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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Test a pair from each table by substituting their values into the given equation and solving.
A) y = 2x + 1 .......... 2 = 2(0) + 1 .......... 2 ≠ 1
B) y = 2x + 1 .......... 1 = 2(0) + 1 .......... 1 = 1
C) y = 2x + 1 .......... -1 = 2(0) + 1 .......... -1 ≠ 1
D) y = 2x + 1 .......... -2 = 2(0) + 1 .......... -2 ≠ 1
The only pair that satisfied the equation was from answer choice B. Therefore, B is the correct answer.
Answer:
A tranlation and a rotaion.
Step-by-step explanation:
In order to map the shapes, you have to translate point A onto point D and then rotate until points C and F, and B and E match up.
Reflection across the x-axis (because there is a negative)
And
Vertical compression (because a is between 0 and 1)
Answer:
138 calories
Step-by-step explanation:
one Oz iced tea = 90/15 = 6
one Oz iced tea = 6 calories
23 Oz iced tea = 6 x 23 = 138 calories