Answer:
A. $161
B. $161 * 12 = $1,932
Step-by-step explanation:
I think it could be b. (cone) if it means the triangle is rotated literally & in 3D around the line. or it could be d. pyramid if it is meaning that the triangle is flipped across the vertical line.
Answer:
See below ↓↓
Step-by-step explanation:
<u>Finding x</u>
- Both the angles containing the x variable are on the same side of the transversal
- There is a property which states that : two angles on the same side of the transversal are supplementary
- Therefore, they add up to 180°
- ⇒ 8x + 12 + 2x + 18 = 180
- ⇒ 10x + 30 = 180
- ⇒ 10x = 150
- ⇒ <u>x = 15</u>
<u></u>
<u>Finding y</u>
- The angles at the top are vertically opposite angles (VOA), meaning that they are equal
- ⇒ 8x + 12 = 3y - 18
- ⇒ 3y = 8(15) + 12 + 18
- ⇒ 3y = 120 + 30
- ⇒ 3y = 150
- <u>⇒ y = 50</u>
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.