Answer:
Option (1)
Step-by-step explanation:
In a geometric series,
Here r = 
For |r| < 1, series will converge.
For |r| > 1, series will diverge.
Option (1)
Given geometric series is,
Common ratio = 
= 
Since, 
Series will converge.
Option (2)
r = 
Since, 2 > 1,
Series will diverge.
Option (3)
Common ratio 'r' = 
Since, 3 > 1,
Series will diverge.
Option (4)
Common ratio 'r' = 
Since, 6 > 1
Series will diverge.
Therefore, Option (1) will be the correct option.
Answer:
The volume of the regular tetrahedron is 283.5 m³
Step-by-step explanation:
The formula of the volume of the regular tetrahedron is V = 
A h, where
∵ The area of the base of a regular tetrahedron is 98.9 m²
∴ A = 98.9 m²
∵ The height of it is 8.6 m
∴ h = 8.6 m
→ Substitute them in the formula of the volume above
∵ V = (98.9)(8.6)
∴ V = 283.5133333 m³
→ Round it to the nearest tenth of a cubic meters
∴ V = 283.5 m³
∴ The volume of the regular tetrahedron is 283.5 m³
Answer:
b^2 + 4 a b - 2 b - 2 a^2 + -5 a
Step-by-step explanation:
Simplify the following:
-2 a (a + b - 5) + 3 (2 b - 5 a) + b (6 a + b - 8)
-2 a (-5 + a + b) = 10 a - 2 a^2 - 2 a b:
10 a - 2 a^2 - 2 a b + 3 (2 b - 5 a) + b (6 a + b - 8)
3 (2 b - 5 a) = 6 b - 15 a:
10 a - 2 a^2 - 2 a b + 6 b - 15 a + b (6 a + b - 8)
b (-8 + 6 a + b) = -8 b + 6 a b + b^2:
10 a - 2 a^2 - 2 a b - 15 a + 6 b + -8 b + 6 a b + b^2
Grouping like terms, 10 a - 2 a^2 - 2 a b - 15 a + 6 b - 8 b + 6 a b + b^2 = b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a):
b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)
a b 6 + a b (-2) = 4 a b:
b^2 + 4 a b + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)
6 b - 8 b = -2 b:
b^2 + 4 a b + -2 b - 2 a^2 + (10 a - 15 a)
10 a - 15 a = -5 a:
Answer: b^2 + 4 a b - 2 b - 2 a^2 + -5 a
Answer:
48
Step-by-step explanation:
A step-by-step solution to 1/6 plus 2/8, with the answer in fraction form.Now we multiply 1 by 8, and get 8, then we multiply 6 by 8 and get 48.
