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

Mrs. Baca uses a phone card to call a relative in Colombia, It cost her 45 cents to talk for 15 minutes. Choose True or False for each statement.
A. For 45 cents, Mrs. Baca can talk for 3 minutes. True or False.
B. The call rate is 3 cents per minute. True or False.
C. The call rate can represent by the ratio 445:15. True or False.
D. Divide 75 by 15 to find the number of minutes Mrs. Baca can talk. True or False.

fnd the highest common factor of -8xy and 20y

Two polygons have a similarity ratio of 4:5. If the perimeter of the first one is 10 inches, then what is the perimeter of the second?
Group of answer choices

11 inches

8 inches

12.5 inches

15 inches

Helppppppppppppp helppppppppppppp

Evaluate.

(jk−1)÷j when j=−4 and k=−0.7

Enter your answer as a decimal in the box.

2 FOR 2.20 UNIT RATE

?/5 =8/10 type the missing number that makes this fraction equal

help me plsss! need help

What is 8 hours and 37 minutes converted into minutes?

What is the answer to the equation?

TRUE OR FALSE

There are whole numbers that are not integers.

All rational numbers are whole numbers.

All integers are whole numbers.

All integers are rational numbers.

For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7

If you spend 3/5 of your $40 gift card, how much money will be left on it?

What are the coordinates of the point (-4, 2) after a translation 2 units left and 2 units up?

A (-2, 0)
B (-6,0)
C (-2, 4)
D (-6, 4)

solve for x. 2/x-3=x/12-4x

Quantity is proportional of 40/8

x+3x+3y+3z=21
Find the value of X.​

The perimeter of a rectangle is 39.2 km, and its diagonal length is 14 km.
Find its length and width

OMG HELP RN I GIVE BRAINLIST

Which of the following correctly describes the solutions to the inequality?



A.
There are 5 solutions. The solutions are the numbers between 4 and 8.
B.
There are an infinite number of solutions. The solutions are all numbers less than 3.
C.
There are 6 solutions. The solutions are the numbers between -2 and 3.
D.
There are an infinite number of solutions. The solutions are all numbers greater than 3.

Lena bought 40 tickets to use at a carnival. She used some of the tickets to ride the bumper cars and play some games. Now she has 24 tickets left. What is the percent of decrease in the number of tickets that he has?

a. 66.6
b. 40
c. 60
d. 80

i need help fast plz

Please help me solve this math problem

factorise
18p+6
please im so bad​

PLEASE HELP ME THIS IS THE 5TH TIME I HAVE HAD TO POST THIS AND GIVING BRAINLIST TO FIRST ANSWER


B.
C.
D.

which inequality matches the graph?

A. x>4
B. x<4
C. x=4
D. x >4​

Jose and Gavin are reading the same book. At the beginning of the month, Jose was

on page 10 and Gavin was on page 37. Jose will read 17 pages per day and Gavin will

read 14 pages per day. Let J represent the page of the book that Jose is on at the end

oft days into the month, and let G represent the page of the book that Gavin is on at

the end oft days into the month. Write an equation for each situation, in terms of t,

and determine what page Jose and Gavin will be on on the day they are both on the

same page.

What is the domain of the absolute value function below?
(will give brainless)!!!!

Which of the equations will be a true statement if p = 10 3 ? Select the two choices that apply.
A. 3.4 ÷ p = 0.034
B. 437 ÷ p = 0.437
C. 53.45 ÷ p = 53.45
D. 6,340 ÷ p = 6.34
E. 2,458.2 ÷ p = 24.582

Determine whether a triangle with the given side lengths is a right triangle.

A linear function and an exponential function are shown below.

Over which interval does the growth rate of the exponential function exceed the growth rate of the linear function?