Answer:
Step-by-step explanation:
Since they have the same base as 2, by the rule of a^m / a^n = a^m-n.
So 2^7 / 2^3 = 2^ 7-3 = 2^4 = 16
Answer: I am really good at math so if you need help just say so
Step-by-step explanation:
Explanation:
The trick is to know about the basic idea of sequences and series and also knowing how i cycles.
The powers of i will result in either: i, −1, −i, or 1.
We can regroup i+i2+i3+⋯+i258+i259 into these categories.
We know that i=i5=i9 and so on. The same goes for the other powers of i.
So:
i+i2+i3+⋯+i258+i259
=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)
We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.
=65(i)+65(i2)+65(i3)+64(i4)
From here on out, it's pretty simple. You just evaluate the expression:
=65(i)+65(−1)+65(−i)+64(1)
=65i−65−65i+64
=−65+64
=−1
So,
i+i2+i3+⋯+i258+i259=-1
Answer: It would take 9 hours for 4 painters to paint 720 feet of fence.
Step-by-step explanation:
1.) Calculate the time needed to paint the 720 ft fence with 2 painters.
a.) Divide 720 by 280 to get how many times greater 720 is than 280.
720 / 280 ≈ 2.57
b.) Multiply the time needed to paint the 280 ft fence with 2 painters by 2.57.
7 * 2.57 ≈ 18
2.) Calculate the time needed to paint the 720 ft fence with 4 painters.
a.) Assuming that each painter paints the same amount of fence, divide the time in half, as 4 painters is double the original amount, so it would take half of the time.
18 / 2 = 9
