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3 years ago

Prove that the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle.

Mathematics

1 answer:

kodGreya [7K]3 years ago

8 0

Answer:

Proven

Step-by-step explanation:

Let ABC be a triangle and D, E and F are midpoints of BC, CA and AB.

The sum of two sides of a triangle is greater than twice the median bisecting the third side,

Hence in ΔABD, AD is a median

⇒ AB + AC > 2(AD)

Hence, we get

BC + AC > 2 (CF )

BC + AB > 2 (BE)

On adding the above inequalities, we get

(AB + AC) + (BC + AC) + (BC + AB )> 2 (AD) + 2 (CD) + 2 (BE )

2(AB + BC + AC) > 2(AD + BE + CF)

AB + BC + AC > AD + BE + CF - Proven

* Sorry I don't have any attachments, use your imagination!

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dolphi86 [110]

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3 years ago

Read 2 more answers

Apple launches an ad campaign for iPhone 12. Managers want to know what is the % of social media mentions that have positive rea

Orlov [11]

Answer:

social media mentions do managers at Apple need to collect, if they want to get a margin of error of 2%

Sample size 'n' = 625

Step-by-step explanation:

Step(i):-

Given data Apple launches an ad campaign for iPhone 12

Managers want to know what is the % of social media mentions that have positive reactions to the new ad campaign

probability of positive reactions p = 1/2

Probability of negative reactions q = 1-p = 1/2

we know that $\sqrt{p(1-p}\leq \frac{1}{2}$

Step(ii):-

Given margin of error = 2 % =0.02

The margin of error is determined by

$M.E = \frac{\sqrt{p(1-p} }{\sqrt{n} }$

$0.02 = \frac{\frac{1}{2} }{\sqrt{n} }$

$\sqrt{n} =\frac{1}{2 X0.02}$

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3 years ago

Find the next three terms. 243, -81, 27, -9...

Katarina [22]

Hi there!

To find the answer, you divide one of the numbers by 3, and some others by -3.

I can show you how to do so! :D

243 ÷ -3 = -81

-81 ÷ 3 = 27

27 ÷ 3 = 9

Next three terms -

9 ÷ 3 = 3

3 ÷ 3 = 1

1 ÷ 3 = 0.3333, the 3 is repeating over and over again

I think this is the answer, based off my notes :)

That's your pattern!

Hope this helps!

Message me if you need anything else, I'd be happy to answer any other questions! :D

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Answer

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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