It moves 65.97 centimeters
Step-by-step explanation:
The length of the circle is 2πr, where
- r is the radius of the circle
- If the angle of an arc is x°, then the length of the arc is × 2πr
∵ The radius of a wheel rolling on the ground is 84 centimeters
∴ r = 84 cm
∵ The wheel rotates through an angle of 45°
- To find the distance that the wheel moves for 45° use the rule above
to find the length of the arc which is equal to the length that the
wheel moves
∴ The distance = × 2π(84)
∴ The distance = 65.97 cm
It moves 65.97 centimeters
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Answer:
720°
Step-by-step explanation:
The "n" in the formula refers to the number of sides. The polygon shown has 6 sides, so the sum of interior angles is ...
S = 180°(6 -2) = 720°
Answer:
see explanation
Step-by-step explanation:
To find the first 4 terms, substitute n = 1, 2, 3, 4 into the n th term formula
n = 1 : 3(1 + 3) = 3 × 4 = 12
n = 2 : 3(2 + 3) = 3 × 5 = 15
n = 3 : 3(3 + 3) = 3 × 6 = 18
n = 4 : 3(4 + 3) = 3 × 7 = 21
The first 4 terms are 12, 15, 18, 21
Substitute n = 50 into the n th term formula
n = 50 : 3(50 + 3) = 3 × 53 = 159 ← 50 th term
Equate n th term formula to 100, that is
3(n + 3) = 100
3n + 9 = 100 ( subtract 9 from both sides )
3n = 91 ( divide both sides by 3 )
n = 30.333...
Thus the first term to have a value larger than 100 is the 31 st term