To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.
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Explanation:
Hello! Please remember to formulate complete questions to receive accurate answers. I will assume that the depicted function derives from:
This describes the equation of a parabola that opens upwards, with its vertex positioned at:
The graph below illustrates this function. What is true about the graphed function f(x)?
- It is accurate that the domain consists of all real numbers, as this is a polynomial function.
- It is also correct that the range includes all real numbers where y ≥ 5
- It is indeed true that this parabola opens upwards
- It is valid to say it does not intersect the x-axis
Answer: By substituting t with 4, we find that 32.5*4 + 5 yields 135 and 28.75 * 4 + 20 results in the same value of 135, confirming the equation is valid.
or
By using 4 as the value for t in the equation, a true statement emerges, indicating that the Burns family will incur a cost of $135 for 4 tickets and parking regardless of whether the choice is lower-level or middle-level seating.
Step-by-step explanation:
In this scenario, we'll define the following variables:
x: total volume of potting soil in liters.
y: quantity of potting soil allocated to each pot in liters.
To determine the number of pots, we can use the expression:
Substituting in the respective values yields:
Reformatting gives us:
When rounding down to the nearest whole number, we find:
The conclusion is:
Yao Xin is capable of filling 18 pots.
Answer:
Please refer to the explanation
Step-by-step explanation:
Given that:
Sarah, Jose, and you all reside on the same street:
The distance between you and Jose is 5 blocks
The distance between Jose and Sarah is 2 blocks
Calculating the distance (b) between you and Sarah:
Since it is not specified if Sarah is closer to you or to Jose;
Thus;
Distance b from you to Sarah will be:
(The distance to Jose ± the distance to Sarah)
b = (5 ± 2)
b = (5 + 2) or (5 - 2)
b = 7 blocks or 3 blocks
