hectictar

24 ÷ 4 = 6   

I am sorry what I said is actually not good, I should have said slant height...

But here is my explanation. You can see how that it is because if you take the triangles and lay them out like this:

Since the base of each triangle is the same length,

area of one blue triange = (1/2)(1/4 * perimeter of base)(slant height)

There are 4 triangles total that area all the same size.. so,

area of all blue triangles = 4 * (1/2)(1/4 * perimeter of base)(slant height)

area of all blue triangles = (1/2)(perimeter of base)(slant height)

If cos(t) = 1/3 and sin(t) is negative,

this is a picture of the triangle ∠t makes:

Now we can use the Pythagorean theorem to find sin(t).

sin²(t) + (1/3)² = 1²

sin²(t) = 1 - 1/9

sin(t) = \(\pm\sqrt{\frac89}=\pm\frac{\sqrt8}{3}\)

The prolem says that sin < 0 , so we know that it is the negative option.

sin(t) = \(-\frac{2\sqrt2}{3}\)

tan = sin / cos

tan(t) = sin(t) / cos(t)

tan(t) = \(-\frac{2\sqrt2}{3}/\frac13\)

tan(t) = \(-\frac{2\sqrt2}{3}\cdot\frac31\)

tan(t) = \(-2\sqrt2\)

LA stands for "lateral area."

Lateral area is the surface area except for the area of the base.

The lateral area of a pyramid = (1/2) * (perimeter of base) * (height)

(-2)² = 4

-2² = -4

Thank you CPhil! 

It's only because of all that double-checking!!

But "usually" is a key word here! Lol 

factors of 12: 1, 2, 3, 4, 6, 12

factors of 32: 1, 2, 4, 8, 16, 32

greatest common factor: 4

That would be one hundred octovigintillion,

\((\frac34)x-4=\frac56\)

Multiply both sides of the equation by the lcm of the denominators.

In this case, it is 12.

\(12((\frac34)x-4)=12(\frac56) \\~\\ (\frac{36}{4})x-48=\frac{60}{6} \\~\\ 9x-48=10\)

If I'm understanding this right,

the position of the source is the center of that circle,

and the range of the signals is the radius of that circle.

The position of the source is the point ( -6, -4)

The signals reach a radius of 6 units.