Answer:
∠2=92°
Step-by-step explanation:
Using an angle formula, -8x+144=2x+74
Simplification:
-8x+144=2x+74
-8x+70=2x
70=10x
x=7
Therefore, each angle is 88°
Now, because ∠2 is adjacent to one of 88°, they add up to 180°
Therefore,
180°=88°+∠2
∠2=92°
Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.
<h3>What is the Area of a Sector?</h3>
Area of a sector of a circle = ∅/360 × πr²
<h3>What is the Length of an Arc?</h3>
Length of arc = ∅/360 × 2πr
Given the following:
- Radius (r) = 9 cm
- Length of arc = 6π cm
- Area of sector = kπ cm²
Find ∅ of the sector using the formula for length of acr:
∅/360 × 2πr = 6π
Plug in the value of r
∅/360 × 2π(9) = 6π
∅/360 × 18π = 6π
Divide both sides by 18π
∅/360 = 6π/18π
∅/360 = 1/3
Multiply both sides by 360
∅ = 1/3 × 360
∅ = 120°
Find the area of the sector:
Area = ∅/360 × πr² = 120/360 × π(9²)
Area = 1/3 × π81
Area = 27π
Therefore, the value of k is 27.
Learn more about area of sector on:
brainly.com/question/22972014
Answer:
B ( 432 units^2)
Step-by-step explanation:
Total surface area= 2*(6*6)+ 4*(15*6)
There are 2 squares at each end of the same size so total area will be 2*(6*6)
If we look at the rectangles( bottom, top and the sides), we can see that all are of same dimensions and there are 4 of them so it's 4*(15*6)
In short, total surface area= 2*(6*6)+ 4*(15*6) = 432 units^2
Hi!
We can set up a proportion then cross multiply to solve this.
45 x 100 = 4500
4500/18 = 250
The answer is 250
Hope this helps! :)
