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2 years ago

If the smallest angle of rotation for a regular polygon is 18, how many sides does polygon have?

Mathematics

2 answers:

Wittaler [7]2 years ago

8 0

Answer:

Step-by-step explanation:

edg did the test

Anna [14]2 years ago

6 0

Answer: There are 20 sides of a given regular polygon.

Step-by-step explanation:

To calculate the sides of a regular polygon, we use the equation:

$\text{Number of sides}=\frac{360^o}{\text{Smallest angle of rotation}}$

We are given:

Smallest angle of rotation = $18^o$

Putting values in above equation, we get:

$\text{Number of sides}=\frac{360^o}{18^o}\\\\\text{Number of sides}=20$

Hence, there are 20 sides of a given regular polygon.

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Which of the following numbers would have 6 at units place after being squared 19,24, 36

Mashutka [201]

Step-by-step explanation:

squaring on both side

36 root is 6

6*6=36

[√6]2

cut root and square

answer 6

3 0

3 years ago

Let f(x,y,z) = ztan-1(y2) i + z3ln(x2 + 1) j + z k. find the flux of f across the part of the paraboloid x2 + y2 + z = 3 that li

Sophie [7]

Consider the closed region $V$ bounded simultaneously by the paraboloid and plane, jointly denoted $S$ . By the divergence theorem,

$\displaystyle\iint_S\mathbf f(x,y,z)\cdot\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$

And since we have

$\nabla\cdot\mathbf f(x,y,z)=1$

the volume integral will be much easier to compute. Converting to cylindrical coordinates, we have

$\displaystyle\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\iiint_V\mathrm dV$
$=\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=2}^{z=3-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=1}r(3-r^2-2)\,\mathrm dr$
$=\dfrac\pi2$

Then the integral over the paraboloid would be the difference of the integral over the total surface and the integral over the disk. Denoting the disk by $D$ , we have

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-\iint_D\mathbf f\cdot\mathrm dS$

Parameterize $D$ by

$\mathbf s(u,v)=u\cos v\,\mathbf i+u\sin v\,\mathbf j+2\,\mathbf k$
$\implies\mathbf s_u\times\mathbf s_v=u\,\mathbf k$

which would give a unit normal vector of $\mathbf k$ . However, the divergence theorem requires that the closed surface $S$ be oriented with outward-pointing normal vectors, which means we should instead use $\mathbf s_v\times\mathbf s_u=-u\,\mathbf k$ .

Now,

$\displaystyle\iint_D\mathbf f\cdot\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(-u\,\mathbf k)\,\mathrm dv\,\mathrm du$
$=\displaystyle-4\pi\int_{u=0}^{u=1}u\,\mathrm du$
$=-2\pi$

So, the flux over the paraboloid alone is

$\displaystyle\iint_{S-D}\mathbf f\cdot\mathrm dS=\frac\pi2-(-2\pi)=\dfrac{5\pi}2$

6 0

3 years ago

The planning department of abstract office supplies has been asked to determine what is the company should introduce a new compu

BabaBlast [244]

Answer:

The company needs to sell 40 desks to break even

Step-by-step explanation:

Application of Equations

There is virtually no limit to the possible situations where equations can help to find the solution of specific problems related to areas like economy, where one could need to establish some important indicators about the business.

B. The fixed cost for Abstract Office Supplies to sell a new computer desk is $14,000. Each desk will cost $150 to produce. The cost function to produce X desks is

C(x)=150x+14,000

A. The revenue for each desk is estimated at $500, for X desks will be

R(x)=500x

C. The company will break even when the cost and the revenue are the same. We'll find how many desks need to be sold for that to happen. We equate

C(x)=R(x)

Or equivalently

150x+14,000=500x

Rearranging

500x-150x=14,000

350x=14,000

Solving for x

x=14,000/350= 40

The company needs to sell 40 desks to break even

4 0

2 years ago

Prove that x-y = √(x+y)^2-4xy?

Svetlanka [38]

Proved Below

$\Longrightarrow x-y = \sqrt{(x+y)^2-4xy}$

$\Longrightarrow x-y = \sqrt{x^2+2(x)(y)+ y^2-4xy}$

$\Longrightarrow x-y = \sqrt{x^2+2xy-4xy+y^2}$

$\Longrightarrow x-y = \sqrt{x^2-2xy+y^2}$

$\Longrightarrow x-y = \sqrt{(x-y)^2}$

$\Longrightarrow x-y =x-y$

6 0

2 years ago

Read 2 more answers

Your friend can clap his hands 28 times in 12 seconds. How many times can your friend clap his hands in 0.5 minute?

Allushta [10]

60 seconds in a minute

12 goes into 60, 5 times,
So 5 * 28 = 140
140 claps per minute

0.5 minute is 30 seconds, half a minute so divide by 2,
140/2 = 70

70 times every 0.5 minutes

7 0

3 years ago