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Setler79 [48]
2 years ago
9

I GIVE BRAINLILSET ......................,,,,,.,

Mathematics
1 answer:
zhannawk [14.2K]2 years ago
4 0

{\bf \red {\huge{answer : }}}

The money increased from 600 pounds to 621 pounds.

621 - 600 = 21

so , the money increased more 21 pounds.

\pink {\sf{hence , \frac{21}{621} \times 100 }}

\red{=  \frac{21}{\cancel{621}} \times  \cancel{100 }  }

\red{=  \frac{21}{\cancel{6.21}} \times  \cancel{1 }  }

\red{=  \frac{\cancel{21}}{\cancel{6.21}} }

\red{=  \frac{3 \frac{79}{207} }{1} }

\red{=  3 \frac{79}{207} }

Therefore , the dog's weight increased by 3 79/207%

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A rotating wind turbine has a diameter of about 145 feet and its circumference is about 456 feet. A smaller model of the turbine
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10/x = 580/185

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Read 2 more answers
Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:
kondaur [170]
\text{Proof by induction:}
\text{Test that the statement holds or n = 1}

LHS = (3 - 2)^{2} = 1
RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS
\text{Thus, the statement holds for the base case.}

\text{Assume the statement holds for some arbitrary term, n= k}
1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}

\text{Prove it is true for n = k + 1}
RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}

LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}
= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}
= \frac{k(6k^{2} + 15k + 11) + 2}{}
= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}
= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}
= RHS

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.
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3 years ago
Please help. This is a question on my final exam.
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The best option here is option B.
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