A cup of coffee at 95 degrees Celsius is placed in a room at 25 degrees Celsius. Suppose that the coffee cools at a rate of 2 degrees Celsius per minute when the temperature of the coffee is 70 degrees. The differential equation describing this has the form

Answers

Answer 1

Answer:

See Explanation

Step-by-step explanation:

For an object at temperature T and supposing that the ambient temperature is Ta then we can write the differential equation that typifies the Newton law of cooling as follows;

dT/dt=-k(T-Tₐ)

So

dT/dt = 2 degrees Celsius per minute

T = 70 degrees Celsius

Ta = 25 degrees Celsius

2 = -k(70 - 25)

-k = 2/(70 - 25)

k = - 0.044

Hence we can write;

dT/dt=-(- 0.044)(95-25)

dT/dt= 3 degrees Celsius per minute


Related Questions

Mr.Bhal has a circular wading pool with a radius of 3.5 feet. He bought a larger pool witha diameter of 21 feet. The measurements of each pool are shown below. How many times the circumference of the old pool is the circumference of the new pool?

Answers

Answer: i think c

Step-by-step explanation:

Please indicate which type of sampling design is most appropriate for each of the following studies. The choices are SRS, stratified random sampling, and matched pair design.

a. A campus newspaper randomly selects 20 common Spring Break destinations and surveys the residents about their attitudes of students spending Spring Break in their city.
b. A developer in West Lafayette wants to know if students who are renting off-campus like their apartment complex. They chose 10 students who lived in 5 different complexes.
c. A researcher wants to know the difference in time it takes to apply brakes between people who are not talking on the phone and people who are talking on a hands-free cell phone. She chose 100 individuals and then drive both ways in a simulator and measured their responses. A student organization has 55 members. Out of these members, five are selected randomly to attend a national conference.

Answers

Answer:

Following are the responses to the given question:

Step-by-step explanation:

In point 1

The random selection stratified: although 50 statements belong to 5 different groups.

In point 2:

Coincide pair design: As we're in the SAME location to measure the difference between the downstream and upstream fractures. Although when calculating a top-down split they need only to calculate the low-up split which corresponds to the top-down split.

In point 3:

Matched layout: As 100 individuals were chosen and ALL were required to give BOTH and document certain responses.

In point 4:

SRS: RANDOMLY has also been selected since 20 spring break goals.

what's the following rotational symmetries of oranges regular hexagon​

Answers

Answer:

rotational symmetry of 60 degrees around the origin - yes

rotational symmetry of 120 degrees around the origin - yes

Step-by-step explanation:

A regular hexagon has 6 congruent angles

the the angles created on the line of symmetry are equal to 60 so the angle of rotational symmetry is 60 degrees.

The regular hexagon, like stated before, has 6 congruent angles so the order of symmetry is 6

Here is a visual from basic-matematics

PLEASE PLEASE HELP I WILL MARK THE BRAINLIEST!!!!!

Answers

Answer:

The average cost of a cat's annual visit is about $23.71 less at A New Leash on Life Animal Clinic than the average cost for a cat's annual visit at No Ruff Stuff Animal Hospital.

Explanation:

As you can see from the data and graph given, the Mean is essentially the average cost and $101.13 (New Leash on Life) is $23.71 less than $121.84 (No Ruff Stuff Animal Hospital).

find-5/6÷(-1/2) write the answer in the lowest terms.​

Answers

Answer:

[tex]\dfrac{-5}{3}[/tex]

Step-by-step explanation:

We need to solve the given expression in the lowest form i.e.

[tex]\dfrac{5}{6}\div (-\dfrac{1}{2})[/tex]

We know that,

[tex]\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{a}{b}\times \dfrac{d}{c}[/tex]

So,

[tex]\dfrac{5}{6}\div (-\dfrac{1}{2})=\dfrac{5}{6}\times (-2)\\\\=\dfrac{-5}{3}[/tex]

So, the lowest form is equal to [tex]\dfrac{-5}{3}[/tex].

-1/3*12+14=2/3*12+2=

Answers

Answer:

10=10

Step-by-step explanation:

_1(12)+14=2(12)+2

3.

In the figure above, sin 52=17/c. Based on the figure, which of the following equations is also true
A. Sin 38= c/17
B. Cos 38=17/c
C. Cos 52=17/c
D. Tan 52=c/17

Answers

Answer:

c. Cos 52 = 17/c

Step-by-step explanation:

sin(x) = cos(90-x)

Find the value of x to the nearest tenth! HELP ME!!!!!!!!!!!!! (PICTURE IS BELOW)

Answers

Answer:

11.4

Step-by-step explanation:

By Pythagoras Theorem:

[tex]x^{2} = {7}^{2} + ( {4}^{2} + {8^{2}}) \\ \\ x^{2} = 49+(16 + 64)\\ \\ x^{2} = 49+80\\ \\ x^{2} = 129 \\ \\ x = \sqrt{129} \\ \\ x = 11.3578167 \\ \\ x = 11.4[/tex]

What the person said 11.4

At the book sale, all books cost less than $5.

Answers

Is This A Good Or Bad Thing?

Answer:

then the books will cost 5.30

Step-by-step explanation:

don't forget to add 6 cents per dollar

The nutritional chart on the side of a box of a cereal states that there are 87 calories in a 3/4 cup serving. How many calories are in 8 cups of the cereal?

Answers

Answer:

Total calories in 8 cup = 928 calories

Step-by-step explanation:

Given:

Calories in 3/4 cup of cereal = 87 calories

Find:

Total calories in 8 cup

Computation:

Total calories in 8 cup = 8 x 87 x [4/3]

Total calories in 8 cup = 928 calories

Arithmetic mean of marks (out of 25) scored by 10 students was 15. One of the student, named Karishma enquired the other 9 students and find the deviations from her marks are noted as −8,−6,−3,−1,0,2,3,4,6. Find Karishma's marks?​

Answers

Answer:

Krishna's marks x marks

so...

xˉ=15

xˉ=15n=10

xˉ=15n=10∑x=x+x−8+x−6+x−3+x−1+x+x+2+x+3+x+4+x+6=10x−3

15=10x-3/10

150+3=10x

x=150/10=15.3 marks

Krishna scored 15.3 marks.

hope it helps you sis...

What is 0.69 expressed as a fraction in simplest form

Answers

Answer:

the answer is 69/100

70+95 Factor the expression using the GCF

giving brain

Answers

Answer:

70 + 95 = 5(14 + 19)

70 + 95 = 5(14 + 19)

gcf = 5

Step-by-step explanation:

70+95

70=2*5*7

95=5*19

70+95=(5*2*7)+(5*19)=(5*14)+(5*19)=5*(14+19)=5*(33)

5*33=165 and 70+95=165                                                                                                  Hope this helps! Please give me brainly!      

what is (x+2)^4 using binomial theorem and pascal’s triangle?

Answers

Answer:

x 4 +8x 3 + 24 x 2 + 32 x + 16

Step-by-step explanation:

Erin bought 4 jars of jelly and 6 jars of peanut butter for $19.32. Adam bought 3 Jars of jelly
and 5 jars of peanut butter for $15.67.
Use x for jars of jelly and y for jars of peanut butter, write the equation for either Erin or Jack.
DO NOT SOLVE
(Worth 10 points)

Answers

Here is your system of equations in two variables.

Equation for Erin:

4x + 6y = 19.32

Equation for Adam:

3x + 5y = 15.67

That's it.

can you help thanks ​

Answers

Answer:

1/48 or .2083

Step-by-step explanation:

dividing by 6 is the same as multiplying by 1/6, so if you multiply 1/8*1/6 you get 1/48

Answer: Reduce the expression, if possible, by cancelling the common factors.

Exact Form:

1/48

Decimal Form:

0.02083

The graph shows the relationship between the distance a car is driven and the number of gallons of gasoline used. Identify the value of d in the point (1, d). What does that point represent?


A. d=25; the unit rate is 25 miles per gallon

B. d=25; the unit rate is 25 gallons per mile

C. d=50; the unit rate is 50 miles per gallon

D. d=50; the unit rate is 50 gallons per mile

Answers

Answer:

B

Step-by-step explanation:

The "x" coordinate goes before the y coordinate. For example, it is (x, y)

To solve:

When the x coordinate, or the gasoline used (In gallons) is 1, then we need to find what d is.

On the graph, d = 25 miles per gallon.

So, the answer is B.

what is the area of yhe following circle?either an exact answer in terms of or use 3.14 for and enter your ansert as a decimal
r=5
units2 ​

Answers

Answer and Step-by-step explanation:

If the radius is 5, then we can plug 5 into the area of a circle equation.

A = [tex]\pi r^{2}[/tex]

A = [tex]\pi (5)^{2}[/tex]

A = 25[tex]\pi[/tex]

The area of a circle with radius 5 is 25[tex]\pi[/tex].

#teamtrees #PAW (Plant And Water)

Isabel owns a T-shirt cart and has a contract with a local sports arena to distribute T-
shirts outside the venue. Isabel is paid a flat rate of $235 and a variable rate per T-
shirt. The following table represents the total amount of money Isabel makes. Let X
denote the number of T-shirts that Isabel sells and let y denote the amount of money
that Isabel makes. What is the estimated amount of money that Isabel makes if she
sells six T-shirts?
T-shirts
o
1
2
3
4
Money
$235
$250
$267
$286
$307

Answers

Answer:

in just going to say 90

Step-by-step explanation:

tell me if i got it right or wrong no hate

Find the missing angle of each triangle.

Answers

Answer:

1 is 64

2 is 85

3 is 56 hope this helps  

Step-by-step explanation:

also how give brainly i want to give u brainly

pls help i need answer

Answers

Answer:

109 degrees

Step-by-step explanation:

23 + 48 = 71

180 - 71 = 109 :)

Answer:

i think the answer is 109 im not sure

Step-by-step explanation:

48+23=71 180-72=109

What is the solution to this system of equations?
2x+y=6
- 2 x - y = 2
(1,-1)
(0,8)
infinitely many solutions
O no solution

Answers

The answer is No solution

plzz help really fast

Answers

Answer:

the answer is 32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Let's do it step by step:

[tex]-16(-5\frac{1}{2} \div 2\frac{3}{4}) = -16(\frac{-5\frac{1}{2}}{2\frac{3}{4}}) = -16(\frac{-\frac{11}{2}}{\frac{11}{4}}) = -16(-\frac{4}{2}) = -16\cdot(-2) = 32[/tex]

The total surface area is _ square centimeters

Answers

Answer:

180 square inches

Step-by-step explanation:

First off since the square will be easiest to do

a=a^2

a=6^2

a=36

now for the triangles

a= height of triangle * base/ 2

a= 12*6/2

a= 36

and since there is 4 of the triangles we multiply 36 by 4

=144

now we add 144 to 36 and we have the total

The three lines shown in the diagram below intersect at the same point. The measures of some of the
angles in degrees are given as...

Answers

Answer:

x =16, y = 151.2

Step-by-step explanation:

Since angle 3/5y and angle 12 and angle 42 lies on the same straight line,

[tex] \frac{3}{5} y + 12 + 42 = 180 \\ \frac{3}{5} y = 180 - 12 - 42 \\ \frac{3}{5} y = 180 - 54 \\ \frac{3}{5} y = 126 \\ y = 126 \div \frac{3}{5} \\ = 126 \times \frac{5}{3} \\ = 151.2[/tex]

Since angle 3(x-2) , 3/5y and 12 lies on the same straight line and we know what y is,

[tex]3(x - 2) + \frac{3}{5} y + 12 = 180 \\ 3(x - 2) + \frac{3}{5} (151.2) + 12 = 180 \\ 3(x - 2) + 126 + 12 = 180 \\ 3(x - 2) = 180 - 12 6 - 12 \\ 3(x - 2) = 42 \\ x - 2 = \frac{42}{3} \\ x = 14 + 2 \\ =16[/tex]

What is the value of the y-intercept of the graph of f(x) = 29(5.2)* ?

Answers

Answer:

(0,29)

Step-by-step explanation:

To find the y-intercept, substitute in

0 for x and solve for y OR use a graphing calculator.

What type of dilation occurs with a scale factor of 1/4?

Answers

Answer:

Congruent

Step-by-step explanation:

If f(x)=x+5,g(x)=1-2x,h(x)=x-2 find fog,foh,goh,gof,hof​

Answers

Answer:

The answer is below

Step-by-step explanation:

Function is a rule, or law that defines the relationship between one variable (the independent variable) and another variable (the dependent variable)

a) fog = f[g(x)] = f(1 - 2x) = 1 - 2x + 5 = 6 - 2x

b) foh = f[h(x)] = f(x - 2) = x - 2 + 5 = x + 3

c) goh = g[h(x)] = g(x - 2) = 1 - 2(x - 2) = 1 - 2x + 4 = 5 - 2x

d) gof = g[f(x)] = g(x + 5) = 1 - 2(x + 5) = 1 - 2x - 10 = 9 - 2x

e) hof = h[f(x)] = h(x + 5) = x + 5 - 2 = x + 3

Round 8 5/9 to the nearest whole number. 9 10 7 8

Answers

Answer:

The answer would be 9,

Step-by-step explanation:

because it is closer to 9 than 8.

This graph shows how fast a race car can travel in a stock car race


What is the meaning of the point with an x-coordinate of 2?



A. The race car travels 2 meters in 180 seconds

B. In 1 second, the race car travels 2 meters

C. In 2 seconds, the race car travels 180 meters.

D. It takes the race car 60 seconds to go 2 meters ​

Answers

Answer:

C. In 2 seconds, the race car travels 180 meters.

Step-by-step explanation:

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