Answer:
We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.
Step-by-step explanation:
We have a 502 positive integers. Therefore we have a numbers 1, 2, 3,.., 500, 501, 502.
For the sum, we can choose the numbers 502 and 488. We get
(502+488)/1000=1000/1000=1.
For the difference, we can choose the numbers 1 and 501. We get
(1-501)/1000=-500/1000=-0.5.
We conlude that always exists two integers so that either their sum or their difference is divisible by 1000.
Answer:
x =4 ±sqrt(5)
Step-by-step explanation:
x2 - 8x + 16 = 5
Complete the square
(x-4)^2 = 5
Take the square root of each side
sqrt((x-4)^2) = ±sqrt(5)
x-4 = ±sqrt(5)
Add 4 to each side
x-4+4 =4 ±sqrt(5)
x =4 ±sqrt(5)
Answer:
s=14(116)
s = 1624
(This is the arc length for <u>RS</u>)
The line T to R cuts the circle in half. Half of a circle in degrees is 360/2. Which is 180.
Now we take the known angle and subtract it from 180 to get the unknown angle which is the angle of RS.
[180-64 = 116]
Arc length = radius * theta
Arc length = 14 * 116 = 1624
[FOR TS BELOW]
s=r(theta)
s= 14(64)
s = 896 (arc length for <u>TS</u>)
