Answer:
(a) 74553
(b) 172120
(c) 234802
Step-by-step explanation:
Given
Solving (a): 1998
Year 1998 means that:
So, we have:
--- approximated
Solving (b): 2003
Year 2003 means that:
So, we have:
--- approximated
Solving (c): 2006
Year 2006 means that:
So, we have:
--- approximated
Answer:
In option a, w < 10
in option b, w = 10 and 2(20) + 2(10) = 40 + 20 = 60 < 150
in option c, w > 10 but 2(60) + 2(20) = 120 + 40 = 160 > 150
In option d, w > 10 but 2(55) + 2(30) = 110 + 60 = 170 > 150
Therefore the corect answer is option b.
Step-by-step explanation:
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:
-2
Step-by-step explanation:
- 5x + 8 = 18
Take + 8 to the right hand side, it turns negative i.e -8
-5x = 18 - 8
-5x = 10
Divide both sides by the coefficient of x which is -5
-5x/5 = 10/-5
x = -2
