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zalisa [80]
3 years ago
7

Simplify (4s5t−7−2s−2t4)3. Write your answer using only positive exponents. Evaluate any numerical powers.

Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

Answer:

−21

Step-by-step explanation:

=12s5t−6t4−6s−21

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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.

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<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

__

<h3>time to 80°C</h3>

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.

__

<h3>temp at 45 minutes</h3>

The temperature after 45 minutes is ...

  f(45) = 20 +160(1/2)^(45/20)

  f(45) ≈ 53.6 . . . . degrees C

After 45 minutes the temperature of the soup will be about 53.6°C.

3 0
1 year ago
Read 2 more answers
4k + 15 greater than -2k + 3
ioda

Answer:

k>-2

Step-by-step explanation:

4k+15>-2k+3

4k-(-2k)+15>3

4k+2k+15>3

6k+15>3

6k>3-15

6k>-12

k>-12/6

k>-2

8 0
3 years ago
A dozen apple costs $2.55.at this rate how much would 8 apple cost?
vladimir2022 [97]
12=2.55 how about 8
8 x 2.55 divided by 12=$1.7
8 0
3 years ago
Which equation could have been used to create this function table?
anzhelika [568]

Answer:

y = x+2 is your answer

Step-by-step explanation:

you add two to x to get y

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3 years ago
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What is the solution to the equation 3 square root x+4+3 square root 2x+8=0? x = –12 x = –4 x = 4 x = 12
Gre4nikov [31]

Answer:

x=-4

Step-by-step explanation:

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