To solve this you need to use the formula for Chord-Chord length. You need to know it, it is ab=cd. with this, we can plug numbers in.
a=30
b=x+1
c=2x-6
d=21
So our new equation is:
30(x+1)=21(2x-6)
30x+30=42x-126
156=12x
x=13
This isn't what the question is askign for though, it wants YZ
Which is A+B or 30+x+1 or 21+13=34.
YZ=34
Congruent means Same Side, Same Shape.
If two angles are congruent, they are to be of the same size and same shape or a fraction of it (Dilation)
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:
This is very easy. First find the volume of the cube, and then add it to the volume of the hemisphere to find the total volume.
The volume of the cube is length x width x height: 8 x 8 x 12 = 768 cm
The volume of the hemisphere is (2/3)πr³ : (2/3)π(4)³ = 134.04 cm
*Radius is 4
Now add: 768 + 134.04 = 902.04 cm
