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Natalija [7]
3 years ago
10

Find the sum of the interior angles of a quadrilateral with 15 sides?

Mathematics
2 answers:
OlgaM077 [116]3 years ago
6 0

Answer:

2,340

Step-by-step explanation:

<u><em>Using Formula</em></u>

=> (n-2)*180

<u><em>Where n is the number of sides. Here, no. of sides is 15</em></u>

=> (15-2)*180

=> 13*180

=> 2,340

Crank3 years ago
5 0

Answer:

2340°

Step-by-step explanation:

To find the sum of interior angles of any shape, use the formula: 180(n - 2), where <em>n</em> is how many sides there are. <em>So</em>,

180(15 - 2)

180(13)

2340

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Andreyy89

Let {s_n}_{n\in\Bbb N} be a sequence that converges to L. This means for any \varepsilon>0, there is some N such that |s_n-L| for all n>N. From this inequality we see that |(s_n-L)-0|, so it follows that s_n-L\to0.

On the other hand, let {s_n-L} be a sequence that converges to 0. This means |(s_n-L)-0| for all large enough n, and we get the simpler inequality for free, |s_n-L|, so it follows that s_n\to L.

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2 years ago
Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)
ELEN [110]

Question:

Find the point (,) on the curve y = \sqrt x that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

Step-by-step explanation:

y = \sqrt x can be represented as: (x,y)

Substitute \sqrt x for y

(x,y) = (x,\sqrt x)

So, next:

Calculate the distance between (x,\sqrt x) and (3,0)

Distance is calculated as:

d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}

So:

d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}

d = \sqrt{(x-3)^2 + (\sqrt x)^2}

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d = \sqrt{x^2 - 6x +9 + x}

Rewrite as:

d = \sqrt{x^2 + x- 6x +9 }

d = \sqrt{x^2 - 5x +9 }

Differentiate using chain rule:

Let

u = x^2 - 5x +9

\frac{du}{dx} = 2x - 5

So:

d = \sqrt u

d = u^\frac{1}{2}

\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}

Chain Rule:

d' = \frac{du}{dx} * \frac{dd}{du}

d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}

d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}

d' = \frac{2x - 5}{2\sqrt u}

Substitute: u = x^2 - 5x +9

d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}

Next, is to minimize (by equating d' to 0)

\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0

Cross Multiply

2x - 5 = 0

Solve for x

2x  =5

x = \frac{5}{2}

Substitute x = \frac{5}{2} in y = \sqrt x

y = \sqrt{\frac{5}{2}}

Split

y = \frac{\sqrt 5}{\sqrt 2}

Rationalize

y = \frac{\sqrt 5}{\sqrt 2} *  \frac{\sqrt 2}{\sqrt 2}

y = \frac{\sqrt {10}}{\sqrt 4}

y = \frac{\sqrt {10}}{2}

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(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})

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We have been given two equations which are as follows:

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x + 4y = 8

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Answer:

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General Formulas and Concepts:

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Slope-Intercept Form: y = mx + b

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y = 3x - 5

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Slope <em>m</em> = 3

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