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oksian1 [2.3K]
3 years ago
8

Decomposition, find f(x) and g(x) so that the function can be

Mathematics
1 answer:
andrew11 [14]3 years ago
3 0

Answer:

steps below

Step-by-step explanation:

f(x) = x + 5

g(x) = x - 4

f(g(x)) = f(x-4) = (x-4) + 5

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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of
maria [59]

Answer:

  305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

<h3>Cooling Model</h3>

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

  y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

  a = 1200 -80 = 1120

  b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

  y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

<h3>Application</h3>

We want y when t=4.

  y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

<em>Additional comment</em>

The differential equation will have a solution of the form ...

  T-T_R=(T_0-T_R)e^{kt}

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

5 0
2 years ago
Number 9 !!!! please answer !!!! explain how u got the answer and the answer of cpurse
storchak [24]

answer:

90 degrees + 28 degrees= 118 degrees

180-118= Z is 62 degrees

13y-1 = 24                                     2x-7 = 39

+1           +1                                          +7     +7

13y = 25                                          2x = 46

/13      /13                                           /2     /2

y = 1.92                                            X = 23

3 0
2 years ago
Read 2 more answers
Six values on the number line above are marked with letters. Which letters represent integers when the value on the number line
r-ruslan [8.4K]

Answer:

  A) L, N, O, P

Step-by-step explanation:

The even numbers on the number line are marked by the letters L, N, O, P.

_____

If a number gives an integer result when divided by 2, it is an even number. Zero is an even number, giving the integer zero when divided by 2.

6 0
3 years ago
Can someone explain ?
Vika [28.1K]

Answer:

see below

Step-by-step explanation:

sqrt(90)

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(9*10)

sqrt(9) sqrt(10)

3*sqrt(10)

8 0
3 years ago
What are the solutions to the equation |x-3|=14
lilavasa [31]
X-3=14
+3    +3
x=17


x-3=-14
  +3   +3
x=-11
5 0
3 years ago
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