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:

$(a + b)^{n} = \sum \limits_{k = 0}^{n} \left(\begin{array}{c}n\\k\end{array}\right)\cdot a^{n-k} \cdot b^{k}$ (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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8 0

1 year ago

How to solve this equation 3x-2y=10,2x 5y=13?

frez [133]

There's an app called photomath that would be useful for these kinds of problems!

4 0

3 years ago

Expand the binomial (2x+5)^5

Whitepunk [10]

That would simplify to 32x^5+400x^4+200x^3+5000x^2+6250x+3125
You would do that because you have to write it repeatedly as (2x+5)(2x+5) and so on.

3 0

3 years ago

C(x) = mx + 500

grin007 [14]

Total cost as the function of shirts is :

C(x) = mx + 500 .

It is given that , The total cost to produce 100 shirts is $800.

800 = 100m + 500

m = 3

So , cost is given by :

C(x) = 3x + 500 .

Now , putting x = 1000 .

We get :

C(x) = 3x + 500

C(x) = 3(1000) + 500

C(x) = $3500

Therefore , cost of producing 1000 shirts is $3500 .

Hence, this is the required solution .

6 0

3 years ago