As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where H(t) is measured in degrees Celsius (C), and time t is measured in minutes. Values of H(t) at selected values of time t are shown in the table above.

a) Use the data in the table to approximate H'(5). Show the computations that led to your answer. Using correct units, explain the meaning of H'(5) in the context of the problem.

b) Is there a time t for 0[tex]\leq[/tex]t[tex]\leq[/tex]12 at which the temperature of the soup is 60C? Justify your answer.

c) The temperature of the soup is also modeled by the twice-differentiable function C for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where C(t) is measured in degrees Celsius (C), and time tis measured in minutes. It is known C(3)= 80 and the derivative of C is given by C'(t)= -3.6e-0.05t. Write an equation for the line tangent to the graph at t=3 and use it to approximate C(5).

d) Based on the model given in part c, at what rate, in degrees Celsius per minute minute, is the rate of change of the temperature of the soup changing at t=3 minutes?

The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]

Which gives;

[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]

Therefore, H'(5) = -2.6°C per minute

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

At t = 12, H(12) = 58 °C

Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]

At t = 3, we have;

[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8

The  value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is -3.6 degrees per minute.

Learn more about calculus and concepts here:

https://brainly.com/question/20336420

Which story represents the equation six-sevenths times one-fourth?

A: Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more milk. How much milk did she drink in all?
B: Mike walked one-fourth mile and then he took the bus for six-sevenths miles to school. How many miles did he travel in total?
C: Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
D: Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left?

Need answer to the question

What is the percent decrease from 16 to 0

Ben currently has $70 in his trip fund. He makes $45 per week doing yard work for his neighbors. He keeps $18 of the $45 for weekly expenses. The remaining amount goes into his trip fund. Which function can be used to determine the amount of money (y), in dollars, that Ben has in his trip fund at the end of xx weeks?

y=70+27x

Ms. Usman buys about 14.4 gallons of gas every other week. How many gallons of ir gas does she buy in a year?​

Using the table find then relative frequency of each color, to 3 decimal places

PLEASE HELP QUICK!

By which rule are these triangles congruent?
A) AAS
B) ASA
C) SAS
D) SSS

Solve 3-x/2<18.
A. X>-42
B. x > -30
C. X< -30
D. X<42

Need answer to the question in the picture above

Mrs Ang bought k apples at 50% each from a supermarket. How much
change did she receive if she paid $10 to the cashier? Express your answer
in cents.

Find the intersection point for the following linear functions.
Rx) = 2x + 3
8(x) = -4x - 27

HELPPPP PLEASEEEEE ​

In a parking lot 30% of the cars are white write this as a decimal

In a group of workers, 16 belonged to a lottery syndicate and 4 did not.

What fraction of the workers did not belong to the syndicate?

1: 4/16

2: 1/5

3: 1/4

4: 3/4

please help I am so lost rn
(please put step by step if you can)
thanks!​

Please please hurry!!!! Answer this question

you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much is your total bill

Solution A is 40% acid and solution B is 80% acid. How many
liters of each should be used in order to make 100 L of a solution
that is 64% acid?

Question

Each data point on the scatter plot represents last month’s necklace and earring sales, in thousands of dollars, at one of the fourteen locations in a nationwide jewelry store chain. The correlation coefficient between necklace sales and earring sales is 0.98.


Wes says that an increase in necklace sales must cause an increase in earring sales. Ann says that an increase in earring sales must cause an increase in necklace sales. Who is correct?

David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $4.45 per pound, and type B coffee costs $5.85 per pound. This month, David made 123 pounds of the blend, for a total cost of $643.95. How many pounds of type B coffee did he use?

"When I started here, there were 500 employees. Since then, we have
added 35% more employees, so we now have a total of employees."

find three solutions for 9x - 2y = 18​

rewrite in simplest terms -6(-7u+6)+2u

ST
16. (26)
A bag contains 3 green marbles and
7 yellow marbles. Find the probability of
drawing a green marble, keeping it, and
drawing another green marble. Write the
probability as a fraction in simplest form.
17.

$145.75 marked up by 33% (round to the nearest cent)

help plsssssssssssssss

I thought of a number. This number double is 7 less than 29. What is my number? hurry please

Help with this please?

A rectangular cube of iron is a side 8 cm. What is it volume.​

7362*637 help please