Answer:
The years are:
- 1000 BCE, 999 BCE, 888 BCE, 777 BCE, 666 BCE, 555BCE, 444 BCE. 333 BCE, 222 BCE, 111 BCE
- 111 CE, 222 CE, 333 CE, 444 CE, 555 CE, 666 CE, 777 CE, 888 CE, 999 CE, 1000CE, 1011 CE, 1101 CE, 1110 CE,1222CE, 1333CE, 1444CE, 1555 CE, 1666 CE, 1777CE, 1888 CE, 1999CE, and 2000 CE
Explanation:
<u>1. Years BC:</u>
a) Years with four digits:
The first number with 3 equal digits is 1000. After that the years go decreasing: 999, 998, 997, ...
b) Years with three digits:
From 999 to 111, the numbers have three digits, thus the only that are solutions ara 999, 888, 777, 666, 555, 444, 333, 222, and 111: 9 numbers
After that the years have two digits, thus no solutions, with two digits.
Hence, we count 10 different years.
<u>2. Years CE</u>
a) Years with three digits:
- 111, 222, 333, 444, 555, 666, 777, 888, 999: 9 years
b) Years with four digits
i) Starting with 1:
- With three 0: 1000: 1 year
- With three 1: 1011, 1101, 1110: 3 years
- With three digits different to 1: 1222, 1333, 1444, 1555, 1666, 1777, 1888, 1999: 8 years
ii) Starting with 2:
- With three 0: 2000: 1 year
The next one with three equal digits is 2111 and it is after 2020 CE.
Therefore, 9 + 1 + 3 + 8 + 1 = 22 years starting with 2.
<u>3. Total</u>
<u />
10 years BC and 22 years CE have exactly three digits the same: 10 + 22 = 32.
Shannon's scooter has a piece of tape stuck to the tire. If
the tire has a diameter of 18 inches, the distance traveled by the piece of
tape in 72 degree rotaion can be solve using:
S= ra, where s is the distance traveled, r is the radius and
a is the angle in radians
s = (18in/2)(72 degree)(pi/180 degrees) = 11.31 in.
Answer:
Step-by-step explanation:
(0,2) (1,0)
Answer:
10.8 meters
Step-by-step explanation:
This situation forms a right triangle, where the length of the kite string is the hypotenuse, the distance from where it is held is the long leg, and the height is the short leg.
Use the pythagorean theorem to solve for c, the length of the kite string.
a² + b² = c²
6² + 9² = c²
36 + 81 = c²
117 = c²
10.8 = c
So, the length of the kite string is 10.8 meters
Answer:B
Step-by-step explanation:
