Tell whether x and y are in a proportional relationship. if so, find the unit rate.

let y be the temperature x hours after midnight. the temperature is 60 degrees fahrenheit at midnight and decreases 2 degrees fahrenheit every 1/2 hour.

y = 60 - 4x

-4°F per hour

Step-by-step explanation:

We have x hours after midnight the temperature is y. Now, the temperature is 60°F at midnight and decreases 2°F every 1/2 hours.

So, the relation between x and y can be written as y = a - bx  ....... (1)

Now, at x = 0, y = 60.

Hence, a =60. {From equation (1)} and y = 60 - bx ...... (2)

Again at x =0.5, y = 60-2 = 58.

Hence, from equation (2), 58 = 60 - b(0.5), ⇒ b = = 4

Therefore, the final relation between x and y is, y = 60 - 4x ...... (3)

So, we can conclude that the relation between x and y is not proportional but linear and the unit rate of change of temperature with respect to time is -4°F per hour. (Answer)

step-by-step explan mxfcg'k; uafwgzfgjhklhgation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: