Drove 50 km on 6 L of gasoline. Which proportion would help determine how far she can travel on a full 40 L tank of gasoline?
2 answers:
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Answer:
He needs to sell 100 souvenirs
Step-by-step explanation:
We want to know the number of souveniers John has to sell
Let the number of souveniers he sold at the game be s
At a rate of $0.25 per souvenier, the amount earned on souveniers for s souveniers will be:
Now, if we added this to the amount he earns per game, we will have the total $35 earned for working at one game.
Thus, mathematically:
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.