According to Newton's Law of Cooling, the temperature T(t) of a hot object, at time t after being placed in an environment with a constant temperature C, is given by T(t)=C+(To-C)e^-kt, where To is the temperature of the object at time t = 0 and k is a constant that depends on the object. If a hot cup of coffee, initially at 190°F, cools to 125°F in 5 minutes when placed in a room with a constant temperature 75°F, how long will it take for the coffee to reach 100°F?​

Answers

Answer 1

Answer:

Given the temperature of an object at time t as

-kt f(t) = T. + Ce +

where TO is the environment temperature, C is the difference in temperature of environment and object.

Given a boliling water at 100 degree celsius is placed in a freezer at 0 degree celsius, so we have

To = 0

C = 100 – 0= 100

After 26 minutes the temperature of water is 50 degree celsius.

f(26) = 0 + 100e -26k = 50

100e 26K = 50

-26 e = 0.5

-26%: In e = ln 0.5

-26% = ln 0.5

In 0.5 k= 26

So the temperature of water after 78 minutes will be,

f(78) = 100e -78 In 0.5 26 = = 12.5 =

The temperature of water after 78 minutes will be approximately 12.5 0 C

Step-by-step explanation:


Related Questions

Which expression is equivalent to 45 divided by (2 - x)

Answers

Answer:

 45

---------

(2 - x)

Step-by-step explanation:

That would be:

 45

---------

(2 - x)

Also valid:  45/(2 - x)

what number multiplied by 5 9 has a product of 1

Answers

I think the answer is five

9
10
11
12
13
An international company has 21.100 employees in one country. If this represents 23.9% of the company's employees, how many employees does it have in
total?

Answers

ok then I don't understand well but I think its 45.10.00

7-2×8+1 evaluate each of the following​

Answers

Answer:

-8

Step-by-step explanation:

u just do the 2x8 first

Hi! So in equations similar to this, you will need to use PEMDAS.

P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Now that you know this, reevaluate your equation.

7-2x8+1

Firstly, you must multiply -2 and 8. Leaving you with -16.

7-16+1

Next, subtract 16 from 7.

-9 + 1

Finally, add -9 and 1.

-8

Your final answer is -8.

A random number generator generates numbers from 1 to 10. What is the probability that the number generator generates a 3 ?

Answers

Answer:

1/10

Step-by-step explanation:

the probability is that it will be 1/10

Can someone help me with this problem?

Answers

Answer:

  16.6 ft^2

Step-by-step explanation:

1 foot = 0.3048 meter

  1.54 m^2 = (1.54 m^2)·(1 ft/(0.3048 m))^2 = 1.54/0.3048^2 ft^2

  ≈ 16.6 ft^2

_____

Additional comment

The idea in units conversion is to multiply by a fraction whose value is 1 (because the numerator and denominator are the same amount), but whose units cancel the ones you don't want and give you the ones you do want.

Here, our conversion factor has m^2 in the denominator and ft^2 in the numerator, so it cancels m^2 in the given number and gives a result in ft^2.

On a map, the scale is 1 inch = 40 miles. What is the actual distance for 3.25 inches shown on the map?

Answers

Answer:

130 Miles

Step-by-step explanation:

A stream drops 30 feet in elevation over a horizontal distance of 2640 feet. What is the stream gradient

Answers

The stream gradient of a stream that drops 30 feet in elevation over a horizontal distance of 2640 feet is 0.01136363636.  

Stream gradient is the ratio of drop in elevation of a stream per units horizontal distance. Therefore,

stream gradient = vertical change in elevation / horizontal distance

where

vertical change in elevation = 30 feet

horizontal distance = 2640 feet

stream gradient = 30 / 2640

stream gradient  = 0.01136363636

read more: https://brainly.com/question/13750927?referrer=searchResults

find the area of the triangle. 20ft, by 21ft. by 29ft.

Answers

Answer:

a=210ft²

The area of the triangle is 210 square feet.

Step-by-step explanation:

This is a right triangle, as shown by the Pythagorean theorem:

[tex]20^{2} +21^{2} =29^{2} \\400+441=841\\841=841[/tex]

The 2 perpendicular legs of a right triangle are also the base and height of a rectangle of the same size. A right triangle is exactly half of that rectangle, and therefore the area of a right triangle is exactly half of the area of that rectangle.

The area of that rectangle is:

[tex]a=b*h\\a=20*21\\a=420[/tex]

And then the area of the triangle is:

[tex]a=\frac{420}{2}\\a=210[/tex]

An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
13,200
26,400
39,600
79,200
158,400

Answers

Answer:

B) 26,400

An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?

13,200

26,400

39,600

79,200

158,400

26400 yards of cable is used.

the answer is B) 26,400

What is unit conversion?

Unit conversion is the process of changing a physical quantity from one unit of measurement to another. For example, converting kilometers to miles, Celsius to Fahrenheit, or liters to gallons. The process involves multiplying or dividing the original measurement by a conversion factor, which is a ratio of equivalent units

To convert miles to yards, we need to multiply by the conversion factor of 1 mile = 1760 yards.

15 miles * 1760 yards/mile = 26,400 yards

So, the electrician will use 26,400 yards of cable.

Hence, 26400 yards of cable is used.

the answer is B) 26,400

To learn more about the unit conversion, visit:

https://brainly.com/question/97386

#SPJ1

Plz help guys!!!!!!!!

Answers

Answer:

3

2

Step-by-step explanation:

at does the point (2, 1.5) represent in this context?

Answers

In what context? Do you mean calculus If you are talking about graphing on a graph plane it would be the two accelerates on the x axis so (left or right) and then the 1.5 accelerates on the y axis so 1.5 on the y axis would be one and halfway to the 2 mark on the y axis so in the middle of 1 to 2 on the y axis the y axis goes (up and down)

A kayak is originally priced at $130. The online retailer vives a Discount and the kayak is now priced at $65. Enter the porcentaje Discount for the cost of the kayak

Answers

Answer:

50% decrease

Step-by-step explanation:

130-65 = 65

65/130 = 0.5

0.5 x 100 = 50

The discount was 50% off


16 +1 -1 = 17-2
True
False

Answers

Answer:

false i think

Step-by-step explanation:

16+1=17-1=16-2=14

2x+3-3 when x=-6



solve

Answers

Answer:

x=9

Step-by-step explanation:

what is the completely factored form of x^4 - 4x^2 + 8x^3 - 32x + 12x^2 - 48? be sure to show all work.

Answers

Answer:

x^4 + 8x^2 + 8x^3 - 32x - 48

Step-by-step explanation:

You have to group the terms so the only terms that are similar are -4x^2 and +12x^2. -4x^2+12x^2 =+8x^2

There aren't any other similar terms so you can leave it as x^4 + 8x^2 + 8x^3 - 32x - 48

Answer:

x^4 + 8 x^3 + 8 x^2 - 32 x - 48

Hope This Helps!!!

Write an equivalent expression by combining like terms. (4/5x+3)-(1/4x-1)

Answers

Answer:

11/20x + 4

Step-by-step explanation:

Well you can jsut solve it normally following the order of operations.

So first you can distribute -(1/4x-1) which turns into 1/4x+1

4/5x+3+1/4x+1 combine like terms and you’d hey 11/20x +4

4.
Identify the vertex of the parabola.



A. . (0, 1)

B. (1, 0)

C. (−1, 0)

D. (0, −1)

Answers

Answer:

B. (1, 0)

Step-by-step explanation:

1,0 should be the vertex for this parabola

...................................................................................................................................................

1,0 should be the correct answer

Answer:

B. (1, 0)

Step-by-step explanation:

The vertex is the point where the two lines meet. In this instance, that is at the point (1, 0).

The hypotenuse of an isosceles right triangle is 4cm longer than either of its legs note that an isosceles right triangle is a right triangle who’s legs are the same length find the exact length of its legs and it’s hypotenuse

Legs ? Cm
Hypotenuse? Cm

Answers

Answer:

Step-by-step explanation:

let the side of triangle=x

hypotenuse=x+4

(x+4)^2=x^2+x^2

x^2+8x+16=2x^2

x^2-8x-16=0

x²-8x=16

x²-8x+16=16+16=32

(x-4)²=16×2=(4√2)²

x-4=±4√2

x=4±4√2

either x=4+4√2=4(1+√2)

or x=4-4√2=-4(√2-1)<0 (rejected)

leg x=4(1+√2)≈4(1+1.414)≈4×2.414≈8.828≈8.83 cm

hypotenuse≈8.83+4=12.83 cm

Find the area of grass

Answers

Answer:

125m²

Step-by-step explanation:

find the area of ​​the green rectangle and remove the area of ​​the yellow rectangle

(12 - 2) * (16 - 2) - (6 * 2.5) =

10 * 14 - 15 =

140 - 15 = 125m²

3/8 is found between which pair of fractions on a number line

Answers

Answer:

2/8 and 4/8

Step-by-step explanation:

Answer:

2/8,4/8 or 1/4,1/2

Step-by-step explanation:

3+1=4 3-1=2

2/8=1/4

4/8=1/2

The radius of a circle is 5 ft. Find its circumference in terms of pi

Answers

Answer:

10 pi

Step-by-step explanation:

circumference of the circle equals = 2π R = 2*pi* radius

so circumference = 2*5*π = 10π = 10 pi (in terms of pi)

Answer:

The formula for the circumference of a circle is C = 2πr, where "C" is the circumference, "π" is pi (approximately equal to 3.14), and "r" is the radius.

Given that the radius of the circle is 5 inches, we can substitute this value into the formula to find the circumference:

C = 2πr

C = 2π(5)

C = 10π

Therefore, the circumference of the circle is 10π inches.

a
Use a trigonometric equation to
determine the leg of this triangle.
10 m
[?] m
30°

Answers

Answer:

use pythogoras therom to solve it and its say to find base its formula is h square - psquare

Please help me ASAP please olease

Answers

Answer:

x=100 degree's

Step-by-step explanation:

Its 100 degrees because you add 80 and 20 degrees and because I think they might be called congruent angles.

Answer:

pretty sure it's just 100, just add 80 and 20, angles are opposite of each other.

Help help help help help help help

Answers

Answer:

6

Step-by-step explanation:

x coordinate goes left and on 6 line

y coordinate goes up and on 1 line

(x, y)

(6, 1)

x coordinate is 6

Write a linear function f with the values f(−1)=8 and f(5)=6.

A function is f(x)=

Answers

9514 1404 393

Answer:

  f(x) = -1/3x +23/3

Step-by-step explanation:

You can use the linear regression function of a graphing calculator or spreadsheet to show you the equation of the line through these points:

  f(x) = -1/3x +23/3

__

Approaching this in the usual way, we recognize we have points ...

  (-1, 8) and (5, 6)

The slope of the line through those points is ...

  m = (y2 -y1)/(x2 -x1)

  m = (6 -8)/(5 -(-1)) = -2/6 = -1/3

Then the point-slope equation of the line is ...

  y - 8 = -1/3(x +1)

Adding 8 gives us a form we can use for a function definition:

  f(x) = -1/3(x +1) +8

  f(x) = -1/3x +7 2/3

HELP ME OUT PLEASE
PLS SEND PICTURE OF WHAT TO DO

Use the data to create a scatter plot. ​​

Answers

Answer:

(2,5)

(3,8)

(4,13)

(5,12)

(6,18)

(7,20)

Plug those into the scatter plot graph

Step-by-step explanation:

The left side is the x axis and the right side is the y axis

There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 212.5 grams of this cereal.

Answers

Answer: 131.76 calories

Step-by-step explanation:

110 calories          x

----------------- = ----------------

177.4 grams     212.5 grams

cross multiply and divide

(110x212.5)

23, 375 / 177.4 grams

x= 131.76

15 POINTS!!!! Can someone simplify this as much as possible? ty!

245 = 50 + 1s

Answers

Step-by-step explanation:

245=50+1s. /-50

195=1s

s=195

in a box of chocolate 1/5 are plain chocolate 1/3 are white chocolate the rest are white​

Answers

...ok and?

finish the question

Answer:

Step-by-step explanation:

[tex]\frac{1}{5}+\frac{1}{3}+x=1[/tex]

[tex]\frac{3}{15}+\frac{5}{15}+x=\frac{1.15}{15}[/tex]

[tex]\frac{8}{15} + x=\frac{15}{15}[/tex]

[tex]\frac{8}{15} - \frac{8}{15} + x=\frac{15}{15}-\frac{8}{15}[/tex]

[tex]x=\frac{7}{15}[/tex]

I think you are missing the question but I bet you are looking for the rest of chocolate in the box.

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