The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
a) Is f'(t) positive or negative? Why?
b) What are the units of f'(35)?
c) Suppose that |f'(35)| = 1.5 and f(35) = 68. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.
At ____ minutes after the coffee was put on the counter, its temperature is ____ and will ____ by about ____ in the next 30 seconds.

Answer:

a

    f'(t) is  negative

b

 The  unit is degC/min

c

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.          

Step-by-step explanation:

From the question we are told we are told that  

   The  equation for the temperature of a cup of coffee place on a counter is

         [tex]H= f(t)[/tex]

Here  t is the time in minutes the  coffee was put on the counter

Generally  f(t)'  is the derivative of  f(t) at it represents the change of the temperature of the cup of coffee with respect to time

 Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence  f(t)' is  negative

Generally the unit of the temperature is in degrees Celsius while that of time is  in minutes

  So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e  degC/min)

  From the question we are told that

        [tex]|f(35)'| =  1.5[/tex]

i.e  the rate of change of temperature after 35 minutes is  1.5

and

         [tex]|f(35)| =  68[/tex]

i.e the temperature of the cup of coffee after 35 minutes is  67 degC

Now after another   t=  30  seconds =  [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the  rate  of change of the temperature of the cup of  coffee is  

          [tex]R =  |f(35)'| *  t[/tex]

=>        [tex]R = 1.5  *  0.5 [/tex]

=>        [tex]R = 0.75  [/tex]    

So

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.  

The value of f'(t)  is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.

The units of  f'(35) = degC/min.

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.    

The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.

1. The value of f'(t)  is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.

2. What are the units of f'(35)?

The units of  f'(35) = degC/min.

3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.    

At ║f'(35)║ = 1.5 and f'(35) = 68

|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.

To know more about Temperature click the link given below.

https://brainly.com/question/16045110

The linear equation has 5(x + 2) = 5x + 2 A) no solution. B) one solution. C) two solutions. D) infinitely many solutions

Brenda has to remote controlled race cars painted red and blue. The red car travel 38 feet in two seconds. The blue car traveled 54 feet in four seconds. Which car was faster and by how much

+0
1. Sam has a rope that measures
(5 x 1/10) + (6 x 1/100) + (8 x 1/1000)
How can this measurement be written as a decimal?

Serena wants to open a licensed child care center. Her state requires that there be no more than 12 children for each teacher. She would like her child care center to serve
29 children
(a) How many teachers will be needed?

Kelly made six batches of cookies his friends asked her to make an extra batch she’s 17 1/4 cups of sugar and needed another 7/8 cups for the extra batch how many cups of sugar will Kelly use all together

I mark as brainliest ​

Domain range and function

Is it carbohydrate, lipid, protein, or nucleic acid?

PLEASE HELP!!! LAST QUESTION AND IM STUCKK.

What is the inverse of the following statement: “If x is a whole number, then x = 5”?
a) If x is not a whole number, then x ≠ 5.
b) If x = 5, then x is a whole number.
c) If x ≠ 5, then x is not a whole number.
d) If x is not a whole number, then x = 5.

given that f (x) x^2 - 3x find f(-4)

On a number line, how are the locations of 9 and -9 related?
A.
The two numbers are opposites in value and lie in opposite direction on the number line.
B.
The two numbers are opposites in value and they lie in the same direction on a number line.
C.
The two numbers are equal in value and lie in opposite direction on the number line.
D.
The two numbers are equal in value and they lie in the same direction on a number line.

If there are 12 eggs in a carton, how many are in 5 cartons?

Rounded to the nearest tenth, what is the perimeter of rectangle ABCD?

A.
48.3 cm
B.
54.6 cm
C.
60.0 cm
D.
173.2 cm

A taxi driver charges a fee if $4 plus 1.50 per mile. If you total was $13 how manu miles did you take

A parachutist descends 30 feet in 2 seconds.Express the rate of the parachutist’s change in height as a unit rate

Write using interval notation

what’s the answer bruh? I need help fr fr

Help me pleaseeeeee!!

car rental agency charges a base rate plus a certain amount per day (d) and can be modeled using the expression 15+ 18d. What is the meaning of 18d in the expression? *
4 points
It is the base rate to rent a car.
It is the cost of renting a car for a day.
It is the total number of days a car can be rented.
It is the portion of the cost based on renting a car for d days.

In the following hypothetical scenarios, classify each of the specified numbers as a parameter or a statistic.

a. There have been 44 Presidents of the United States, and 36% of them were Democrats. The 36% here is a:________
b. In a 2015 Gallup poll of 1025 adults living in the United States, 53% said they trust the judicial branch of the federal government. The 53% here is a:________
c. The survey results from 12 local parks show the mean height of 60 ft for mature oak trees. The mean height of 60 ft is a:_________
d. The 72 employees at ABC company have a mean income of $52,317 with a standard deviation of $36,829. The $36,829 is a:______
e. In a random sample of homeowners in the United States, it is found that 34% of the sampled homeowners renew their home warranty. The 34% here is a:______

The value for √10 is approximately between 3 and 4. Approximate further to find the values to the tenths place that √10 is between.

Can you answer both and tell me the answer please

Select each transformation that carries a square onto itself.
a reflection over one of the square's sides
3 rotation of 180' clockwise about the square's center
a rotation of 90: clockwise about the squares center
a rotation of 180: clockwise about one of the squares vertices
: reflection over one of the souare s diagonals

f
[tex]f(x)2 - 5[/tex]
​

Identify the x- and y- intercept of the graph of the equation -3x + 6y = 24

a school is having a pizza party. each pizza is cut into 12 slices. which explains whether it is better to estimate a greater or lesser number than the actual number of people that will eat pizza

Hats cost $4 each while scarves cost $3 each. John buys 5 items (all hats and scarves) and spends a total of $17. How many hats did he buy?

I need HELP class is about to start and I don’t know any of this

Melissa is saving $25 that she earned for washing her mom’s car. She earns $19 every week for doing chores, which she also saves. Which equation can be used to find t, the amount of money Melissa will have saved at the end of n weeks of doing chores.

Bill is a builder.
On Monday he made mortar mix.
He used 24kg of sand and 5 kg of cement.
On Tuesday Bill will make the same type of mortar mix.
He will use 36 kg of sand.
How much cement does he need to make the same type of mortar mix?