1.

If the temperature of a liquid can be measured in kelvin units as `x^(@)K` or in fahrenheit units as `y^(@)F`, the relation between the two systems of measurement of temperature is given by the linear equation. `y=(9)/(5)(x- 273)+32` (i) find the temperature of the liquid in fahrenheit, if the temperature of the liquid is 313 K. (ii) If the temperature in kelvin.

Answer» Given relation is `" " y=(9)/(5)(x-273)+32`
(i) Given, `x=313 .^(@)K` then from Eq. (i), we get
`y=(9)/(5)(313-273)+32`
`=(9)/(5)xx40+32=9xx8+32=72+32=104^(@)F`
(ii) Given, `y=158^(@)F`, then from Eq. (i), we get
`158=(9)/(5)(x - 273) +32`
`implies " " 158=(9(x - 273)+32xx5)/(5)`
`implies " " 158xx5=9(x-273)+160`
`implies " " 790=9(x-273)+160`
`implies " " 790-160=9(x-273)`
`implies " " 9(x - 273) = 630`
`implies " " x- 273 = (630)/(9)= 70 implies x- 273=70`
`because " " x = 70+273= 343 ^(@)K`


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