The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
9514 1404 393
Answer:
Rotation 90° CCW
Step-by-step explanation:
Note that Figure 1 has a small appendage off the larger rectangle. That appendage is pointing East (to the right).
In Figure 2, that same appendage is pointing North (up).
If you are facing East and you want to face North, you will find that you need to turn 90° in the counterclockwise direction. That is the transformation that was done here:
rotation 90° CCW about the origin
Answer:
<u><em>The difference between iPhone 11 and Spinal cord repairence is 99,300$</em></u>.
Step-by-step explanation:
To be honest, this is a really weird question. But a<em><u> spinal cord injury</u></em> can cost up to <u><em>100,000$ a year</em></u>. And an<u><em> iPhone 11 cost around 700$</em></u>. It really just depends on what repairence the person got, but if I am wrong then I hope you the best with your question lol. And since Alex didnt break his phone, you wouldnt count the repairs for the iPhone 11.
Answer: both the left and right sides go to +∞
<u>Step-by-step explanation:</u>
End behavior can be determined by two things:
- Sign of the leading coefficient
- Degree of the function
<u>Sign of leading coefficient</u>:
positive: right side goes to +∞
negative: right side goes to -∞
⇒ Leading coefficient of this function is 3 so the right side goes to +∞
<u>Degree (exponent of leading coefficient)</u>:
even: both the left and right sides point in the SAME direction
odd: the left and right sides point in OPPOSITE directions
⇒ Degree of this function is 4 so the left side will point in the same direction as the right side.
<h2>
Maximum area is 25 m²</h2>
Explanation:
Let L be the length and W be the width.
Aidan has 20 ft of fence with which to build a rectangular dog run.
Fencing = 2L + 2W = 20 ft
L + W = 10
W = 10 - L
We need to find what is the largest area that can be enclosed.
Area = Length x Width
A = LW
A = L x (10-L) = 10 L - L²
For maximum area differential is zero
So we have
dA = 0
10 - 2 L = 0
L = 5 m
W = 10 - 5 = 5 m
Area = 5 x 5 = 25 m²
Maximum area is 25 m²
