Answer:
Area shaded portion = 16/3 π - 8√3
Step-by-step explanation:
The shaded portion consists of 2 equal segment
∵ Two circles have the same radii = 4
∵ The the length of the common chord of the two circles = 4
∴ The central angle of each segment = π/3 (60° equilateral Δ)
∵ Area segment = area sector - area Δ
∵ Area sector = 1/2 r²Ф = 1/2 × (4)² × π/3 = 8/3 π
∵ Area Δ = 1/4 s² √3 = 1/4 × (4)² × √3 = 4√3
∴ Area segment = 8/3 π - 4√3
∴ Area shaded portion = 2(8/3 π - 4√3) = 16/3 π - 8√3
It is being distributed ( ex: 5(1), bring the 5 over and multiply: 5). Since -1 is the term that is distributing for both 8m and 32, multiplying both would equal= -8m (8m x -1, + x - = negative), +32 (notice the positive, - x - = positive). In conclusion, this would be -8m+32.
Answer:
volume of xy-plane outside the cone = 16π/3
Step-by-step explanation:
using cylindrical coordinates
z² = x² +y² =====>z²=r²=====>z=r
x² + y² =4 ====>r = 2
So, the volume ∫∫∫dV equal
∫(θ = 0 to 2π) ∫(r = 0 to 2) ∫z=0 to r) 1 x (r dz dr dθ) via cylindrical coordinates
= ∫(θ = 0 to 2π) ∫(r = 0 to 2) r² dr dθ
= ∫(θ = 0 to 2π) (1/3)r³ {for r = 0 to 2} dθ
= 2π x 8/3
= 16π/3
Answer:
Step-by-step explanation:
Given: Perimeter of triangle= 72 units
Measure of one of the side= x units
Measure of second side = 3x units
We know the perimeter of triangle is equal to sum of all sides.
Now, finding the possible value of x
forming an inequality to determine the value of x
Remember triangle has three sides, however, measure of only two sides are given.
⇒ 
⇒ 
Dividing both side by 4
⇒ 
∴ The inequality to represents all possible values of x is
