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2 years ago

If a regular polygon has 72 sides and an order of 72,what is the polygon’s rotational angle?

Mathematics

1 answer:

Misha Larkins [42]2 years ago

7 0

Answer:

The rotational angle of a regular polygon with 72 sides is 5º.

Step-by-step explanation:

The rotational angle ( $\theta$ ), measured in sexagesimal degrees, of polygon of $n$ sides is the angle of a complete revolution divided by the number of sides ( $n$ ). That is:

$\theta = \frac{360}{n}$ (1)

If we know that $n = 72$ , the rotational angle is:

$\theta = \frac{360}{72}$

$\theta = 5^{\circ}$

The rotational angle of a regular polygon with 72 sides is 5º.

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Which is greater between |5| amd |2|

pshichka [43]

Answer:

|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.

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2 years ago

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Tristán wants to build a square garden in his backyard if the garden is going to be 64 ft2 how many feet of material will he nee

Alex777 [14]

Answer:

Tristan will need 32 feet of material for the perimeter of the garden.

Step-by-step explanation:

Given that

Area of square garden = A = 64 square feet

Perimeter = P = ?

We know that for calculation of perimeter, length of side of square is required which is not directly given in the question. The area will be used to calculate length of side and then length will be used to calculate the perimeter.

So,

$Area = A = s^2$

s is for side

Putting the value of area

$64 = a^2$

Taking square root on both sides

$\sqrt{s^2} = \sqrt{64}\\s = 8\ feet$

The length of side is 8 feet.

Perimeter will be:

$P = 4*s\\P = 4*8\\P = 32\ feet$

Hence,

Tristan will need 32 feet of material for the perimeter of the garden.

3 0

2 years ago

Lots of point up for grabs

Burka [1]

Minus a from both sides
x-a=-2by²
times both sides by -1
a-x=2by²
divide both sides by 2b
$\frac{a-x}{2b}=y^2$
sqrt both sides
$y= \sqrt{\frac{a-x}{2b}}$

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2 years ago

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A bicycle shop advertised all mountain bikes priced at a 1/3 discount. If the original cost of the bikes is $327, what is the ne

nataly862011 [7]

Answer- B

Explanation- 327 divided by 3 would be 109 and a 109 + 109 would equal 218 and 218 would be 2/3 of 327

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1 year ago

1.) Find the length of the arc of the graph x^4 = y^6 from x = 1 to x = 8.

xxTIMURxx [149]

First, rewrite the equation so that y is a function of x :

$x^4 = y^6 \implies \left(x^4\right)^{1/6} = \left(y^6\right)^{1/6} \implies x^{4/6} = y^{6/6} \implies y = x^{2/3}$

(If you were to plot the actual curve, you would have both $y=x^{2/3}$ and $y=-x^{2/3}$ , but one curve is a reflection of the other, so the arc length for 1 ≤ x ≤ 8 would be the same on both curves. It doesn't matter which "half-curve" you choose to work with.)

The arc length is then given by the definite integral,

$\displaystyle \int_1^8 \sqrt{1 + \left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx$

We have

$y = x^{2/3} \implies \dfrac{\mathrm dy}{\mathrm dx} = \dfrac23x^{-1/3} \implies \left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2 = \dfrac49x^{-2/3}$

Then in the integral,

$\displaystyle \int_1^8 \sqrt{1 + \frac49x^{-2/3}}\,\mathrm dx = \int_1^8 \sqrt{\frac49x^{-2/3}}\sqrt{\frac94x^{2/3}+1}\,\mathrm dx = \int_1^8 \frac23x^{-1/3} \sqrt{\frac94x^{2/3}+1}\,\mathrm dx$

Substitute

$u = \dfrac94x^{2/3}+1 \text{ and } \mathrm du = \dfrac{18}{12}x^{-1/3}\,\mathrm dx = \dfrac32x^{-1/3}\,\mathrm dx$

This transforms the integral to

$\displaystyle \frac49 \int_{13/4}^{10} \sqrt{u}\,\mathrm du$

and computing it is trivial:

$\displaystyle \frac49 \int_{13/4}^{10} u^{1/2} \,\mathrm du = \frac49\cdot\frac23 u^{3/2}\bigg|_{13/4}^{10} = \frac8{27} \left(10^{3/2} - \left(\frac{13}4\right)^{3/2}\right)$

We can simplify this further to

$\displaystyle \frac8{27} \left(10\sqrt{10} - \frac{13\sqrt{13}}8\right) = \boxed{\frac{80\sqrt{10}-13\sqrt{13}}{27}}$

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2 years ago