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?

As A Bowl Of Soup Cools, The Temperature Of The Soup Is Given By The Twice-differentiable Function H

Answers

Answer 1

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;

a) H'(5) is approximately -2.6 degrees Celsius per minute.b) Yesc) The equation for the line tangent is y = -3.6·t + 90.8The approximate value of C(5) is 72.8 °C

d) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.

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

58 °C < 60 < 90 °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 equation for the tangent is; y = -3.6·x + 90.8

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

C(5) ≈ 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.

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Related Questions

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?

Answers

Step-by-step explanation:

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

is 64% acid

There should be 40 L of solution A and 60 L of solution B should be added in order to make 100 L of a solution that is 64% acidic.

What is equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, solution A is 40% acidic and solution B is 80% acidic, they are mixed to get a 100 L solution which is 64% acidic.

Establishing the equations,

A+B = 100

A = 100-B.......(i)

40% of A + 80% of B = 64% of 100

0.4A + 0.8B = 64......(ii)

Solving the equations,

0.4(100-B) + 0.8B = 64

40 - 0.4B + 0.8B = 64

0.4B = 24

B = 24/0.4

B = 60

Putting, B = 60 in Eq(i)

A = 100-60

A = 40

Hence, The amount of solutions needed is A = 40 L and B = 60 L.

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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?

Answers

Answer:

C I think.

Step-by-step explanation:

I don't know for sure, but A, B and D all talk about adding or subtracting the answers together, while C tells us to find the fraction of a fraction so I'm pretty sure you multiply. Hope this helps!

PLEASE HELP QUICK!

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

Answers

Answer:

ASA

Step-by-step explanation:

Angle marked the same way are congruent, so the two triangles have a side in common and the two adjacent angles congruent, so it's ASA

Answer:

The answer is Option B.) ASA

Explanation:

With the ASA rule, all triangles are congruent.

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Answer:

4689594

Step-by-step explanation:

help plsssssssssssssss

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Answer:

Last answer, height is 150 ft

Step-by-step explanation:

from the graph, you can clearly see, when T=3, H=150

Which means The firework is at a height of 150 feet

Answer:

D

Step-by-step explanation:

At 3 seconds, the firework is at a height of 150 feet

Answer is D. third option

The firework is at a height of 150 feet

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

Answers

Answer:

44u-36

Step-by-step explanation:

42u-36+2u

44u-36

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

Answers

Answer:  The table is shown below.

Explanation:

For each row, divide the color counts over the total. For example, we have 9 red in bag one out of 61 total. This leads to a relative frequency of 9/61 = 0.1475 which rounds to 0.148; so approximately 14.8% of the items in bag one are red. This represents the top left corner of the table.

As another example, we have 5 brown out of 60 total in bag ten. That leads to a relative frequency of 5/60 = 0.0833 = 0.083 (see the bottom right corner of the table).

Take note that for any given row, adding up the relative frequencies will yield the value of 1 (though there might be some slight rounding error along the way).

Need answer to the question in the picture above

Answers

Answer:

solution given :

Since opposite side and side of a congruent triangle are equal.

Now

the statement which is true is:

<HDG=~ <HFE

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Answers

A and b good luck (:(:
the answers are A and B

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

Answers

The solution of the given equation will be C -x< 30

What does it mean to solve an equation?

An equation represents the equality of two or more mathematical expressions.

A Solutions to an equation are those values of the variables, involved in that equation for which the equation is true.

We have been given the equation as 3-x/2<18.

Now solving for x

3-x/2<18.

Eliminate 3

-x/2 < 18 - 3

-x/2 < 15

Multiply by 2 on both sides;

-x/2 < 15 (2)

-x< 30

Therefore, the solution of the given equation will be C -x< 30

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What is the percent decrease from 16 to 0

Answers

The percentage that decreases is 1

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?

Answers

Answer:

Wes

Step-by-step explanation:

This represents a positive correlation, meaning that when x increases, so does y. Because of x, y increases meaning that Wes is correct

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

Answers

Answer:

x=-5 and y= 4

Step-by-step explanation:

To eliminate x, add up both equations

9y= 36

divide both sides by 9

y=36/9

y= 8

To eliminate y, multiply the first equation by 8

-16x + 8y = 112

2x+ 8y= 22

Subtract equation 2 from equation 1

-18x = 90

Divide both sides by -18

x= 90/-18

x= -5

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

Answers

Answer:

374.4 gallons

Step-by-step explanation:

there are 52 weeks in a year

every other week means once every two weeks

52 / 2 =26

14.4 gallons x 26 = 374.4 gallons

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

Answers

Answer:

he starts with 70 and $45-18=27 so he makes $27 to add to those $70

Step-by-step explanation:

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?

Answers

Step-by-step explanation:

x = pounds A

y = pounds B

x + y = 123

4.45x + 5.85y = $643.95

from the first equation we get

x = 123 - y

and we use that in the second equation :

4.45×(123 - y) + 5.85y = 643.95

547.35 - 4.45y + 5.85y = 643.95

1.4y = 96.6

y = 69

x = 123 - y = 123 - 69 = 54

so, he used 69 pounds of B coffee.

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.

Answers

Answer:

The apples may have costed 0.50 cents each, and she may have bought 10, which would result in her paying 10 dollars, and receiving 5 dollars in change.

Step-by-step explanation:

Multiply 10 (the amount she gave to the cashier) by 0.50%, it equals 5, so that's how much she paid, and since she gave a 10 dollar bill, she should get 5 dollars in change.

T^T

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

Answers

Answer:

11

Step-by-step explanation:

11*2=22

29-7 =22

Answer:

11

Step-by-step explanation:

Let x be your number

Is means equals

2x = 29-7

2x= 22

2x/2 = 22/2

x =11

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

Answers

Answer:

  $189.48

Step-by-step explanation:

  $145.75 + 30% × 145.75 = $145.75×1.30 ≈ $189.48

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

Answers

Answer:

HI THERE

the answer is number 1 !!

correct me if I'm wrong

HELPPPP PLEASEEEEE ​

Answers

I’m not rly sure what it means by flipping the card …. I’m assuming there’s more to this question but if it’s what I think it is the only way this equation will be true is by switching the + Symbol to - (subtraction) which would be 1-2= 3-4 since it would 1=1 making the equation true

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.

Answers

Answer:

the probability would be 30% but as a fraction it would be 3/10

Step-by-step explanation:

Answer:

7/15

Step-by-step explanation:

The probability of the first one is 7/10 and the second one is 6/9. Multiply them together and you get 42/90, which simplifies to 7/15.

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

Answers

Answer:

Assuming that the question is asking how many employees there are, your answer would be 675.

Step-by-step explanation:

First, to find 35% of 500, you can use this equation (35 x 500) / 100 Second, solve the equation (The answer is 175) Third, you add 500 + 175 to get 675

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

Answers

Answer:

[tex](x,y) = \left(5,\dfrac{27}2 \right), \left(0,-9), \left(9, -\dfrac 92 \right)[/tex]

Step-by-step explanation:

Need answer to the question

Answers

Answer:

B) Symmetric property of congruence

Step-by-step explanation:

The angles 1 and 2 are marked as congruent

If a ≅ b, then b ≅ a, this is called the symmetric property of congruence:

The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first.

Correct choice is B

Answer:

Symmetric property of similarity

Step-by-step explanation:

If a=a then that's reflexive propertyIf a=b and b=c then a=c, transitive property

Please please hurry!!!! Answer this question

Answers

we cant if we dont know the points

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

Answers

Answer:

$4.32

Step-by-step explanation:

If you are splitting it evenly, just divide 12.96 by 3

12.96 / 3 = $4.32

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

Answers

Answer:

(-5, -7)

Step-by-step explanation:

Answer:

[tex](-5,-7)[/tex]

Step-by-step explanation:

[tex]f(x)=2x+3[/tex]

[tex]g(x)=-4x-27[/tex]

[tex]2x+3=-4x-27[/tex]

[tex]6x+3=-27[/tex]

[tex]6x=-30[/tex]

[tex]x=-5[/tex]

[tex]f(-5)=2(-5)+3[/tex]

[tex]f(-5)=-10+3[/tex]

[tex]f(-5)=-7[/tex]

Therefore, the point of intersection is [tex](-5,-7)[/tex]

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

Answers

Answer:

0.3

Step-by-step explanation:

Answer:

[tex]{ \tt{30\% = 0.3}} \\ [/tex]

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

Answers

A rectangular cube of iron is a side 8 cm.Given, side (a) = 8 cm.We know, volume of a cube [tex] = {a}^{3} [/tex]Therefore, the volume

[tex] = {8}^{3} \: \: cm ^{3} \\ = 512 \: \: {cm}^{3} [/tex]

Answer:

The volume is 512 cube centimetres.

Hope you could get an idea from here.

Doubt clarification - use comment section.

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