Question

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

Answer 1

(10)(-½) = (-5)
Hope it helps you.

Answer 2

Let the temperature be initially be t.

Let
`\displaystyle{ d_n` be the temperature after day 1 of the period where the teperature decreases.

For example,


`\displaystyle{ d_1` is the temperature after the first day


`\displaystyle{ d_2` is the temperature after the second day

and so on...

The temperatures during these 10 days are:


`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`

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:


`d_5-d_4=(t-5\cdot 5)-(t-4\cdot5)=t-25-t+20=-5`


In general, the equation can be given as :


`d_n-d_(n-1)=-5`


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