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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Answer:
100 points
Step-by-step explanation:
-75 + 200 = 125
125 - 25 = 100
Answer:
22.38 g of silicone-32 will be present in 300 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
where,
= quantity of the substance remaining
= initial quantity of the substance
= time elapsed
= half life of the substance
From the information given we know:
- The initial quantity of silicone-32 is 30 g.
- The time elapsed is 300 years.
- The half life of silicone-32 is 710 years.
So, to find the quantity of silicone-32 remaining we apply the above equation
22.38 g of silicone-32 will be present in 300 years.
Finding the midpoint between two points on a line involves three steps:
1. Find the distance between the two points
2. Find half of that distance
3. Either add that half to the lowest point, or subtract it from the highest point.
To find the distance between 52 and -18, we can take the absolute value of their difference. The reason we take the absolute value is to force the sign to be positive, since distances can never be negative. -18 - 52 = -70, and |-70| = 70.
Second, we find half of that distance, which in this case would be 70/2 = 35.
Finally, we add that value to -18 to find a midpoint of -18 + 35 = 17.
