A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience i
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According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.
<h3>How to approximate the value of a irrational number by binomial theorem</h3>Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:
(1)
Where:
- a, b - Constants of the binomial.
- n - Grade of the power binomial.
- k - Index of the k-th element of the power binomial.
If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:
√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
To learn more on binomial expansions: brainly.com/question/12249986
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Consider the center of the nonagon. If we join the center to all the vertices, the central angle of 360°, is divided into 9 equal angles, each with a measure of:
360°/9=40°
So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one.
similarly if we rotate 80 ° c.wise or c.c.wise
in general, a nonagon has a rotational symmetry of 40°n,
where n∈{...-3, -2, -1, 0, 1, 2, 3}...
where 40°n, for n negative, means we are rotating clockwise.
Answer: any angle which is a multiple of 40°
360°/9=40°
So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one.
similarly if we rotate 80 ° c.wise or c.c.wise
in general, a nonagon has a rotational symmetry of 40°n,
where n∈{...-3, -2, -1, 0, 1, 2, 3}...
where 40°n, for n negative, means we are rotating clockwise.
Answer: any angle which is a multiple of 40°