2. Suppose we define H(t) to be the outdoor temperature, in degrees Fahrenheit,

Question

2. Suppose we define H(t) to be the outdoor temperature, in degrees Fahrenheit, at the Rowdy statue t hours after midnight on March 27, 2018. (a) Does this define a function? If not, what adjustments would need to be made so that it does? If so, for what values of t is H(t) defined? (b) Is H(10) defined? If so, what does it represent? (c) Mariann wants to write an expression using H for the temperature, in degrees Fahrenheit, at the Rowdy statue m minutes after midnight on March 27. She is having trouble deciding whether the expression should be H(60m ), H (m /60), H (60/m), or something else. What is a correct expression? If Mariann were one of your students, how would you help her find a correct expression? (d) Write an expression using H for the temperature, in degrees Fahrenheit, at the Rowdy statue d days after midnight on April 27, 2018. 3. A dump truck dumps gravel off a ledge; the gravel falls and forms a cone. The diameter and height of the cone both increase as the gravel continues to fall. Let d(t) and h(t) represent the diameter and height in feet, respectively, of the gravel pile t seconds after dumping begins (a) Suppose we write A(t)- ndlt)2. In terms of the gravel pile, what does A(t) represent? (b) Use function notation to express the volume of the gravel pile in such a way that your e shows the relationship between the pile's volume and its diameter and height, and shows that the volume, diameter, and height change over time

Explanation / Answer

I am solving the Q2 as per Chegg guidelines, post multiple question to get the remaining answers

Q2)

a) The function doesn't contain the entire domain and entire range. Since the temperature of the city status can never be less than certain negative value. similarly the input value t must also be positive

It is not a one-one function since there can be one to many mappings.

The H(t) is defined for only integral values of t

b) H(10) is defined, the t represents the temperature in hours after midnight so after 10 hours, the time will be 10:00 AM next day

Hence H(10) will define the temperature at the Rowdy statue at 10:00 AM on March 28.2018

c)

1 hour = 60 minutes

so, t hours will have 60 * t minutes of time units

Now, we have to divide the value by 60 in order to represents the function in minute scale

Hence, the answer must be H(m/60)

Example:

For 1 hour, the function will be H(1) which will temperature at 1:00 AM on 28th March,2018

1 hour - 60 minutes, H(60/60) = H(1)

d)

H(t) represents the temperature on March 27.2018

Number of days between March 27,2018 and April 27,2018 will be 31 days

Hence temperature on April 27 will be H(t + 31 * 24) = H(t+744)

Now we need to add another d days as per problem, so d days will have d * 24 number of hours

Hence the required expression will be H(t + 744 + 24d)

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