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:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
= 
n = 9
r = 3
= ⁹P₃
= 
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 × 
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
Answer: c = -5, -8
Step-by-step explanation:
c^2 +13c+40=0
(c+5)(c+8)=40
c = -5, -8
Answer:
2.15cm^3
Step-by-step explanation:
V = Mass / Density
21.93g / 10.2g/cm^3
2.15cm^3
Let's say the numbers are "a" and "b"
hmm say "a" is the smaller, and "b" the greater
so "b" is "4 more than 5 times" "a"
so... 5 times "a" is 5*a or 5a
4 more than "that", will be "that" + 4
or
5a + 4
so.. whatever "a" is, "b" is 5a+4
now, their sum is 22, as opposed to "zz" hehe
so
solve for "a", to see what the smaller one is
what's "b"? well, b = 5a + 4
