A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 67°C, it is cooling at a rate of 1°C per minute.

Let y = T − Ts, where T(t) is the temperature of the coffee in degrees Celsius at time t and Ts is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for y(t) = Aekt.

Find: A and k

After how many minutes is the temperature of the coffee 67°C? (Round your answer to two decimal places.)
Answer:

Answers

Answer 1

The temperature of coffee will reach 67 °C

The rate of temperature change is most directly related to the difference between the body temperature and room temperature.

[tex]\frac{dT}{dt} =-k(T-T1)[/tex]

This equation's solution using the initial condition

T(0) = T0

T(t) = Tr + (T0 - Tr)

At the moment, the cooling rate

k × (T(t) - Tr)

We can write that according to the text

T1 = Tr + (T0 - Tr)

Solving the system of equations generates the unknown time:

t = [tex]\frac{69-20}{1} (ln\frac{95-20}{69-20})[/tex]

t = 21 min.

Hence the coffee will reach the temperature 67°C in 21 minutes.

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Related Questions


There are 151 people in the 6th
grade class. It costs $24 for each
person to go snorkeling. How
much did they pay altogether?

Answers

3624 is the correct answer because if you times 151 by 24 you will get 3624

Answer:

Step-by-step explanation:

it cost $3,624

The bill at a restaurant came to $136.40. The patrons decided to leave a 15% tip. What was the total bill including tip?

Answers

Answer: 156.86

Step-by-step explanation:

Simplify 3^2 + 3(6 - 2^2) ÷ 6.

Answers

Fractions simplification

Apply PEMDAS method. Eliminate parenthesis first.

Then (3^2 + 3•6 - 3•2^2 )/ 6 = (3^2 + 3•6 - 3•2^2 )/ 6

now eliminate exponents

= [3• 3 + 3•6 + 3•4] / 6

= 3•5/6 now multiplicate

3•5= 15

Then

= 15/6 = 2 + 3/6 = 2 + 1/2 = 2.5

y + 7 ≥ –1 and y∕4 + 3 ≤ 5.

Answers

Answer:

first one

y can be every number so it can be a -6 to infinity

[tex] - 1 < y [/tex]

[tex]y = - 6 \: or \: \infty [/tex]

second two

y<8

[tex]y < 8 \: or \infty [/tex]

if a varies equal directly with b, and a=8 when b=20 what is the value of a when b= 14.5

Answers

[tex]\frac{8}{a}=\frac{20}{14.5}[/tex][tex]20a=8\cdot14.5[/tex][tex]a=\frac{116}{20}=5.8[/tex]

2x – 1 over 5 - 3x +2 over 4

Answers

we have

(2x-1)/5-(3x+2)/4

{4(2x-1)-5(3x+2)}/20

{8x-4-15x-10}/20

{-7x-14}

5-(3x+2)/4

4(2x-1

Line CD passes through (0,1) and is parallel to x+y=3. Write the standard form of the equation of line CD

Answers

The standard form of the equation of line CD is x + y = 1

What is standard form of equation of a line?

The standard form ;of equation of s line is written in the form

Ax + By = C

Line that are parallel has equal slope hence solving for the slope of line

x + y = 3 we have

y = -x + 3

The slope is -1

Equation of line CD passing through points ( 0, 1 )

( y - 1 ) = -1 * ( x - 0 )

y - 1 = -1 * x

y = -x + 1

writing to standard form

x + y = 1

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Please help I couldn’t go to school today and I don’t understand

Answers

Answer:

the value of x is 2

Step-by-step explanation:

3x + 6

x = 6 ÷ 3

x = 2

3x + 6

3× 2 + 6

6+6

12

-4 + 8x

-4 + 8×2

-4+16

12

Helppppppp will give brainiest to first right answer

Answers

Answer:

1 degrees F

Step-by-step explanation:

-3+12-6=3

3/3 = 1

1 degrees F

:]

C) 1 degree F

You would do -3+12-6 ( which is 3) and divide that by 3 (the number of numbers) to get the average (1). Now you know that 1 degree is your answer.

Which is a counterexample for the conditional statement shown?

If the numerator of a fraction is larger than the denominator of the fraction, then the fraction is greater than 1.

any fraction with a denominator of 0
any fraction with a numerator of 0
any fraction with a positive numerator and a negative denominator
any fraction with a negative numerator and a positive denominator

Answers

Answer:  Choice C

any fraction with a positive numerator and a negative denominator

======================================================

Explanation:

Consider the fraction 10/(-5) where we divide 10 over -5

The numerator 10 is larger than the denominator -5, as any positive number is larger than a negative number. But 10/(-5) simplifies to -2 which is not greater than 1.

This is one counterexample to show that the original conditional statement is false.

Your lunch in the hospital cafeteria cost $6.50. Based on working 50 weeks per year, how much will you spend on lunch per year?

Answers

The total amount spent on lunch per year would be 325 dollars.

What is the fundamental principle of multiplication?

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have been given that Your lunch in the hospital cafeteria cost $6.50. Based on working 50 weeks per year, then;

The lunch in the hospital cafeteria cost = $6.50.

The total amount spend on lunch per year;

6.50 x 50

325

Hence, the total amount spent on lunch per year would be 325 dollars.

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Give a parametric representation of the parabola y = (x+7)^2 -5

Answers

We have to find the parametric representation of the parabola y = (x+7)² - 5, which is represented in vertex form.

Parametric representations use a third variable on which we define x and y.

We will call this variable t.

We can start with defining t as:

[tex]\begin{gathered} t=x+7 \\ \Rightarrow x(t)=t-7 \end{gathered}[/tex]

We then have already x in function of t.

Then, we can use the definition of t to find y(t):

[tex]\begin{gathered} y(t)=(x(t)+7)^2-5 \\ y(t)=(t-7+7)^2-5 \\ y(t)=t^2-5 \end{gathered}[/tex]

We then have x and y defined in function of t.

Answer: we can represent the parabola in a parametric form as

x(t) = t-7

y(t) = t² - 5

The combination of both integer and rational numbers gives

Answers

Answer:

Step-by-step explanation: Answer is real number

Choose the place where the digit 1 sits in this number 988,172,430,056

Answers

The number 1 sits in the 100 millions place.

The 100 millions place is 8 spaces to the left of the decimal. Hence, considering 1 is 8 spaces from where a decimal place could be, then 1 is in the 100 millions place.

Hope this helps!

Complete the point slope equation of the line through -2,6 and 1,1

Answers

Answer:

3y = -5x + 8

Step-by-step explanation:

Point Slope Equation Of A Straight Line:
              y - y1 = m(x - x1)

where m = slope of the line and (x1, y1) is any point on the line

Slope is given by rise/run

For any two point (x1, y1) and (x2, y2) on the line

rise = y2 - y1  
and
run = x2 - x1


Given points (-2, 6) and (1, 1)
rise = 1 - 6 = -5
run = 1 - (-2) = 1 + 2 = 3

rise/run = m = -5/3

Equation using the point (1, 1) is
y - 1 = -5/3(x - 1)

y - 1 = -5/3x + 5/3

Multiply both sides by 3 to get

3(y - 1) = 3 x (-5/3)x + 3(5/3)
3y - 3 = -5x + 5
3y = -5x + 8

0,2% of what number is 8?

Answers

LE THE UNKNOWN NUMBER BE x WHEN I SOLVE

[tex] \frac{0.2}{100} \times x = 8 \\ \frac{0.2x}{100} = 8 \\ [/tex]

I WILL USE CROSS MULTIPLICATION

[tex]0.2x = 8(100) \\ 0.2x = 800 \\ \frac{0.2x}{0.2} = \frac{800}{0.2} \\ x = 4000[/tex]

OF ( 4000) IS 0.2% OF 8.

HOPE THIS HELPS.

How would you find the area of each of your rooms without furniture?

Answers

Given that you have a room that has dimensions l and w wherein l is the length of the room while w is the width of the room (shown in a diagram below).

the area of the room can be computed using the equation

[tex]A_{room}=l\times w[/tex]

Basically, we just multiply the length and the width of the room.

Hey there Ms or Mr could you please help me out with this problem? Just a heads up, this is my assignment not a quiz. My assignment is about distance and midpoint formula.

Answers

EXPLANATION

Let's see the facts:

Midpoint = (-2,5)

A=(4,7)

Let the point of B as B=(x,y)

Then,

[tex]\frac{x+4}{2}=-2,\frac{y+7}{2}=5[/tex]

Multiplying the frist equation by 2:

[tex]x+4=-2\cdot2[/tex]

Subtracting -4 to both sides:

[tex]x=-4-4[/tex]

Simplifying:

[tex]x=-8[/tex]

Multiplying the second equation by 2:

[tex]y+7=2\cdot5[/tex]

Subtracting -7 to both sides:

[tex]y=10-7=\text{ 3}[/tex]

The coordinates of the point B are:

B=(-8,3)

five friends are going to share 1/2 of a pizza. How much of a whole pizza will each friend eat?which equation can be used to solve the problem above?A.5÷1/2=nB.1\2÷5=nC.n÷5=1/2D.n÷1\2=5

Answers

In this case the answer is very simple .

Step 01:

Data

5 friends

1/2 pizza

Step 02:

We must distribute the pizza among 5 friends.

[tex]\frac{\frac{1}{2\text{ }}\text{ pizza}}{5\text{ friends}}\text{ = n}[/tex]

The answer is:

Option B.

1\2÷5=n

(50 x 2) plus (15 x 2)

Answers

Answer:

130

Step-by-step explanation:

100+30

Answer:

130

Step-by-step explanation:

100+30=130

Determine whether the sequence 15,13,11,9 is an arithmetic sequence if yes, identify the common difference.

Answers

The sequence is not an arithmetic sequence because. The n-term for an arithmetic sequence is:

[tex]a_n\text{ = }a_1\text{ + }(n-1)d[/tex]

where d is the difference between two consecutive numbers. In this case d = 2. Because

15-13 = 2

13-11 = 2

11- 9 = 2

now, the first term for 15,13,11,9 is 15 = a_1, the second term would be:

[tex]a_2\text{ = }a_1\text{ + }(2-1)d\text{ }[/tex]

that is equivalent to say:

[tex]a_2\text{ = 15 + }(2)2=19\ne13\text{ }[/tex]

So we can conclude that 15,13,11,9 is not an arithmetic sequence.

Write an equation for the function whose graph is shown to the right

Answers

In this problem we have that

the parent function or original function is

[tex]y=\sqrt[]{x}[/tex]

the transformation is a translation of 2 units at left

so

the rule is

(x,y) ------> (x-2,y)

therefore

the equation of the given graph is

[tex]y=\sqrt[]{x+2}[/tex]

the supplement of an angle is 30 degrees more than the measure of the
what is the measure of
the angle?
angle,

Answers

Answer:

x = 75°

Step-by-step explanation:

supplementary angles sum to 180°

let x be the angle then x + 30 is the supplementary angle , so

x + x + 30 = 180

2x + 30 = 180 ( subtract 30 from both sides )

2x = 150 ( divide both sides by 2 )

x = 75

x + 30 = 75 + 30 = 105

the angle is 75° and the supplementary angle is 105°

if the company decides to produce 2,000 containers of regular crunchy peanut butter, how many containers of new extra crunchy peanut butter would it produce?

Answers

The number of extra crunchy peanut butter that the company would produce (current production units) is 1,700 containers.

How is the number determined?

Using the mathematical operation of subtraction, the number of units to be produced can be determined.

First, we have that the ending inventory for the last period was 300 containers.

This ending inventory is subtracted from the required production level, to determine the number of containers to produce for this period.

Thus, to meet the production requirements, the company would produce additional 1,700 containers of crunchy peanut butter.

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Question Completion:

Ending inventory of regular crunchy peanut butter from last period = 300 containers.

Javier exercises for 2 1/2 hours every Saturday. His exercisesincludes two parts. If he spends the same amount of timeon each part how many hours does he spend weightlifting?

Answers

According to the given data we have the following:

Javier exercises for 2 1/2 hours every Saturday, hence, he exercises for 2.5 hours.

In order to calculate the amount of time he spend weightlifting we would make the following calculation:

amount of time he spend weightlifting=total training per day/2

amount of time he spend weightlifting=2.5 hours/2

amount of time he spend weightlifting=1.25 hours

Therefore, he spends weightlifting 1 hour and 25 minutes every saturday

I need an answer for 1,2,3,4,5, and 6

Answers

Using alternate exterior angles,

[tex]3x-31=x+59\\\\2x=90\\\\x=45\\\\\implies 3x-31=x+59=104[/tex]

So,

[tex]\angle 1[/tex]: 76 degrees using linear pairs

[tex]\angle 2[/tex]: 104 degrees using corresponding angles

[tex]\angle 3[/tex]: 76 degrees using vertical angles

[tex]\angle 4[/tex]: 104 degrees using same-side interior angles

[tex]\angle 5[/tex]: 76 degrees using linear pairs

[tex]\angle 6[/tex]: 76 degrees using vertical angles

A university claims its recent graduates earn an average annual salary of
$45,000. You draw a random sample of 40 recent graduates and find that their
average salary is $46,000, and calculate the standard error of the sample mean
as 436.81. What is the t ratio for this result?

Answers

Answer:

t-ratio = 0.362

Step-by-step explanation:

In hypothesis testing,

The t-ratio is given by the formula:

[tex]\dfrac{X-\mu}{s}[/tex]

where μ is the hypothesized mean, X the sample mean and s the sample standard deviation

The Standard Error of the Mean SEM = [tex]\large \text{{$\dfrac{s}{\sqrt{n}}$}}[/tex]  where n is the sample size.

We We are given:

X = 46,000
μ= 45,000

SEM = 436.81

n = 40

We can find the sample standard deviation
s = SEM x √n
s = 436.81 x √ 40

s = 2762.3

Therefore

t-ratio = (46000 - 45000)/2762.3 = 0.362

What is the diameter of a sphere with a volume of 80487 in^3, to the nearest tenth ofan inch?

Answers

EXPLANATION

If the volume of a sphere is 80487 in^3, the diameter would be given by the following relationship:

[tex]\text{Volume}=\frac{4}{3}\cdot\pi\cdot r^3[/tex]

Replacing terms:

[tex]80487=\frac{4}{3}\cdot\pi\cdot r^3[/tex]

Isolating r^3:

[tex]\frac{80487}{\pi}\cdot\frac{3}{4}=r^3[/tex]

Applying the cubic root to both sides:

[tex]\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}=r[/tex]

Switching sides:

[tex]r=\sqrt[]{\frac{80487}{\pi}\cdot\frac{3}{4}}[/tex]

Multiplying numbers:

[tex]undefined[/tex]

the numberof blocks has 9 in the ones places.The number in the hundreds place is one more than the number in the tens place. Those two numbers equal 11. How many blocks are there?

Answers

Based on the given information, we can express the following

[tex]\begin{gathered} h=1+t \\ h+t=11 \end{gathered}[/tex]

Because the digit of hundreds is 1 more the tens, and they sum 11. Let's combine the function to find t

[tex]\begin{gathered} h+t=11 \\ 1+t+t=11 \\ 2t=11-1 \\ t=\frac{10}{2}=5 \end{gathered}[/tex]

So, the digit of tens is 5.

Let's find the hundreds.

[tex]h=1+t=1+5=6[/tex]

The number of hundreds is 6.

Hence, the number of blocks is 659.

What are the x intercept of the equation f(x)=3(x-7)(4x+2)

Answers

The x-intercepts are

x = 7

and

x = -1/2

SOLUTION:

we need to find the value of x where y or f(x) is 0

the expression x-7 will be zero if x=7

the expression 4x+2 will be zero if x = -1/2

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