a barrel of water contains 60 gallons of water if 21 gallons leaked out what percent of water was left in the barrel
2 answers:
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Answer:
The numbers he picked are 11, 17 and 24
Step-by-step explanation:
To solve this, we will work with the information we are given, interpreting it properly.
From the information given , we can already decode that the first of the three numbers is 11. We can write that number down.
The next piece of information we are given is that the range is 13.
The range of a data set is the difference between the highest and lowest numbers in the data set.
Let us say that our highest number is x
Now, we know that the highest number of the data set is 24
Finally, from the information given, we can see that the median number is 17. This is the middle number of the data set. we can simply write that down since the number of figures in our data set is an odd number.
Hence the numbers picked are
11, 17 and 24 arranging them in an ascending order
Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.
Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.
The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.
The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes 42.528 minutes for the temperature of the coffee to reach 180 °F.
Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.
The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.
The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes 42.528 minutes for the temperature of the coffee to reach 180 °F.