Question

33. A scientist is measuring the temperature change in a chemical compound. The temperature dropped 11°F per hour from the original temperature. After four hours, the temperature was 90°F. Find the compound's original temperature.
34. A mountain climber ascend 800 feet per hour from his original position. After six hours, his final position is 11,600 feet above sea level. Find the climbers original position.

Answer 1

Answer:

Step-by-step explanation:

Given that temperature dropped 11 degree per hour

Rate of change of temperature with respect to one hour = -11

Let T be temp and t be time in hours.

Since rate of change is constant we have linear relation

$T=-11t+C$, where C is temperature when t =0

Given that

$T(4) = -11(4)+C=90\\C =134$

So original temperature = C =134

34) Slope = 800

Hence if h is the height and t is time in hour,

$h=800t+C$ where C is the original height

$h(6) = 800(6)+C =11600\\C = 6800$

Original position = 6800 feet.

Answer 2

33.
134 degrees. You just multiply the change per hour (11) by the amount of hours (4) and add that to the temp after 4 hours (90) and 44+90=134.

34.
6,800 ft. above sea level. Pretty much same explanation as above.