(ii) Make a graph of- dw versus t. dt 15 15 10 10 dWidt dWidt 5 10 20 30 40 10 20 30 40 time time -6 -5 -10 -10 -15 -15 15 15 10 10 dWidt dWidt 10 20 30 40 10 20 30 40 time time -6 -6 -10 -10 -15 -15
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Please answer parts C and D(i,ii).
![(ii) Make a graph of-
dw
versus t.
dt
15
15
10
10
dWidt
dWidt
5
10
20
30
40
10
20
30
40
time
time
-6
-5
-10
-10
-15
-15
15
15
10
10
dWidt
dWidt
10
20
30
40
10
20
30
40
time
time
-6
-6
-10
-10
-15
-15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e609613-0e56-44ff-94f4-9c892075812d%2F48876d80-3eef-4543-a0bb-363eeb713aec%2F4jhwzkt_processed.png&w=3840&q=75)
![Water is leaking out of a tank. The amount of water in the tank t minutes after it springs a leak is given by W(t) gallons.
dw
(a) Explain what means in practical terms.
dt
dw
tells us the change in the amount of water in the tank we expect in a minute's time.
dt
dw
tells us the amount of water left in the tank after a minute's time.
dt
dw
tells us the amount of water drained from the tank in a minute's time.
dt
dw
positive or negative?
dt
(b) As water leaks out of the tank, is.
positive
O negative
(c) For the first 6 minutes, water is leaking from the tank at a rate of 5 gallons per minute. What do you conclude about the nature of the function W during this period?
Since water is leaking out of the tank at a rate of 5 gallons per minute, the amount W of water in the tank is changing by 5
X gallons per minute. Thus W is ---Select---
v function of t with slope -5
(d) After about 6 minutes, the hole in the tank suddenly gets larger, and water begins to leak out of the tank at 14 gallons per minute.
(i) Make a graph of W versus t. Be sure to incorporate linearity where it is appropriate.
500
500
400
400
300
300
water
water
200
200
100
100
10
20
30
40
10
20
30
40
time
time
500
500
400
400
300
300
water
water
200
200
100
100
10
20
30
40
10
20
30
40
time
time](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e609613-0e56-44ff-94f4-9c892075812d%2F48876d80-3eef-4543-a0bb-363eeb713aec%2Fx5u119r_processed.png&w=3840&q=75)
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