Let's find the rate that the inlet and outlet pipe can fill and empty the reservoirs. remember that rate*time = work done so if we let the rate of the inlet pipe be i and the outlet pipe be 0 we have
i(24) = 1
o(28) = 1
if you're confused about what the 1 is, it is the number of reservoirs because in the problem, it gives us the time it takes for each pipe to either empty or fill 1 reservoir. solving for r and t gives us:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
in the first 6 hours the inlet pipe fills up (1/24)(6) = 1/4 reservoirs and the outlet pipe empties (1/28)(6) = 3/14 reservoirs so to find out how many reservoirs are filled we subtract emptied amount from filled amount:
1/4 - 3/14 = 1/28 reservoirs (note that if the amount emptied is greater than the amount filled you will obtain a negative answer. please just change that negative number to 0 because a negative answer simply means that emptying rate is greater than filling rate so you end up with no water).
now we need to figure out how long it will take to fill up 1 reservoir given we have already filled up 1/28 reservoirs and that the outlet pipe is finally closed. to put it in simple terms, how long will it take for the inlet pipe to fill up the rest of the 27/28 of the reservoir. good thing we've already found the rate the inlet pipe fills up reservoirs so we have the equation:
(1/24)t = 27/28
solving for t, we have 23.14 hours. make sure you remember to add 6 to the answer because the question wants us to include that time in our answer. doing so gives 29.14 hours.
let me know if you have any questions!
For this case we must solve the following equation:
We group the variable terms of the left side of the equation, the terms that are adding from one side pass to the other side subtracting and vice versa:
Thus, the value of the variable is 11.76
ANswer:
Answer:
0 less-than-or-equal-to x less-than infinity
Step-by-step explanation:
The square root function, y=√x, is defined for non-negative numbers. Its domain is ...
0 ≤ x < ∞
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<em>Comment on the question</em>
This shows up again and again in domain problems, so is worth remembering. The value under the radical cannot be negative (but it can be zero).
Thank you for your question!
In order to get the cost of 1 kg of cabbage, divide the cost by the quantity:
1.20/2.5
0.48
Now, multiply the amount for 1 kg to 3.75, because you need 3.75 times the amount.
0.48 * 3.75
1.80
So, it would cost 1.80 pounds for 3.75 kg.
Hope this helped!
The interest rate she would pay would be is $7,200
