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3 years ago

Which is the best definition of a triangle

1 answer:

5 0

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted △ABC. In Euclidean geometry any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.

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The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit in

Marina86 [1]

Answer:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

Step-by-step explanation:

Assuming this complete problem: "The following formula for the sum of the cubes of the first n integers is proved in Appendix E. Use it to evaluate the limit . 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2"

We have the following formula in order to find the sum of cubes:

$\lim_{n\to\infty} \sum_{n=1}^{\infty} i^3$

We can express this formula like this:

$\lim_{n\to\infty} \sum_{n=1}^{\infty}i^3 =\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

And using this property we need to proof that: 1^3+2^3+3^3+...+n^3=[n(n+1)/2]^2

$\lim_{n\to\infty} [\frac{n(n+1)}{2}]^2$

If we operate and we take out the 1/4 as a factor we got this:

$\lim_{n\to\infty} \frac{n^2(n+1)^2}{n^4}$

We can cancel $n^2$ and we got

$\lim_{n\to\infty} \frac{(n+1)^2}{n^2}$

We can reorder the terms like this:

$\lim_{n\to\infty} (\frac{n+1}{n})^2$

We can do some algebra and we got:

$\lim_{n\to\infty} (1+\frac{1}{n})^2$

We can solve the square and we got:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2})$

And when we apply the limit we got that:

$\lim_{n\to\infty} (1+ \frac{2}{n} +\frac{1}{n^2}) =1$

3 0

3 years ago

Jimmy has 40apples and Karl has 20 how many more apples does jimmy has from Karl

Makovka662 [10]

Answer: Jimmy has 20 more apples than Karl.

Step-by-step explanation:

40 - 20 = 20

5 0

3 years ago

Read 2 more answers

Where did we get one?

77julia77 [94]

Answer:

The -1 came from factoring.

The equation is multiplied by 8 because 8 could be pulled from 16x-8.

16 can be divided by 8 2 times and 8 can only divided by 8 once.

so factoring it makes the equation 8(2x-1)

5 0

3 years ago

Can someone help me with this?<br> I am not understanding this and the diagram<br> Thanks

Pavel [41]

Answer:

a) m∠FGH= 28°

b) m∠HGI = 28°

c) m ∠FGI = 56°

Step-by-step explanation:

GH bisects ∠FGI. So, ∠FGH = ∠HGI

5x - 2 = 6x -8

5x - 6x = 2 - 8

-x = - 6

x = 6

a) m∠FGH = 5x - 2 = 5 * 6 - 2 = 30 - 2 = 28°

b) m∠HGI = 6x - 8 = 6 * 6 - 8 = 36 - 8 = 28°

c) m ∠FGI = m∠FGH + m∠HGI = 28° +28° = 56°

7 0

3 years ago

Which number produces an irrational number when added to 3/4?

S_A_V [24]

Any irrational number produces an irrational number when added to 3/4.

This is because 3/4 is rational (it can be represented as a ratio of two integers). You can get an irrational number only when you add rational to irrational (because rational to rational produces a rational sum).

6 0

4 years ago