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Alinara [238K]
3 years ago
12

3

Mathematics
1 answer:
Bas_tet [7]3 years ago
7 0

Answer:

<em>The height of the candle after 23 hours is 20.4 centimeters</em>

Step-by-step explanation:

<u>Mathematical Modeling</u>

To model a real-life situation, a mathematical model can be built in such a way it accurately represents the variables measured in the system.

This problem requires to build a model for the height of a candle as a linear function of the time it has been burning. If the time is expressed in hours and the height is in centimeters, then the linear function can be written as:

H(t)=mt+b

Where m and b are constants we need to find. We are provided two points of reference: After 15 hours of burning, the candle has a height of 22 centimeters. This is the point (15,22).

We also know after 27 hours of burning, the height is 19.6 cm. This is the point (27,19.6). This data is enough to accurately define the function. Let's substitute the first point:

22=15m+b\qquad\qquad [1]

Substituting the second point:

19.6=27m+b\qquad\qquad [2]

Subtracting [1] - [2]:

22-19.6=15m-27m

\Rightarrow 12m=-2.4

Solving for m:

m=-2.4/12=-0.2

Using this value in [1]:

22=15(-0.2)+b

22=-3+b

Solving for b:

b=25

The function is now complete:

H(t)=-0.2t+25

Finally, substitute t=23:

H(23)=-0.2(23)+25=20.4

The height of the candle after 23 hours is 20.4 centimeters

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Nalia worked 3.5 hours more than lisa together they worked a total of 18 hours lisa worked h hours
andre [41]

Answer:

7.25 and 10.75 Hours

Step-by-step explanation:

Total hours Nalia and Lisa worked = 18 Hours

Nalia worked 3.5 hours then Lisa which is h hours

⇒h + (h + 3.5) = 18

2h + 3.5 = 18\\2h = 18 - 3.5\\2h = 14.5\\h = \frac{14.5}{2} \\h = 7.25

Lisa has worked for 7.25 hours

Nalia has worked for = 7.25 + 3.5 = 10.75 hours

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Answer:

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Step-by-step explanation:

I calculator

12.4+-3.9=8.5

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Volgvan

The correct answer is (4,1).

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