6>x take 12 from both sides
Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.
<h3>How do we verify if a sequence converges of diverges?</h3>
Suppose an infinity sequence defined by:
Then we have to calculate the following limit:
If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.
In this problem, the function that defines the sequence is:
Hence the limit is:
Hence, the infinite sequence converges, as the limit does not go to infinity.
More can be learned about convergent sequences at brainly.com/question/6635869
#SPJ1
Answer:
(8 * x) + 2x = 60
8x + 2x = 60
10x = 60
/10 /10
x = 6
8 is a constant that is being multiplied by an unknown number which we will name x. It is then being added to two times the unknown number(x), so we multiply x by 2, which is 2x. The final product will be 60, so in the equation it'll then equal 60.
We consider "a number" to be a variable that withholds an unknown value, which is x (or any other variable you prefer).
Answer:
B
Step-by-step explanation:
A is not a function because the same x value is repeated twice with different y values. The same goes for C and D so the answer is C.
Let a, b, and c be the times each pump will fill the tank when working alone.
Therefore, in 1 hour;
1/a +1/b = 1/(6/5) = 5/6 ---- (1)
1/a+1/c = 1/(3/2) = 2/3 ---- (2)
1/b+1/c = 1/(2) = 1/2 ---- (3)
From equation (1)
1/a = 5/6-1/b
Substituting for 1/a in eqn (2)
5/6-1/b+1/c = 2/3
-1/b +1/c = -1/6 => 1/c = 1/b - 1/6 --- (4)
Using eqn (4) in eqn (3)
1/b+1/b-1/6 = 1/2
2/b-1/6 = 1/2
2/b =1/2+1/6 = 2/3
1/b = 1/3
Then,
1/c = 1/3 - 1/6 = 1/6
1/a = 5/6 - 1/3 = 1/2
This means, in 1 hour and with all the pumps working together, the tank will be filled to;
1/a+1/b+1/c = 1/2+1/3+1/6 = 1 (filled fully).
Therefore, it will take 1 hour to fill the tank when all pumps are working together.
