Answer:
Net
Step-by-step explanation:
The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.
Answer:
Workdone = 3200 lb.ft
Step-by-step explanation:
We are told that the bucket is filled with 40 lb of water but water leaks out of a hole in the bucket at a rate of 0.2lb/s
Thus,
Weight of water at any given time (t) would be;
w(t) = 40 - 0.2t - - - - (1)
We are told the bucket is pulled up at a rate of 2ft/s.
Thus, height at time (t); y = 0 + 2t = 2t
Since y = 2t,
Then,t = y/2
Put y/2 for t in eq 1
Thus; w(y) = 40 - 0.2(y/2)
w(y) = 40 - 0.1y
Now, at y = 80 ft, we have;
w(80) = 40 - 0.1(80)
w(80) = 40 - 8 = 32 lb
Since 32 lbs are left, it means there is always water in the bucket.
Thus, work done is;
W = 80,0[∫(Total weight).dy]
W = 80,0[∫[(weight of rope) + (weight of bucket) + (weight of water)]dy]
W = 80,0[∫[0 + 4 + 40 - 0.1y]dy]
Integrating, we have;
W = [44y - y²/20] at boundary of 80 and 0
So,
W = [44(80) - 80²/20] - [0 - 0²/20]
W = 3200 lb.ft
The solution is x = -2.27 and x= 5.28
Let me attach the picture
19) The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)
33) The sum of the <em>geometric</em> series is 1700. (Correct choice: E)
<h3>How to determine the sum of a given series</h3>
19) <em>Arithmetic</em> series are sets of elements generated by a <em>linear</em> expression of the form:
aₙ = a₁ + (n - 1) · d (1)
Where:
- aₙ - n-th term of the series
- a₁ - First term of the series
- n - Index of the n-th term of the series.
- d - Change between two consecutive elements of the series.
If we know that a₁ = 27, n = 20 and d = - 5, then sum of the first 20 terms of the series is:
x = 27 + 22 + 17 + 12 + 7 + 2 + (- 3) + (- 8) + (- 13) + (- 18) + (- 23) + (- 28) + (- 33) + (- 38) + (- 43) + (- 48) + (- 53) + (- 58) + (- 63) + (- 68)
x = - 397
The sum of the <em>arithmetic</em> series is - 397. (Correct choice: E)
33) <em>Geometric</em> series are sets of elements generated by a <em>exponential</em> expression of the form:
aₙ = a₁ · rⁿ (2)
Where:
- aₙ - n-th term of the series
- a₁ - First term of the series
- r - Ratio between two consecutive elements of the series.
If we know that a₁ = 1458 and r = 1 / 3, then the sum of the first 6 terms of the geometric series is:
x = 1458 + 162 + 54 + 18 + 6 + 2
x = 1700
The sum of the <em>geometric</em> series is 1700. (Correct choice: E)
To learn more on geometric series: brainly.com/question/4617980
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Value of p=6
36-12 = 24
24/4=6
