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Natalka [10]
3 years ago
8

Find the value of 105 squred using bionomial expansion using (a+b) squred=a squred+2ab + b squred

Mathematics
1 answer:
skad [1K]3 years ago
8 0

Answer:

<h2>11025</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about: </h3>
  • algebra
<h3>let's solve:</h3>
  1. \sf rewrite \: 105 \: as \: 100 + 5 :  \\  \sf (100 + 5 {)}^{2}
  2. \sf use \: (a + b {)}^{2}  =  {a}^{2}  + 2ab +  {b}^{2} \:  to \: simplify :  \\  \sf  {100}^{2}  + 2.100.5 +  {5}^{2}
  3. \sf simplify \: squres :  \\  \sf 10000 + 2.100.5 + 25
  4. \sf simplify \: multipication :  \\  \sf10000 + 1000 + 25
  5. \sf simplify \: addition :  \\  \sf \: 11025
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There is a mountain with 45 bat caves in a row. Every cave has at least 2 bats and there are 490 bats in all. Any 7 caves in a r
zhannawk [14.2K]

Answer:

12

Step-by-step explanation:

The first cave has 7 times more bats than the last cave.  So if the 45th cave has b bats, then the first cave has 7b bats.

There are 77 bats in every row of 7 caves.  So if there are 7b bats in the first cave, then there are 77−7b bats in caves 2 through 7.

Since there are also 77 bats in caves 2 through 8, that means cave #8 must have 7b bats.  Repeating this logic:

#1 = 7b

#2-#7 = 77−7b

#8 = 7b

#9-#14 = 77−7b

#15 = 7b

#16-21 = 77−7b

#22 = 7b

#23-28 = 77−7b

#29 = 7b

So the first 29 caves have 5(7b) + 4(77−7b) = 308 + 7b bats.

Now we do the same thing from the other end.  If cave #45 has b bats, then caves #39-#44 have 77−b bats.  And since caves #38-44 have 77 bats, then cave #38 has b bats.  Therefore:

#45 = b

#39-44 = 77−b

#38 = b

#32-37 = 77−b

#31 = b

So caves 31 through 45 have 3b + 2(77−b) = 154 + b bats.

Adding that to the first 29 caves, plus x number of bats in cave #30:

308 + 7b + x + 154 + b = 462 + 8b + x

We know this equals 490.

490 = 462 + 8b + x

28 = 8b + x

x is a maximum when b is a minimum, which is b = 2.

28 = 8(2) + x

x = 12

There are at most 12 bats in the 30th cave.

8 0
3 years ago
2/3 of the product of 3/8 and 16
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2/3(3/8x16). 2/3(6). 4. The answer is 4 :)
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Answer: D.

Step-by-step explanation:

3000/250=120

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12 months in a year. So 18 months= 1 year and 6 months. Izzys dog is 10 1/2= 10 years and six months. Then subtract 1 year and 6 months by 10 year and six months and it would be exactly 9 years older.
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The time X it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with
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