Eight less than one-fourth of a number is 4

1 answer:

6 0

1/4n-8=1/4 would be first because it says less than so you switch it. then you put the 8 since it's in the same subtraction problem. Then the word "is" indicates the equal sign. and the n represents "a number" since it is unknown.

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Suppose you cool a pot of soup in a 20°C room. Right when you take the soup off the stove, you measure its temperature to be 180

dezoksy [38]

Answer:

28.3 minutes
53.6°C

Step-by-step explanation:

The temperature of the soup is described by Newton's Law of Cooling, which says the rate of change of temperature is proportional to the difference between the temperatures of the soup and the room. The solution to this differential equation is the exponential function ...

f(t) = a +b·c^(t/τ)

where a is the room temperature, b is the initial difference in temperature, and c is the fractional change in the difference in temperature over time period τ.

<h3>application</h3>

For the given scenario, we find ...

a = room temperature = 20 . . . . degrees C

b = (180 -20) = 160 . . . . degrees C

c = (100 -20)/(180 -20) = 80/160 = 1/2 . . . . in τ = 20 minutes

So, the formula for the temperature of the soup is ...

f(t) = 20 +160(1/2)^(t/20) . . . . . . . degrees C after t minutes

Solving for t when f(t) = 80, we find ...

80 = 20 +160(1/2)^(t/20)

3/8 = (1/2)^(t/20) . . . . . subtract 20, divide by 160

20×log(3/8)/log(1/2) = t ≈ 28.3 . . . take logarithms, divide by coefficient of t

It will take about 28.3 minutes to cool to 80°C.