What is the 7th term in the geometric sequence in which a10 is 9 and a13 is -72?
1 answer:
Recall, a geometric series has this form with constants A for n=0, and k, the ratio of two consecutive terms n/(n+1)
you are given two values, for n=13 and n=10, put both into the equation
Two equations with two unknown values A and k, you can solve for those.
Solving both for A,
The general equation for the series is then,
use n=7
you are given two values, for n=13 and n=10, put both into the equation
Two equations with two unknown values A and k, you can solve for those.
Solving both for A,
The general equation for the series is then,
use n=7
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Given:
The number of members in an organization since the year 2000 can be represented by the function
where, x represents the number of years after 2000.
To find:
The statement which best describes the term 5.
Solution:
We have,
It is clear that 5 is a constant because it is free from variable x.
At x=0,
It means, 5 is the initial number of members in the organization.
Therefore, there are 5 members in the organization in year 2000.
Answer:
For (a) ±< cos ( π /6) , sin( π /6 ) > = ± < 1 /2 , √ 3 /2 > For (b)= < √ 3 /2 ,- 1 /2 > For (c) see attachment.
Step-by-step explanation:
y'atx=π/6 is 2cos(π/6)=√3.
This direction θ=ψ is given by tanψ=√3.
Inversely, ψ=tan−1√3 is π/6. For the opposite direction ,
it is π+π/6.
The unit vector in the direction θ=π/6 is
<cos(π/6),sin(π/6)>.
For the opposite direction, it is
<cos(π+π/6),sin(π+π/6)>
=<−cos(π/6),−sin(π/6)> .
For Part (b)
That is, the slope of the tangent line is √3. So
(1,√3)
gives the direction of the line and
(√3,−1)
gives the direction of the perpendicular line.
(Note that (b,−a)⊥(a,b) for any vector.)
For Part C
See the link
