Answer:
π
V-foam = 4r³( 2 - ----- )
3
Step-by-step explanation:
Let r denote the radius of the sphere. The volume of the sphere is expressed as
V = (4/3)(π)(r³).
Next, understand that the cube's side length is 2r, hence the cube's volume is
V = (2r)³, which equals 8r³.
The volume of the foam is derived from the cube's volume subtracting that of the sphere:
V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to
π
V-foam = 4r³( 2 - ----- )
3
To determine which functions depict the arithmetic sequence 8, 1.5, -5, -11.5,... follow these steps:
<span>f(n) = –6.5n + 14.5... correct
f(1) = 8
f(2) = 1.5
f(3) = -5
f(4) = -11.5
f(n) = –1.5n + 9.5... incorrect
f(1) = 8
f(2) = 6.5
f(n) = 6.5n + 1.5... incorrect
f(1) = 8
f(2) = 14.5
f(1) = 8, f(n + 1) = f(n) – 6.5... correct
f(2) = 8 - 6.5 = 1.5
f(3) = 1.5 - 6.5 = -5
f(4) = -5 - 6.5 = -11.5
f(1) = 8, f(n + 1) = f(n) – 1.5... incorrect
f(2) = 8 - 1.5 = 6.5
f(1) = 8, f(n + 1) = f(n) + 6.5... incorrect
f(2) = 8 + 6.5 = 14.5
The valid functions are:
</span>f(n) = –6.5n + 14.5 and f(1) = 8, f(n + 1) = f(n) – 6.5.
For a rectangle, the perimeter can be calculated as P=2l+2w. Assuming the length is horizontal and the width is vertical, the span between the x coordinates will give the length, while the span between the y coordinates will determine the width. Once these measurements are obtained, you can apply them to the perimeter formula. |7 -(-7)| = 14 gives l = 14, |5-(-2)| = 7 gives w=7. Therefore, P=2(14)+2(7), which results in P= 28+14, thus, P= 42.
A 40-degree angle may be applicable for this question
