smit715674
28.12.2019 •
Mathematics
Atank having a capacity of 100 gallons is half full of fresh water. a pipe is open that lets treated sewage enter the tank at a rate of 4 gal/min. at the same time, a drain is open to allow the mixture to leave the tank at a rate of 2 gal/min. if the treated sewage contains 10 grams of usable potassium per gallon, what is the concentration of potassium in the tank when it is full?
Solved
Show answers
More tips
- C Computers and Internet Porn Banner: What It Is and How to Get Rid Of It?...
- F Food and Cooking How many stages of coffee roasting are there?...
- F Food and Cooking From Latte to Espresso: Which Coffee Drink is the Most Popular on Earth?...
- F Food and Cooking Experts Name Top 5 Healthiest Teas...
- C Computers and Internet Google Search Tips and Tricks: Everything You Need to Know...
- H Health and Medicine Discover the Hidden Principles and Real Results of the Japanese Diet...
- H Health and Medicine Liver Cleansing - Rejuvenation for the Body?...
- S Style and Beauty Is Photoepilation the Solution to Unwanted Hair Forever?...
- S Style and Beauty Unbelievable Hairstyles for Long Hair - 2021 Trends...
- H Health and Medicine When can it be said that a person has a normal pulse?...
Answers on questions: Mathematics
- M Mathematics Haley placed 5 of the bookmarks end to end draw a point on the number line below to represent the total length of the 5 bookmarks label the point b...
- M Mathematics Anna, vickie, and luana are sisters. anna is 3 years older than vickie and luana is 2 years younger than vickie. use v for vickie’s age. write expressions to show the ages...
- M Mathematics Find the midpoint of the line segment whose endpoints are (2.6, 5.1) and (3, 4.7). (0.2, 0.2) (1.45, 4.9) (2.8, 4.9)...
- M Mathematics Franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6....
- M Mathematics Apoint t on a segment with endpoints d (1, 4) and f (7, 1) partitions the segment in a 2: 1 ratio. find t. you must show all work to receive credit....
- M Mathematics Which statement is true about the solutions for the equation 4y + 6 = -2 infinitely many solutions two solutions one solution no solution...
- M Mathematics The wind was blowing quite strongly when jenny was baby-sitting. she was outside with the children, and they were throwing their large plastic ball up into the air. the...
- M Mathematics What is the name of the line that the function approaches? a. y-axisb. there is no such linec. the unknown lined. asymptote...
- M Mathematics Two angles are supplementary.one anglemeasures 15 degrees more than 4 times the other. what is the measure of the larger angle in degress...
- M Mathematics Rob says all numbers have an even number of factors marcia says some numbers have an odd number who is correct...
Ответ:
2.4 grams/gal.
Step-by-step explanation:
This question can be considered as the mathematical modeling of a tank. The key point here is the concentration has to diminish gradually as the time passes. The water exiting the tank must include some ratio of the potassium added. Thus, a common mistake would be assuming the exit flow as pure water. We should structure a logical model as the following:
The volume of water in the tank (V-total)= Change in volume in a minute (İnlet flow - exit flow) + initial volume (50 gal). This is equal to (4 gal/min - 2 gal/min) + 50 gal= 50 gal + 2gal/min*t where t represents time in minutes and the representation will be V-tot= 50 + 2*t
Next, we have to calculate the amount and the change of pottassium per unit time. We know that 10 grams of potassium is introduced in each minute to the tank. However, some amount in proportion to the exit flow will leave as potassium will totally dissolve in the water (and we should assume that it will dissolve homogeneously as soon as it is introduced). Thus, at a certain time, the total amount of potassium introduced will be 10 grams*t. The amount of potasium leaving will be in proportion to exit flow and total time. The leaving potassium amount can be modelled as (2 gal/min)/V-tot*10 grams*t. (2 gal/min)/V-tot term represents the ratio of leaving amount of potassium and 10 grams*t is introduced so when it is multiplied by the ratio, we will have the exact amount left at a certain time. Thus, the weight term is 10 grams*t-(2 gal/min)/V-tot*10 grams*t.
The concentration formula is weight/volume. Thus the concentration at a certain time will be when the weight term is taken in a common t parenthesis.
Now, we have to calculate how much time it would take for a tank to be filled. The total capacity is 100 gallons and at the beginning, where is only 50 gallons. Thus, we have to calculate the amount of time required for another 50 gallons to accumulate in the tank. We know that 2 gallons are accumulated in the tank per minute, thus at t=25 the tank will be full. So, in the formula we have to insert 25 for t.
V-tot at t=25 is 100 gallons since the tank will be full. Thus, inserting t=25 and V-tot is 100, we get the result 2.4 grams/gal.
Ответ:
The answer is 5/6 because there is 5 other numbers on the cube