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2 years ago

For the dilation with center (0,0) shown on the graph, your friend says the scale factor is 8/3

Mathematics

1 answer:

olchik [2.2K]2 years ago

3 0

Answer:

It actually depends on where the point of letter is

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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8 0

1 year ago

Express 31% as a fraction in its lowest form

Natasha2012 [34]

31 ------ 100 that's is what I got in the lowest form x

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2 years ago

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations

Ipatiy [6.2K]

Answer:

a) geometric

Step-by-step explanation:

a) geometric

An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term, but it is not like this, so it is a geometric sequence.

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2 years ago

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Is -7-5+3=1 true or false

grigory [225]

-7-5+3=1
-12+3=1
-9≠1. As a result, this is False. Hope it help!

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2 years ago

A party of 5 wants to tip 20% of their total $175 bill. If divided evenly, how much should each person tip?

Mashcka [7]

20% of $175 is $35. Divided between 5 people (35/5=7) would be 7. So each person should tip $7.

6 0

3 years ago

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For the dilation with center​ (0,0) shown on the​ graph, your friend says the scale factor is 8/3

For the dilation with center (0,0) shown on the graph, your friend says the scale factor is 8/3