Find an explicit formula for the geometric sequence 96,24,6,1.5,...
2 answers:
Answer: 96 / 4 ^n-1
Step-by-step explanation:
This is a geometric sequence with a first term of 96. The common ratio is the division of the 2nd term by the first term. This will be:
24/96 = 1/4
a = 96
r = 1/4
The formula will be:
ar ^n-1
= 96 × (1/4)^n-1
The concluding part is explained in the attached file.
You might be interested in
Answer:
The answer is and
Step-by-step explanation:
Given:
-4x-2y=14
-10x+7y=-24
Now, to solve it by elimination:
......(1)
......(2)
So, we multiply the equation (1) by 7 we get:
And, we multiply the equation (2) by 2 we get:
Now, adding both the new equations:
<em>Dividing both the sides by -8 we get:</em>
Now, putting the value of in equation (1):
<em>Subtracting both sides by 25 we get:</em>
<em>Dividing both sides by -2 we get:</em>
Therefore, the answer is and
<u>ANSWER: </u>
170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
<u>SOLUTION: </u>
First, set up a table. Fill in the unknowns with variables x and y. The table is attached below
From this, we can easily set up the two equations.
Sum of values of two acids = Value of mixture
0.1x + 0.65y = 1122
For convenience, we'll multiply the entire equation by 100,
10x + 65y = 112200 ------ (1)
Now, Sum of amounts of each acid = Amount of mixture
x + y = 1870 ---------(2)
multiply (2) with 10 for easy calculation and derive the equation into one variable.
10x + 10y = 18700
Subtracting equation (2) from (1),
( + ) 10x + 65y = 112200
( − ) 10x + 10y = 18700
we get the solution as,
0 + 55y = 93500
Thus, 55y = 93500
y = 1700
Substituting y = 1700 in (2),
x + 1700 = 1870
x = 1870 - 1700
x = 170
So, we have x = 170 and y = 1700
We can conclude that 170 liters of 10% hydrochloric acid must be mixed with 1700 liters of 65% hydrochloric acid solution to obtain 1870 liters of 60% solution.
