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3 years ago

The area of a circle is 100 π.what is the lenght of the side of a tegular hexagon inscribed in a circle.

1 answer:

8 0

This logic, geometric logic at that.

First find the radius of the circle.

$area = \pi {r}^{2} \\$
We find the radius by a little algebraic manipulation.

$area = \pi {r}^{2} \\ \sqrt{ \frac{area}{\pi} } = r \\ \sqrt{ \frac{100\pi}{\pi} } = r \\ radius = 10$

Answer:

The height of the hexagon is 10 units (whatever the units are, every measurement needs units). All the sides of a polygon are equal, and it's a regular hexagon, which is a polygon. It's simple thinking, mostly people get into trouble when they over think it

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Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.

jok3333 [9.3K]

Answer:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

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

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

$\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}$

And, the distance from P to (0, -2) will be:

$\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}$

So sum of the two distances must be 6. Therefore:

$d_1+d_2=6$

Now, by substitution:

$(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6$

Simplify. We can subtract the second term from the left:

$\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}$

Square both sides:

$(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)$

We can cancel the x² terms and continue squaring:

$y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4$

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

$-8y=36-12\sqrt{x^2+(y+2)^2}$

We can divide both sides by -4:

$2y=-9+3\sqrt{x^2+(y+2)^2}$

Adding 9 to both sides yields:

$2y+9=3\sqrt{x^2+(y+2)^2}$

And, we will square both sides one final time.

$4y^2+36y+81=9(x^2+(y^2+4y+4))$

Distribute:

$4y^2+36y+81=9x^2+9y^2+36y+36$

The 36y will cancel. So:

$4y^2+81=9x^2+9y^2+36$

Subtracting 4y² and 36 from both sides yields:

$9x^2+5y^2=45$

And dividing both sides by 45 produces:

$\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1$

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0

2 years ago

Read 2 more answers

Which is a solution to the equation y=5x-6

Vilka [71]

$y=5x-6 \\ \\ the \ graph\ of \ a \ linear \ equation \ is \ a \ straight \ line$

4 0

3 years ago

Read 2 more answers

Evaluate: log216 Select the appropriate response A) 0 B) -1 C) 7

stepladder [879]

Answer:

Step-by-step explanation:

log2(16)

log2(2^4)

4 log2(2)

4 × 1

It should be 4

3 0

3 years ago

You made some snacks for a party. You have 24 cheese snacks, 18 yogurt snacks, and 32 vegetable snacks. Total number of snacks.

Papessa [141]

The answer is 74 snacks.
24+32 =56
56+18=74

3 0

3 years ago

Read 2 more answers

The radius of a circle can be found by dividing the circumference of the circle by 6.28. What is the radius of a circle that has

steposvetlana [31]

The radius of a circle is found by doing this :
circumference ÷ 6.28 = radius

The circumference here is 17.27 feet :
circumference ÷ 6.28 = radius
so
17.27 ÷ 6.28 = 2.75

The radius of the circle is 2.75 feet.

5 0

3 years ago