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What are the 2 numbers if the arithmetic mean is 7 and the geometric mean is 3?
Wiki User
∙ 11y ago
(x+y)/2=7; x+y=14; y=14-x
3=√(xy); xy=9; y=9/x
Use substitution:
14-x=9/x; 14x - x2=9; x2 - 14x +9=0
Use the quadratic formula:
x=[14±√(196-36)]/2; x=[14±√160]/2; x=[14±4√10]/2
x=7+2√10 or x=7-2√10
If x=7+2√10, then y=14-(7+2√10)=7-2√10
If x=7-2√10, then y=14-(7-2√10)=7+2√10
The first pair's geometric mean is √[(7+2√10)(7-2√10)]=√[72-(2√10)2]=√(49-40)=√9=3.
The first pair's arithmetic mean is (7+2√10 +7-2√10)/2=14/2=7
The second pair's geometric mean is √[(7-2√10)(7+2√10)]=√[72-(2√10)2]=√(49-40)=√9=3.
The second pair's arithmetic mean is (7-2√10 +7+2√10)/2=14/2=7
That's it!
Wiki User
∙ 11y ago
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What is the geometric mean of two numbers 2 and 12?
Geometric mean of 2 and 12 is 4.898979485566356. Look at link: "Calculation of the geometric mean of two numbers".
What is the Formula of geometric mean for 2 numbers?
The geometric mean of two numbers is the square root of their product. For example, the geometric mean of 4 and 25 is 10.
What is the geometric means between 2 and 24?
Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".
Is 0 1 -2 a geometric or arithmetic?
Neither.
What are the numbers whose sum is 3 form an arithmetic sequence and their squares form geometric sequence?
The numbers are: 1-sqrt(2), 1 and 1+sqrt(2) or approximately -0.414214, 1 and 2.414214
What is a geometric property?
1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.
Q4 The arithmetic mean of 2 numbers is 34 and their geometric mean is 16 One of the numbers will be?
4
What is the Mean for the following set of numbers 10 12 8 5 2?
the arithmetic mean for the set of numbers is 7.4. but the geometric mean is 6.25826929.
What is the Relation between geometric mean and arithmetic mean?
The mean of the numbers a1, a2, a3, ..., an is equal to (a1 + a2 + a3 +... + an)/n. This number is also called the average or the arithmetic mean.The geometric mean of the positive numbers a1, a2, a3, ... an is the n-th roots of [(a1)(a2)(a3)...(an)]Given two positive numbers a and b, suppose that a< b. The arithmetic mean, m, is then equal to (1/2)(a + b), and, a, m, b is an arithmetic sequence. The geometric mean, g, is the square root of ab, and, a, g, b is a geometric sequence. For example, the arithmetic mean of 4 and 25 is 14.5 [(1/2)(4 + 25)], and arithmetic sequence is 4, 14.5, 25. The geometric mean of 4 and 25 is 10 (the square root of 100), and the geometric sequence is 4, 10, 25.It is a theorem of elementary algebra that, for any positive numbers a1, a2, a3, ..., an, the arithmetic mean is greater than or equal to the geometric mean. That is:(1/n)(a1, a2, a3, ..., an) ≥ n-th roots of [(a1)(a2)(a3)...(an)]
What is the geometric mean of 2 and 4?
3mean is the average, so 2 + 4 = 6; 6 / 2 = 3* * * * *The above is the arithmetic mean which is NOT the same thing as the geometric mean.The geometric mean of n non-negative numbers is the nth root of their product.So GM(2, 4) = sqrt(8) = 2.828 (approx).
What is the geometric mean of two numbers 2 and 12?
Geometric mean of 2 and 12 is 4.898979485566356. Look at link: "Calculation of the geometric mean of two numbers".
What is the Formula of geometric mean for 2 numbers?
The geometric mean of two numbers is the square root of their product. For example, the geometric mean of 4 and 25 is 10.
Properties and limitations of geometric mean?
In a given sequence, there are two possible means calculatable: Arithmetic Mean, and Geometric Mean. The arithmetic mean, as we all know, is calculated from the sum of all the numbers divided by how many numbers there are: Sumn/n. The Geometric sum is calculated by multiplying all the numbers within the sequence together and taking the nth root of this value: (Productn)(1/n).In a geometric series, N(i)= a(ri), the geometric mean is found to be a(rn-1), where n is the number of elements within the series. this decreases or increases exponentially depending on the r value. If r1, increasing.Limitation Of Geometric Mean are:-1) Geometric mean cannot be computed when there are both negative and positive values in a series or more observations are having zero value.2)Compared to Arithmetic Mean this average is more difficult to compute and interpret.-Iwin
What is the first and second arithmetic mean between two numbers?
Any two numbers can have only one arithmetic mean. If the numbers are x and y, then their arithmetic mean is (x + y)/2.
What is the geometric means between 2 and 24?
Geometric mean between 2 and 24 is 6.928203230275509. Look at link: "Calculation of the geometric mean of two numbers".
Is -10 -6 -2 2 6 arithmetic or geometric or neither?
Its an arithmetic progression with a step of +4.
Is 0 1 -2 a geometric or arithmetic?
Neither.
