Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 205 degrees Fahrenheit when freshly poured, and 2.5 minutes later has cooled to 195 degrees in a room at 70 degrees, determine when the coffee reaches a temperature of 160 degrees.

Answers

Answer 1

Answer:

Tt = 70 + 135e^-0.031t

13 minutes

Explanation:

Given that :

Initial temperature, Ti = 205°

Temperature after 2.5 minutes = 195°

Temperature of room, Ts= 70

Using the relation :

Tt = Ts + Ce^-kt

Temperature after time, t

When freshly poured, t = 0

205 = 70 + Ce^-0k

205 = 70 + C

C = 205 - 70 = 135°

T after 2.5 minutes to find proportionality constant, k

Tt = Ts + Ce^-kt

195 = 70 + 135e^-2.5k

125 = 135e^-2.5k

125 / 135 = e^-2.5k

0.9259 = e^-2.5k

Take In of both sides :

−0.076989 = - 2.5k

k = −0.076989 / - 2.5

k = 0.031

Equation becomes :

Tt = 70 + 135e^-0.031t

t when Tt = 160

160 = 70 + 135e^-0.031k

90 = 135e^-0.031t

90/135 = e^-0.031t

0.6667 = e^-0.031t

In(0.6667) = - 0.031t

−0.405465 = - 0.031t

t = 0.405465/ 0.031

t = 13.071

t = 13 minutes


Related Questions

which particles do not affect the stability of the atom

Answers

electrons


20charachters

Electrons are the particle pr4esent inside the atom that does not affect the stability of the atom,

What is radioactivity?

The ability of some unstable atoms to emit nuclear radiation spontaneously, typically in the form of alpha or beta particles frequently accompanied by gamma rays, is known as radioactivity.

An overabundance of neutrons or protons can make the nucleus of an atom unstable.

A radioactivity atom will try to become stable by extruding other particles, such as protons or neutrons, or by releasing energy in various ways.

Thus, Electrons are the particle present inside the atom that does not affect the stability of the atom,

To learn more about radioactivity here, refer to the link;

https://brainly.com/question/13950350

#SPJ2

What is the speed of a train if it covers 69 km in 45
minutes.

Answers

Answer:

1.4km/h

Explanation:

distance/time = speed

69/45=1.4km/h

If rider A is moving 8 meters per second, and rider B is moving 3 meters per second, how far away from rider A was rider B when first observed at the start of the graph?

Answers

Answer:

the answer is 32

Explanation:

he was riding pretty far

17. During a game of tug of war, two teams of students pull on opposite sides of a rope. During the
game, the rope begins to accelerate towards the left. What must be true about the forces acting on the
rope at the time of the acceleration towards the left?
A. The team pulling towards the right is pulling with a force greater than the team pulling towards the left.
B. The team pulling towards the right is pulling with a force equal to the team pulling towards the left.
C. The team pulling towards the right is pulling with a force less than the team pulling towards the left.
D. The team pulling towards the right stopped pulling the rope while the team pulling towards the left
continued

Answers

Answer:

c

Explanation:

The answer is letter c

A certain brand of hotdog cooker works by applying a potential difference of 144 V across opposite ends of a hot dog and allowing it to cook by means of the thermal energy produced. The current is 10.5 A, and the energy required to cook one hot dog is 60.6 kJ. If the rate at which energy is supplied is unchanged, how long will it take to cook three hot dogs simultaneously

Answers

Answer:

120.237 seconds

Explanation:

Given that:

V = 144 V

I = 10.5 A

H = 60.6 kJ

Using the formula:

H = I²RT

From H = I²RT; making T the subject, we have:

[tex]T = \dfrac{H}{I^2R}[/tex]

where;

[tex]R = \dfrac{V}{I}[/tex]

[tex]T = \dfrac{H}{V \times I}[/tex]

[tex]T = \dfrac{60.6 \times 10^3 }{144 \times 10.5}[/tex]

T = 40.079

[tex]T_{neq} = 3T[/tex]

[tex]T_{neq} =3 \times 40.079[/tex]

[tex]\mathbf{T_{neq} =120.237 \ sec}[/tex]

Four people are pulling in different directions on a shopping cart. The magnitude of their pulling forces and the directions relative to straight east are indicated below. Jane: 80 pounds, straight east (0 degrees relative to east) Brittany: 100 pounds, north (90 degrees relative to east) Robyn: 80 pounds, southwest (225 degrees relative to east) Scott: 100 pounds, northwest (135 degrees relative to east)
Which way with the shopping cart go?

Answers

Answer:

17⁰ north of west

Explanation:

We shall represent forces by vector notations . i will represent unit vector towards east and j will represent unit vector towards north .

Jane: 80 pounds, straight east

F₁ = 80 i

Brittany: 100 pounds, north (90 degrees relative to east)

F₂ = 100 j

Robyn: 80 pounds, southwest (225 degrees relative to east ) or 45⁰ south of west

F₃ = - 80cos 45  i - 80 sin45 j = - 80/√2 x ( i + j )

= - 40√2 ( i + j )

Scott: 100 pounds, northwest (135 degrees relative to east) or 45⁰ west of north .

F₄ = - 100 cos 45 i + 100 sin45 j =  50√2 ( - i + j )

Resultant force

= F₁ + F₂ + F₃ + F₄

F =  80 i + 100 j + - 40√2 ( i + j ) + 50√2 ( - i + j )

F = 80 i - 90√2 i + 110√2 j

80 i - 127.26 i + 114.14 j

F = - 47.26 i + 114.14 j

Direction of force

TanФ = 114.14 / 47.26 = 2.4

Ф = 67⁰

67⁰ north of west .

At what latitude are there almost no differences between the seasons? Explain
why this occurs?

Answers

Answer:

The four-season year is typical only in the mid-latitudes. The mid-latitudes are places that are neither near the poles nor near the Equator. The farther north you go, the bigger the differences in the seasons.

Explanation:

hope this helps have a good day :) ❤

At a latitude equal to zero degrees there is little seasonal variation. This phenomenon is due each day the Sun's rays strike the Earth's surface at approximately the same angle near the Equator.

The Equator is the line of (zero degrees) latitude around the middle of the Earth.

Moroever, the intensity of solar radiation and therefore also the temperature at the Earth's surface largely depends on the angle of incidence of the Sun's rays.

At 0° latitude, there is a very little seasonal variation because all days the Sun's rays strike the Earth's surface at approximately the same angle. At the Equator, the Sun's rays strike the Earth's surface at an angle of 90°, causing warmer temperatures compared to higher latitudes.

In additon, at 0° latitude, all days also have the same number of hours of light and dark (i.e., approximately 12 hours of sunlight).

In conclusion, at a latitude equal to zero degrees (i.e., at the Equator) there is little seasonal variation. This phenomenon is due each day the Sun's rays strike the Earth's surface at approximately the same angle near the Equator.

Learn more in:

https://brainly.com/question/744653

This is from P.E , que some please help me

Answers

Answer:

I know that 2 is called a foul I dont know about 1 though

Can you explain how newtons second law of force can be used in football and explain if possible

Answers

Answer:

Newtons 2nd Law of motion affects football as well. This law states the greater the mass of an object, the less the acceleration. This means that the more the objects weighs, the more difficult it is to move the object.

Explanation:

this is my best answer i can give you and mark me brainliest plz

A 0.75 kg golf ball is being launched from the ground. What is its potential energy​

Answers

Explanation:

the question it's not complete as I don't know the height as the formula for potential energy is : PE = mgh

(m) - mass acceleration due to gravity

(g) - acceleration due to gravity (9.8 m/s2)

(h) - height

If the solid, purple line represents a prey population
(e.g., rabbits) and the dashed, red line represents a predator population (e.g., coyotes), which of the following statements is a reasonable conclusion based on the graph?

Answers

Answer:

There is no correlation that can be made between the predator and prey populations.

Explanation:

Ermrmrm.

A weightlifter holds a 1,500 N barbell 1 meter above the ground. One end of a 2-meter-long chain hangs from the center of the barbell. The chain has a total weight of 400 N. How much work (in J) is required to lift the barbell to a height of 2 m

Answers

Answer:

1800 J

Explanation:

We are given that

Weightlifter hold weight, w=1500N

Height of weightlifter from ground,h=1m

Length of chain=2m

Total weight of chain, w'=400 N

We have to find the work done required to lift the barbell to height of 2m.

Total work done=Work done to lift  a barbell and half of the chain+ work done  to lift the upper half of the chain

Total work done=[tex]1500+\frac{1}{2}(400)+\frac{1}{2}(400)(\frac{1}{2}(1))[/tex]

Total work done=[tex]1700+100[/tex]

Total work done=1800 J

Hence, work done is required to lift the barbell to a height of 2 m=1800 J

The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would....
A Increase
B Decrease
C Stay the Same
D Vary with day and night

Answers

Answer:The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would..

Explanation: It would decrease.

The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would decrease because the acceleration due by gravity on the moon is less than the acceleration due to gravity on the earth, therefore the correct answer is option C.

What is gravity?

It can be defined as the force by which a body attracts another body towards its center as the result of the gravitational pull of one body and another.

In comparison to the Earth, the Moon is less massive. Your weight would drop if you traveled to the moon because the acceleration caused by gravity there is lower than that caused by gravity here on Earth.

As a result of the less gravity on the moon, the weight would decrease.

Thus, the correct answer is option C.

To learn more about gravity from here, refer to the link;

brainly.com/question/4014727

#SPJ2

Review Conceptual Example 6 as background for this problem. A car is traveling to the left, which is the negative direction. The direction of travel remains the same throughout this problem. The car's initial speed is 17.8 m/s, and during a 4.68-second interval, it changes to a final speed of (a)23.5 m/s and (b)15.3 m/s. In each case, find the acceleration (magnitude and algebraic sign).

Answers

Answer:

(a) 1.21 m/s² (b) 1.75 m/s²

Explanation:

The initial speed of the car, u = 17.8 m/s

Case 1.

Final speed of the car, v = 23.5 m/s

Time, t = 4.68-s

Acceleration = rate of change of velocity

[tex]a=\dfrac{23.5 -17.8 }{4.68}\\\\a=1.21\ m/s^2[/tex]

Case 2.

Final speed of the car, v = 15.3 m/s

[tex]a=\dfrac{23.5 -15.3}{4.68}\\\\a=1.75\ m/s^2[/tex]

Hence, this is the required solution.

Acceleration is the change in the velocity of a body with time.

What is acceleration?

The term acceleration is the change in the velocity of a body with time. We have to find the acceleration in two separate cases;

Case 1;

a = -(23.5 m/s - 17.8 m/s)/4.68-s

a = -1.2 m/s^2

Case 2;

a = -(15.3 m/s - 17.8 m/s)/4.68-s

a = 0.53 ms-2

Learn more about acceleration: https://brainly.com/question/12134554

There is a very long straw of charge that is uniformly charged in electro static equilibrium. It has a charge per unit length of 4.0E-9 C/m (4.0 nC/m) and a radius of 0.5 m. What is the strength of the electric field a distance of 10.0 m from its center outside the straw

Answers

Answer:

2880 N/c

Explanation:

Given that:

Charge per unit length ; λ = 4 * 10^-9

radius, r = 10

Radius, R = 0.5m

Using the relation :

2λr / 4πE0R²

Columb's constant, k = 1/4πE0 =. 9* 10^9Nm²/C²

Hence, we have :

2λrk/ R²

(2 * 4 * 10^-9 * 10 * 9 * 10^9) / 0.5^2

(720 ÷ 0.25)

= 2880 N/c

T Or F- True or False There three types of cloud's are .

Answers

Answer:

There are three main cloud types.

The foundation consists of 10 major cloud types. In addition to cirrus, stratus, cumulus, and nimbus clouds, there are cirrostratus, cirrocumulus, altostratus, altocumulus, stratocumulus, nimbostratus, and cumulonimbus clouds. The following table places these cloud types into the four major cloud groups.

Explanation:

So false, depends what you have learned and your grade level ig

The plates of a parallel plate capacitor each have an area of 0.40 m2 and are separated by a distance of 0.02 m. They are charged until the potential difference between the plates is 3000 V. The charged capacitor is then isolated. Determine the magnitude of the electric field between the capacitor plates.

Answers

Answer:

 E = -1.5 10⁵ N / C

Explanation:

In a capacitor the electric field is uniform between the blades, therefore we use the expression

                   V = - E s

                   E = - V / s

let's calculate

                   E = - 3000 / 0.02

                   E = -1.5 10⁵ N / C

the sign indicates that the field and the potential are opposite, when one increases the gold decreases

A place kicker must kick the football from a point [06] m from the goal and clear a bar 3.00 m above the ground. The ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0 degrees above the horizontal. (a) By how much (m) does the ball clear (positive value) or fall short (negative value) of the cross bar? (This is vertical distance above or below the cross bar.) (b) When it gets to the cross bar, what is the vertical component of the ball’s velocity (m/s)? (Is it rising or falling-pay attention to the sign?)

Answers

Answer:

Explanation:

Horizontal component of initial velocity of throw = 20 cos 53 = 12 m /s

Vertical component = 20 sin 53 = 15.97 m /s

Distance to be travelled horizontally = 6 m .

time taken by ball to travel this distance = 6 / 12 = 0.5 s

vertical displacement during this period can be calculated as follows .

Initial vertical velocity = 15.97 m /s

time of travel = .5 s

acceleration = - 9.8 m /s²

s = ut - 1/2 g t²

= 15.97 x .5 - .5 x 9.8 x 0.5²

= 7.985 - 1.225

= 6.76 m

Goal post is 6 m high , so ball will cross the goal post .76 m or 76 cm above cross bar  .

b ) vertical component of ball when it crosses the goal post . Let it be v .

v = u - gt

Applying this formula for vertical movement ,

v = 15.97 - 9.8 x .5

= 15.97 - 4.9

= 11.07 m /s .

Imagine visitors moving into and out of an art gallery as a model of a
chemical reaction at equilibrium. Which situation represents a system in
dynamic equilibrium?
O A. Some visitors stay for a long time, while others go back outside
quickly
B. Visitors enter the art gallery at the same rate as other visitors
leave.
C. Some visitors stand looking at one painting for a long time, while
others move quickly past the paintings and go outside again.
D. No visitors enter or leave the art gallery.

Answers

Option B. Visitors enter the art gallery at the same rate as other visitors leave.

Answer:

B) Visitors enter the art gallery at the same rate as other visitors

leave.

Explanation:

A.P.E.X

Please help me I’ll mark brainless

Answers

I haven’t learned this in quite a while, but from what I remember it should be A! I could be wrong but hopefully this helps

Answer:

ITS B NOT A

Explanation:

You are walking on a moving walkway in the airport. The length of the walkway is 59.1 m. If your velocity relative to the walkway is 2.35 m/s, and the walkway moves with a velocity of 1.85 m/s, how long will it take you to reach the other end of the walkway

Answers

Answer:

14.1seconds approx

Explanation:

Given data

Distance= 59.1m

Your velocity= 2.35m/s

Walkway velocity= 1.85m/s

Total velocity= 2.35+1.85= 4.2m/s

We know that

Velocity= distance/time

time= distance/velocity

substitute

time= 59.1/4.2

time= 14.07

time=14.1seconds approx

Hence the time is 14.1seconds approx

A transformer has 1500 turns on the primary coil and 30 000 turns on the secondary coil. What is the potential difference across the secondary coil, if the primary coil has a potential difference of 20 000V?
please help :/

Answers

Answer:

turle

Explanation:

What is the period, in seconds, that corresponds to each of
the following frequencies: (a) 10 Hz, (b) 0.2 Hz, (c) 60 Hz?

Answers

Answer:

0.1s,5s,0.017s

Explanation:

T=1÷frequency

Answer:

a =

✔ 6

The period is

✔ 2 seconds.

b =

✔ pi

Explanation:

Graph the function using the graphing calculator. Find the least positive value of t at which the pendulum is in the center.

t =

✔0.5 sec

To the nearest thousandth, find the position of the pendulum when t = 4.25 sec.

d =

✔ 4.243 in.

Can Magnetic poles effects each other​

Answers

Answer:

Explanation:

But the reality is that: Multiple magnetic fields would fight each other. This could weaken Earth's protective magnetic field by up to 90% during a polar flip. Earth's magnetic field is what shields us from harmful space radiation which can damage cells, cause cancer, and fry electronic circuits and electrical grids.

How do magnetic poles interact? Magnetic poles that are alike repel each other, and magnetic poles that are unlike attract each other. The area of magnetic force around a magnet. The magnetic field lines spread out from the north pole, curve around, and return to the south pole.

When two magnets are brought together, the opposite poles will attract one another, but the like poles will repel one another. This is similar to electric charges. The earth is like a giant magnet, but unlike two free hanging magnets, the north pole of a magnet is attracted to the north pole of the earth.

Magnetic forces are non contact forces; they pull or push on objects without touching them. Magnets are only attracted to a few 'magnetic' metals and not all matter. Magnets are attracted to and repel other magnets.

(hope this helps can i plz have brainlist :D hehe)

A trough is 7 meters long, 2 meters wide, and 1 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 1 meters, and base, on top, of length 2 meters). The trough is full of water (density 1000 kg m 3 ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use g

Answers

Answer:

68600Nm

Explanation:

Given that:

Lenght, L = 7

Width, W = 2

Depth, d = 1

Triangle = with height 1 meters, and base, on top, of length 2 meters

Area of triangle = 0.5 * base * height

Area of triangle = 0.5 * 2 * 1 = 1m²

Volume = area * length

Volume = 1m² * 7m

Volume = 7m³

Weight of water = Volume * density * g

g = acceleration due to gravity

Density of water , d = 1000kg/m³

Weight = 7m³ * 1000kg/m³ * 9.8m/s²

Weight = 68,600 Kgm/s² = 68600 N

Workdone = Force * distance = weight * depth

Workdone = 68600N * 1m

Workdone = 68600Nm

A football of mass 2.5kg is lifted up to the top of a cliff that is 180m high. How much
potential energy does the football gain?

Answers

The potential energy of the football with mass 2.5 kg which is lifted up to the top of a cliff is 4410 Joules.

What is Potential energy?

Potential energy is the stored energy which depends upon the relative position of the various parts of a system of objects. Potential energy is the product of mass of the object, acceleration due to gravity, and the height. The SI unit of potential energy is Joule (J).

PE = m × g × h

PE = Potential energy,

m = mass of the object,

g = acceleration due to gravity,

h = height

PE = 2.5 × 9.8 × 180

PE = 4410 Joules

Therefore, the potential energy of the football is 4410 Joules.

Learn more about Potential energy here:

https://brainly.com/question/24284560

#SPJ1

Which of the following sentences is an example concerns smerne might have at lunchtime?
I would be to have brocoll stead of fres,
I wonder if my chicken is ooked all the way
I have never ordered smething I did not ke,
of ordered a salad with the dressing on the site

Answers

Answer:

yes

Explanation:

becausw yesnssjsdkwww

Which of the following is a physical quantity that has a magnitude but not
direction?
- vector
- frame of reference
- scalar
- resultant

Answers

The answer is (Scalar) hope this helped!!

Answer:

Scalar

Explanation:

A scalar quantity is a physical quantity that has magnitude but no directional attribute.

An example of a scalar is speed and distance.

A vector is a physical quantity that has both magnitude and direction.

An example is displacement and velocity.

Scalar has only the magnitude value specified and nothing else.

What simple machine can best be described as "a simple machine that uses an inclined plane wrapped around a rod"?

a wedge
a screw
a wheel and axle
a lever

Answers

A screw I think I’m sorry if you get it wrong

Answer:

It is a screw.

Explanation:

If a solid metal sphere and a hollow metal sphere of equal diameters are each given the same charge, the electric field (E) midway between the center and the surface is...A. greater for the solid sphere than for the hollow sphere.B. greater for the hollow sphere than for the solid sphere.C. zero for bothD. equal in magnitude for both, but one is opposite in direction from the other.

Answers

Answer:

C. zero for both

Explanation:

In case of solid metal sphere , when it is given any charge , all the charges are transferred on the surface and within surface no charge exists . In case of hollow metal sphere , all charges reside on surface . In this way , in both solid and hollow sphere , all charge reside on the surface and no charge resides inside it . Hence due to absence of any charge inside  , there is no electric field inside the sphere in both the cases .  

Hence in both the case electric field is zero .

option C is correct .

Other Questions
Is this organelle more likely to be found in animal cells or plant cells PLEASE HELP ME :( !!! explain how the creation of a National Bank was a result of both long-term and short-term causes? Who here is from PR ( Puerto Rico) WILL GIVE BRAINLIEST 12 (3 + 4) =36 + 480.84123 + 12415 + 16 Solve the inequality 1/3(x-6)>2 The function f is defined by the following rule.Find f(x) for each x-value in the table. 3x-4/5=-1/2 what is the value of x ? help me out14 < n - 22 Due today- helpCastro promised to end American control over Cuban businesses. He forced Americans to leave the island. Many Americans lost their land and businesses in Cuba. He also promised to increase healthcare and education for all Cubans.Based on his actions, how do you think Americans felt about Fidel Castro?Why do you think Castro was popular with the Cuban people? 14. Which is the equation of the line that passes through the points (4, 3) and (6, 2)? A. y = x 1 B. y = 0.5x 1 C. y = -0.5x + 5 D. y = -0.5x + 1 What tool does Twain use inthis excerpt from hisautobiographical narrative tomake it interesting?18- I lit in the middle of thefloor, shot there by theelectric suddenness of thesurprise.A. Character DescriptionB. ImageryC. Dialogue I NEED HELP PLEASE ENGLISH PEOPLEIDENTIFYING SENTENCES AND SENTENCE FRAGMENTS Identify each of the following groups of words as a sentence or a sentence fragment. On the line provided, write S for sentence or F for fragment. Example 1. F After attending the film festival. 2. S The film festival begins Monday. From as far as India and China, for example, and from as close as our neighbors, Canada and Mexico. Which line from the prologue of Romeo and Juliet reveals the ending of the play?From ancient grudge break to new mutiny,Where civil blood makes civil hands unclean.From forth the fatal loins of these two foesA pair of star-crossd lovers take their life Which describes the correct pairing of DNA bases?A. C with C, and G with GO B. C with T, and G with AO c. C with A, and G with TO D. C with G, and A with T Subtract 01101011-00101010 Which version of the verb partager" correctly completes the sentence? "Aprs le film, nousune pizza au caf."O A. partagonsO B. partagezO C. partageonsO D. partagent The Soviet Union blockaded Berlin to: A: establish Communist control over the entire city.B: force the U.S. to accept a policy of disarmament.C: prevent Great Britain from forming a trade agreement with Germany.D: None of these choices are correct. when you and your friend are doing something, would it be hablo or hablamos? Mis amigo y yo ____ Evidence that is in view of the police does not require a search warrant, but can be legally seized is called _______ ________ ________(The lines have 3 words)