Calculate the center angle a if the lenght of the circular arc 31,4cm and the radius of the circle 9cm

Mathematics

2 answers:

Fed [463]4 years ago

3 0

Answer:

3.49 radians

Step-by-step explanation:

The arc length formula is s = rФ, where r is the radius and Ф is the central angle. We know s and r and need to calculate Ф.

From s = rФ we get Ф = central angle = s/r

Here, that central angle Ф is (31.4 cm) / 9 cm = 3.49 radians

DanielleElmas [232]4 years ago

3 0

Answer:

3.48 radian

Step-by-step explanation:

length of arc= radius * center angle

31.4 = 9 * angle

angle is in radian

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r-ruslan [8.4K]

Answer:

The polygon area is $51.5 U^{2}$

Step-by-step explanation:

Points:

(2,7), (8,2), (6,11), (6,5), (11,6)

1. The area of the polygon could be calculate with the eqation:

$A=\frac{1}{2}\left[\begin{array}{ccc}x_{1} &y_{1}\\x_{2} &y_{2}\\x_{3} &y_{3}\\x_{4} &y_{4}\\x_{5} &y_{5}\end{array}\right]$

2. Replace the coordinates in equation for A:

$A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]$

3. Solve the determinant, and calculate A:

$A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]\\A=\frac{1}{2}[(6)(7)+(11)(11)+(8)(6)+(6)(2)]-[(2)(11)+(6)(6)+(11)(2)+(8)(5)]\\A=\frac{1}{2}[42+121+48+12]-[22+36+22+40]\\A=\frac{1}{2}[223]-[120]\\\\A=\frac{1}{2}[103]=51,5 U^{2}$