The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. what does the average rate of change of d(t) from t = 2 to t = 5 represent?

Answer

Find out what does the average rate of change of d(t) from t = 2 to t = 5 represent .

To prove

Formula

As given

The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t²

 where d equals the distance traveled at time t seconds .

Now

d(5) = 16 × 5 × 5

      = 400 feet

d(2) = 16 × 2 × 2

      = 64 feet

Now

Change in time = 5 - 2

                          = 3 second

put all the values in the above formula

Average rate of change is 112 feet/second.

The average rate of change of height is speed.

The average rate of change of d(t) on t ∈ [2, 5] represents the ball's average speed over that interval of time.

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: