The population of a local species of flies can be found using an infinite geometric series where a1 = 940 and the common ratio i
s one fifth. write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.
1 answer:
A. Sigma notation
The formula for finding the nth value of the geometric series is given as:
an = a1 * r^n
Where,
an = nth value of the series
<span>a1 = 1st value in the geometric series = 940</span>
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite geometric series is given as:
<span>S = a1 / (1 – r)</span>
Substituting the given values:
S = 940 / (1 – 1/5)
<span>S = 1,175</span>
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Answer: The answer is x = 6 units.
Step-by-step explanation: Please refer to the attached diagram
The diagram in the question shows two triangles placed on each other and for convenience sake has been labelled ABDCE. Triangle ABC is a right angled triangle, and so is triangle ADE. From the marks on the lines, we can infer that line AD is equal in measurement to line DB. Also line AE is equal in measurement to line EC.
Therefore we can see the similarity in both triangles, if AD and AE equals DB and EC, then it follows that DE equals BC.
Hence if AD = DB and
AE = EC, and
DE = BC
Then, x - 3 = ½x
(½x can also be expressed as x/2)
x - 3 = x/2
By cross multiplication we now have
2(x - 3) = x
2x - 6 = x
By collecting like terms we now have
2x - x = 6
x = 6
