form 38
___
1
Or just 38
