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3 years ago

Which one of the following formulas will find the sum of interior angles of a polygon with n sides

2 answers:

4 0

The way to understand this is that any polygon with sides greater than or equal to 3 will produce a set of triangles. From basic geometric properties, the angle sum of each triangle is 180°.

Consider a five-sided shape (a pentagon).
From one vertex, we can construct three triangles from the four points we have remaining. This is because the adjacent two points can never construct a triangle.

By doing this, we can see that there are three triangles that we have made. Thus, we know the total summation of angles will have to add up to 180 · 3 = 540°

Now, let's consider a general polygon, one with n sides.
By picking one vertex, we can construct a maximum of (n - 2) triangles, because the two adjacent points do not and will never construct any triangles.

Thus, we can say the sum of the interior angles is generalised as the formula:
180(n - 2)

Travka [436]3 years ago

3 0

Every added angle to a polygon adds another 180 degrees to the sum of the angles. The starting point is 180 degrees for a triangle (n=3). So the general formula is 180*(n-2). Fill in n=3 to test if 180 comes out, it does!!

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You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$

The tangent line is horizontal when the slope is 0; this happens for

$-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}=0\implies\sin(2\theta)=-1\implies2\theta=-\dfrac\pi2+2n\pi\implies\theta=-\dfrac\pi4+n\pi$

where $n$ is any integer. In the interval $0\le\theta\le2\pi$ , this happens for $n=1,2$ , or

$\theta=\dfrac{3\pi}4\text{ and }\theta=\dfrac{7\pi}4$

i.e at the points

$(r,\theta)=\left(e^{3\pi/4},\dfrac{3\pi}4\right)$

and

$(r,\theta)=\left(e^{7\pi/4},\dfrac{7\pi}4\right)$

8 0

3 years ago

A playground sits on a square lot with a perimeter of 600 feet. Two diagonal paths cross the lot. To the nearest foot,how long i

Elina [12.6K]

Answer:

The playground is a square with two diagonal paths turning it into triangles. If we use the formula for 45° 45° 90° triangles to determine the length of the hypotenuse (path).

The length for one path is 600ft so 600(sqrt/2) = 858.528ft

Each path is 858.53ft.

3 0

4 years ago

If x < 11 and x >4, which whole numbers are solutions for x? PLEASE HELP ITS DUE TOMORROW!

Harrizon [31]

Answer:

Step-by-step explanation:

If x < 11 and x > 4, then 4 < x < 11.

x is greater than 4 and less than 11.

Your answer: 5, 6, 7, 8, 9 and 10.

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4 years ago

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What is the area of this trapezoid <br> 18<br> 20<br> 24<br> 60

faust18 [17]

Answer:

518400, I think. I dunno for sure....

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4 years ago

Please I NEED HELP AS SOON AS POSSIBLE! Two students were given the same problem of 2x - 4 = 6 to solve . Student A got an answe

tatyana61 [14]

Answer:

Student A is correct and student B made the mistake

Step-by-step explanation:

Student B divided 2 on both sides before subtracting four, when they should've done it the other way around: add four on both sides and then divide by 2 to solve for x

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3 years ago

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