Step-by-step explanation:
S = ∫ 2π y ds
ds = √(1 + (dx/dy)²) dy
ds = √(1 + (8y)²) dy
ds = √(1 + 64y²) dy
S = ∫₁² 2π y √(1 + 64y²) dy
S = π/64 ∫₁² 128y √(1 + 64y²) dy
S = π/64 [⅔ (1 + 64y²)^(³/₂)] |₁²
S = π/96 (1 + 64y²)^(³/₂) |₁²
S = π/96 (1 + 256)^(³/₂) − π/96 (1 + 64)^(³/₂)
S = π/96 (257√257) − π/96 (65√65)
S = π/96 (257√257 − 65√65)
Answer: 200cm
Step-by-step explanation:
The center Planck is a square of length 8cm.
The 4 next planks are of 16 cm each
And the next 4 Planks are of 32 cm each.
8 + 4(8×2) + 4(8×4)
8 + 4(16) + 4(32)
8 + 64 + 128
200 cm
Length of the original plank is 200cm
Answer: 36.65 inches
Step-by-step explanation:
The length of arc with a central angle x and radius r in a circle is given by :-
Given : Radius of a circle = 60 inches
Central angle =
Now, the of length of arc is given by :-
Hence, the length of arc = 36.65 inches.
This would probably be B.
First put the numbers in order to find the median:
26, 27, 28, 32, 32, 33, 35, 36, 38, 40, 42, 48
The number in the middle will be the median. In this case, there is an even number of data points so we will have to average the two numbers in the middle:
33 + 35 = 68...68/2 = 34. Therefore the median is 34
Now to get the inequality, add and subtract 6 from 34:
34 + 6 = 40
34 - 6 = 28
So the inequality is:
28 < x < 40
