Find the 7th term of the geometric sequence1/8, 1/2, 2, ...
1 answer:
Answer:
512
Explanation:
Given sequence:
1/8, 1/2, 2, ...
Unknown:
The 7th term of the geometric sequence = ?
Solution:
To solve this problem, we apply the formula below;
Sₙ = arⁿ⁻¹
a is the first term
r is the common ratio
n is the nth term
r = =
= 4
Input the parameters and solve;
Sₙ = x 4⁷⁻¹
Sₙ = x 4⁶ = 512
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Answer:
58.27 N
Explanation:
the data we have is:
mass:
coefficient of friction:
and we also know the acceleration of gravity is
We need to do an analysis of horizontal and vertical forces acting on the object:
-------
Vertically the forces acting on the object:
- Normal force
(acting up from the object)
- weight:
(acting down from)
so the sum of forces in the vertical axis "y" are:
from Newton's second Law we know that , so:
and since the object is not accelerating in the vertical direction (the movement is only horizontal) , and:
-----------
now let's analyze the horizontal forces
- frictional force:
and since
-->
- force to move the object:
and the two forces just mentioned must be opposite, thus the sum of forces in the "x" axis is:
and we are told that the crate moves at a steady speed, thus there is no acceleration:
and we get:
substituting known values: