phantomboy
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Need help with math problem
The temperature of a lake drops by the same amount each day for 10 days. The temperature drops by a total of 5 degrees.

Drag the numbers to form the equation that represents the change in the lake's temperature each day.

( ? ) ( ? ) = ( ? )

5, -5, 10, -10, 1/2, -1/2, 1/10, -1/10
Thanks

Respuesta :

SergioSalazar
(10)(-½) = (-5)
Hope it helps you.
Let the temperature be initially be t.

Let [tex]\displaystyle{ d_n[/tex] be the temperature after day 1 of the period where the teperature decreases.

For example,

[tex]\displaystyle{ d_1[/tex] is the temperature after the first day

[tex]\displaystyle{ d_2[/tex] is the temperature after the second day

and so on...

The temperatures during these 10 days are:

[tex]d_0=t\\\\d_1=t-5\\\\d_2=(t-5)-5=t-2\cdot5\\\\d_3=(t-2\cdot5)-5=t-3\cdot5\\\\.\\\\.\\\\d_{10}=t-10\cdot5 [/tex]

The change of the temperature each day, is given by the difference of the temperature in 2 consecutive days, for example day 4 and day 5:

[tex]d_5-d_4=(t-5\cdot 5)-(t-4\cdot5)=t-25-t+20=-5[/tex]


In general, the equation can be given as :

[tex]d_n-d_{n-1}=-5[/tex]


Remark: we cannot see the letters to "drag", so adopt them according to the variables that we defined in the solution.



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