math problem..need urgent

Question

𝐶=59(𝐹−32) The equation above shows how temperature 𝐹, measured in degrees Fahrenheit, relates to a temperature 𝐶, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius. A) I onlyB) II onlyC) III onlyD) I and II only

akibsifat · Answer

hsshsj

satis · Answer

given:- c= 5/9(f−32) or f = 9/5c+32 statement i :c= 5/9(f−32) dc/df = 5/9dc = 5/9 x df hence, a temperature increase of 1 degree fahrenheit is equivalent to a temperature increase of 5/9 x 1 = 5/9 degree celsius. therefore, statement i is true. statement ii :
c= 5/9(f−32) f = 9/5 *c + 32df/dc = 9/5df = 9/5 x dc hence, a temperature increase of 1 degree celsius is equivalent to a temperature increase of 9/5 x 1 = 1.8 degrees fahrenheit. therefore, statement ii is true. statement iil : c= 5/9(f−32) 
dc/df = 5/9dc = 5/9 x dfhence, a temperature increase of 5/9 degree fahrenheit is equivalent to a temperature increase of 5/9 x 5/9 = 25/81 degree celsius. therefore, statement iii is false.thus, the correct answer is d) i and ii only

latt1928 · Answer

𝐶=59(𝐹−32)
this relates the temperature 
f in degrees fahrenheit to the temperature 
c in degrees celsius.
i) a temperature increase of 1 degree fahrenheit is equivalent to a temperature increase of 5/9 degree celsius.
the relationship between 
f and 𝐶  implies that for every 1-degree increase in fahrenheit, the celsius value increases by:
9/5  degrees celsius.
therefore, this statement is incorrect because it claims a 1-degree fahrenheit increase leads to a 9/5 degree celsius increase, not 59 degrees.

ii) a temperature increase of 1 degree celsius is equivalent to a temperature increase of 1.8 degrees fahrenheit.
we can rearrange the equation for f in terms of 𝐶:
f= (5/9 c)+32
this implies that for every 1-degree increase in celsius, fahrenheit increases by 9/5=1.8 degree
this statement is correct.

iii) a temperature increase of 59 degrees fahrenheit is equivalent to a temperature increase of 1 degree celsius.
this is incorrect because a 1-degree increase in celsius corresponds to a 1.8-degree increase in fahrenheit, not 59 degrees.

conclusion:
only statement ii is correct.
answer - b) ii-only

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