(a) Triangles ABC and ABD are equilateral triangles, so have internal angles of 60°. The angle CBD is the sum of the measures of angles CBA and ABD, both of which are 60°.
angle CBD measures 120° = 2π/3 radians
(b) The area of the left shaded area is the area of circle A minus twice the area of circular segment CBD. The area of a circular segment that subtends an arc of α radians is
... A = (1/2)r²(α - sin(α))
Then the area of the left shaded area is
... (area of circle) - 2 × (area of segment)
... = π·r² - r²(2π/3 - sin(2π/3)) = r²(π/3 + sin(2π/3))
For a radius of 6 cm, the area of the left shaded area is
... (6 cm)²(π/3 + (√3)/2) ≈ 68.876 cm²
Then the area of both shaded areas is
... shaded area ≈ 2 × 68.876 cm² ≈ 137.752 cm²
_____
(If you erroneously use the 3-digit value 3.14 for π, then you will get the erroneous 4-digit number 137.7 cm² for the shaded area. The number of significant digits in your value of π should be at least the number of significant digits you want in your answer. For the correct 4-digit answer 137.8 cm², you should use at least a 4-digit value for π, such as 3.142.)
Answer:
The area of the clock
Step-by-step explanation:
We have been given the face of the clock that is
So that is also the circumference of the clock.
Since the clock is circular in shape.
So
From here we will calculate the value of radius of the clock that is circular in shape.
Then
Now to find the area of the clock we will put this value of (r) in the equation of area of the circle.
Now
So the area of the face of the clock =
Answer:
The answer is 316
Step-by-step explanation:
I did a test it is the right answer everyone els is wrong :/
Answer:
12.57cm
Step-by-step explanation:
circumference =2^r
=2×22/7×2
=12.57cm
Y=3x-13
3x+2y=19
The solution to the system of equations is x = 5 and y = 2.
Given that:
The system of equations:
y = 3x - 13 (1)
3x + 2y = 19 (2)
Step 1: Solve equation (1) for Y:
y = 3x - 13
Step 2: Substitute y from equation (1) into equation (2):
3x + 2(3x - 13) = 19
Step 3: Simplify the equation and solve for x:
3x + 6x - 26 = 19
9x - 26 = 19
9x = 19 + 26
9x = 45
x = 45/9
x = 5
Step 4: Substitute x = 5 into equation (1) to find Y:
y = 3(5) - 13
y = 15 - 13
y = 2
So, the values of x and y are 5 and 2, respectively.
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