Mathematics, 01.01.2021 20:30 ExperimentsDIYS

Fido's leash is tied to a stake at the center of his yard, which is in the shape of a regular hexagon. His leash is exactly long enough to reach the midpoint of each side of his yard. If the fraction of the area of Fido's yard that he is able to reach while on his leash is expressed in simplest radical form as [(sqrt{a})/b] * pi, what is the value of the product ab?

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Answer from: SoccerHalo

a = 3

b = 6

The product ab = 3 x 6 = 18

Step-by-step explanation:

Data Given:

Fraction of the area of Fido's yard = $\pi x \frac{\sqrt{a} }{b}$

Let X be the side of the hexagon.

So, the area of the Hexagon is:

Area of the Hexagon = $\frac{3\sqrt{3} }{2} X^{2}$

Now, we have to calculate the length of Fido's Leash by using Lw of Sine

Law of Sine = $\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

$\frac{0.5S}{sin30}$ = $\frac{Length}{sin60}$

Solving for Length, where sin30 = 1/2 and sin60 = $\frac{\sqrt{3} }{2}$

Suppose Length = Y

Y = $\frac{\sqrt{3} }{2}$ X

Now, as we have got the length we can calculate the area that Fido can cover,

So, the area covered by Fido = $\pi$ x $Y^{2}$

Area = $\pi$ x $(\frac{\sqrt{3} }{2}X) ^{2}$

Area = $\pi$ x $\frac{3}{4}$ x $X^{2}$

So, now, we can get the fraction of the area of Fido's Yard by dividing the area of hexagon by area that fido can cover.

Fraction of the area of Fido's yard = $\pi x \frac{\sqrt{a} }{b}$

$\pi$ x $\frac{3}{4}$ x $X^{2}$ / $\frac{3\sqrt{3} }{2} X^{2}$

$\pi$ x $\frac{3}{4}$ / $\frac{3\sqrt{3} }{2}$

6 $\pi$ / $12\sqrt{3}$

$\pi$ / $2\sqrt{3}$

Which can be rewritten as by multiplying and dividing by $\sqrt{3}$

$\sqrt{3} \pi$ / 6

By comparing the above equation and the given equation we can find a and b :

So,

a = 3

b = 6

And the product ab = 3 x 6 = 18

Answer from: Quest

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

Which construction does the image below demonstrate? 1. an equilateral triangle circumscribed abou

Answer from: Quest

step-by-step explanation:

when the line is solid:

it's either < or >

when the line is dashed:

it's either < or >

this > inequality sign means:

greater thanmore thanaboveexceeds

this < inequality sign means:

less thanfewer thanbelow

this > inequality sign means:

greater than/equal tono less thanat leastminimum of

this < inequality sign means:

less than/equal tono more thanat mostmaximum of

about the problem:

since the line is solid, that means it's either < or >

srry i'm not done ! i'll

Which inequality is represented by the graph? which test point holds true for the inequality?

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Fido's leash is tied to a stake at the center of his yard, which is in the shape of a regular hexago...