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 185 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 167 degrees in a room at 60 degrees, determine when the coffee reaches a temperature of 137 degrees.

Answers

Answer 1

Answer:

9.4 secs

Step-by-step explanation:

From Newton's law of cooling;

T(t) = Ts + Do e^-kt

Where;

D0= initial temperature difference

Ts= Temperature of the surroundings

t= time

K = positive constant

Do = 185 - 60 = 125 degrees

167 = 60 + 125 e^-3k

167 - 60 = 125 e^-3k

107/125 = e^-3k

ln(e^-3k) = ln(107/125)

-3k = -0.1555

k = 0.1555/3

k = 0.0518

Substituting the value of k to find the time taken to reach 137 degrees

T(t) = Ts + Do e^-kt

137 = 60 + 125 e^-(0.0518t)

137 - 60 = 125 e^-(0.0518t)

77 = 125 e^-(0.0518t)

e^-(0.0518t)= 77/125

ln [e^-(0.0518t)] = ln(77/125)

-0.0518t = -0.4845

t = 0.4845/0.0518

t = 9.4 secs


Related Questions

how many solutions does x² – 36 = 0 have?

Answers

Answer:

2 solutions

Step-by-step explanation:

x2=36

x= positive or negative 6 so 2

if my answer helps please mark as brainliest.

Answer:

2

Step-by-step explanation:

x

2

36

=

0

Use the quadratic formula to find the solutions.

b

±

b

2

4

(

a

c

)

2

a

Substitute the values

a

=

1

,

b

=

0

, and

c

=

36

into the quadratic formula and solve for

x

.

0

±

0

2

4

(

1

36

)

2

1

Simplify.

x

=

±

6

The final answer is the combination of both solutions.

x

=

6

,

6

PLEASE HELP ;-; Ill GIVE BRAINLY
What is the solution to the following system of equations? Explain how you know.

Answers

Answer:

-3,1

Step-by-step explanation:

When you are doing Systems Of Equations using a graph, the point where the lines intersect is your answer

PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.

Answers

Answer:

y=36+12x

Step-by-step explanation:

I should be y=36+12x

The scatter plot shows the test scores of a group of students who studied for different amounts of time in a week. A graph shows Hours Spent Studying on x axis and Test Score on y axis .The graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 100 at increments of 10. The ordered pairs 0, 21 and 0.8, 32 and 1.2,35 and 1.5,39 and 2.1, 42 and 2.3,45 and 2.5,49 and 2.7, 50 and 3, 67 and 4.6, 56 and 5, 69 and 5.3,70 and 5.7,74 and 6.4,78 and 7.2,80 and 7.5,84 and 8.5,88 and 8.7,92 and 9.5,96 are shown on the graph. What will most likely happen to the test scores of students if the number of hours they study increases? Test scores will increase because the graph shows a negative association. Test scores will increase because the graph shows a positive association. Test scores will decrease because the graph shows a positive association. Test scores will decrease because the graph shows a negative association.

Answers

Answer:

Test scores will increase because the graph shows a positive association.

Step-by-step explanation:

Since it is going upwards to the right instead of going downwards and for the people who steady more hours they get better scores on there test.

btw i just took it and got it right

From given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.

What is scatter plot?

"A type of data representation that shows the relationship between two numerical variables. "

What is positive association?

"When the values of one variable tend to increase as the values of the other variable increase, then two variable have positive association."

What is negative association?

"When the values of one variable tend to decrease as the values of the other variable increase, then two variable have negative association."

For given question,

The scatter plot shows the test scores of a group of students who studied for different amounts of time in a week.

A scatter plot shows Hours Spent Studying on x axis and Test Score on y axis .

Also we have been given the ordered pairs

(0, 21), (0.8, 32), (1.2, 35),  (1.5, 39), (2.1, 42), (2.3, 45) and (2.5, 49) and   (2.7, 50) and (3, 67) and (4.6, 56) and (5, 69) and (5.3, 70) and (5.7, 74) and (6.4, 78) and (7.2, 80) and (7.5, 84) and (8.5, 88) and (8.7, 92) and (9.5, 96)

From the given data points of scatter plot,

as x - value increases, y - value also increases.

This means,  if the number of hours they study increases, the test scores will increase.

Here, the values of one variable tend to increase as the values of the other variable increase.

This means, there is positive association in variables Hours Spent Studying and Test Scores.

Therefore, from given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.

Learn more about the positive association here:

https://brainly.com/question/858660

#SPJ2

Casper write the algebraic expression 5b + 3.79. I represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese. Identify any variables, coefficients, and termsin the expression. Tell me what each represents

Answers

Answer:

5 is a co efficient and b is a variable together is a term, 3.79 is a constant/term the whole equation is an expression.

The total cost of buying 5 bagels and a container of cream cheese is $28.79 and in the expression 5 is constant, b is variable, and 3.79 is constant representing the cost of the container.

What is an expression?

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.

For example 3x +5y

Given the expression for the total cost,

C = 5b + 3.79 where b is the number of bagels.

Cost of 5 bangles

C = 5(5) + 3.79 =$ 28.79

Cost of container = $3.79

Thus b is the only variable and 5b represents the cost of bagels while by the sum of container cost 3.79 total costs are created.

Hence "The total cost is $28.39 and container cost is $3.79 while b is variable".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ2

Solve.
The number line shows xx
3
ODIO
AN
1
a.
Each fourth on the number line is divided into
how many equal parts?
b. Each of these parts is what fraction of the whole?
C.
How many eighths of the whole are shaded?
d. -
X

Answers

Step-by-step explanation:

answer for d is 3 over 8....

that's all I know from the qn and can help u... sorry

Suppose you have a student loan of ​$45,000 with an APR of 9​% for 30 years. Complete parts​ (a) through​ (c) below.

Answers

A.through
Sana makatulong

Find the value of x.
x = [?]

Answers

Answer:

14

Step-by-step explanation:

Since both the chords are equidistant from the center of the circle, so their lengths would be same.

x = 2*7 = 14

Pier 1 Imports is running a 10% sale on furniture. If Amanda spent $378.99 on furniture before tax, what was the price of the furniture before the discount and tax?

Answers

Answer:

$421.10

Step-by-step explanation:

If the discount is 10%, that means the sale price is 90% of the original price.

Write the equation that represents that:

378.99 = 0.9x. Solve for x. Divide both sides by 0.9

378.99/0.9 = 421.10

That is the price before the discount and tax.

Help plz:)))I’ll mark u Brainliest

Answers

Answer:

18 foot ladder will reach at 14.4 feet up the wall.

Step-by-step explanation:

Triangles formed by the ladder against wall and the ground are similar,

ΔABC ~ ΔDEC

Therefore, their corresponding sides will be proportional.

[tex]\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}[/tex]

[tex]\frac{AB}{DE}= \frac{BC}{EC}[/tex]

[tex]\frac{18}{10}=\frac{BC}{8}[/tex]

BC = [tex]\frac{18\times 8}{10}[/tex]

     = 14.4

Therefore, 18 foot ladder will reach at 14.4 feet up the wall.

solve if x=11. x+44/2x​

Answers

Answer:

substitute 11 into the equation:

[tex]\frac{11+44}{2(11)}[/tex] = [tex]\frac{55}{22}[/tex] or 2.5

Answer:

253

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Step-by-step explanation:

Step 1: Define

x + 44/2x

x = 11

Step 2: Evaluate

Substitute in x:                                                                                                  11 + 44/2(11)[BPEMDAS] Divide:                                                                                         11 + 22(11)[BPEMDAS] Multiply:                                                                                      11 + 242[BPEMDAS] Add:                                                                                               253

Find the equation of the exponential function represented by the table below:

Answers

Answer:

[tex]y =5(3)^x[/tex]

Step-by-step explanation:

Given

The attached table

Required

Determine the equation of the table

The table represents an exponential function. So, we make use of

[tex]y = ab^x[/tex]

When x = 0, y= 5.

So:

[tex]y = ab^x[/tex] becomes

[tex]5 = ab^0[/tex]

[tex]5 = a*1[/tex]

[tex]5 = a[/tex]

[tex]a = 5[/tex]

When x = 1; y = 15

So;

[tex]y = ab^x[/tex] becomes

[tex]15 = a * b^1[/tex]

[tex]15 = a * b[/tex]

Substitute 5 for a

[tex]15 = 5 * b[/tex]

Divide both sides by 5

[tex]\frac{15}{5} = \frac{5 * b}{5}[/tex]

[tex]3 = b[/tex]

[tex]b = 3[/tex]

Substitute values for a and b in: [tex]y = ab^x[/tex]

[tex]y =5(3)^x[/tex]

Jennifer is saving money to buy a bike. The bike costs $258. She has $125 saved, and each week she adds $19 to her savings.

How long will it take her to save enough money to buy the bike?

It will take her___
weeks to save for the bike.

Answers

Answer:

7 weeks

Step-by-step explanation:

Answer:

7 weeks

Step-by-step explanation:

Best Buy bought a television for $175. Then,
Best Buy sold it for $360. What percentage
was the markup?

Answers

Answer:

105.7143%

Step-by-step explanation:

pls make me brainliest

PLEASE HELP !!! ILL GIVE BRAINLIEST!! *DONT SKIP* ILL GIVE 40 POINTS.

Answers

Answer:

5.5

Step-by-step explanation:

The answer is 5.5 to you answer.hope it helps

A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6 days. Its average brightness is 3.5 and the brightness changes by /-0.25. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days: B(t)=4.2 +0.45sin(2pit/4.4)
A) Find the rate of change of the brightness after t days.
B) Find the rate of increase after one day.

Answers

Answer:

a) The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

b) The rate of increase after one day is of 0.0915.

Step-by-step explanation:

The brightness after t days is given by:

[tex]B(t) = 4.2 + 0.45\sin{(\frac{2\pi t}{4.4})} = 4.2 + 0.45\sin{(0.4545\pi t)}[/tex]

A) Find the rate of change of the brightness after t days.

This is [tex]B^{\prime}(t)[/tex]

The derivative of a constant is 0, the derivative of [tex]\sin{at}[/tex] is [tex]a\cos{at}[/tex]

So, in this case, we have that:

[tex]B^{\prime}(t) = 0.45*0.4545\pi\cos{(0.4545\pi t)} = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

B) Find the rate of increase after one day.

This is [tex]B^{\prime}(1)[/tex]. So

[tex]B^{\prime}(1) = 0.204525\pi\cos{(0.4545\pi)} = 0.0915[/tex]

The rate of increase after one day is of 0.0915.


Would the hypotenuse of a right triangle with a vertical length of 6 and a horizontal length of 10 have the same slope as the hypotenuse of the blue and red
triangles shown in the graph?

Answers

No

1. Vertical 6, horizontal 10
6/10 = 3/5 slope

2. (Red) vertical -2, horizontal 3
-2/3 does not equal 3/5

3. (Blue) vertical 4, horizontal 6
4/6 = 2/3 but does not equal 3/5

Write formulas for the following mathematical statement.
The difference between the selling price and cost price is profit.
(1 Point)
profit=S.P-C.P
profit=S.P+C.P
profit=C.P-S.P
profit=C.P+S.P

Answers

Answer:

[tex]Profit = SP - CP[/tex]

Step-by-step explanation:

Given

[tex]S.P = Selling\ Price[/tex]

[tex]C.P = Cost\ Price[/tex]

Required

Represent the profit, mathematically

The profit is the difference between SP and CP.

This is represented as:

[tex]Profit = SP - CP[/tex]

Due to expected droughts, the farmer will only be planting crops on 3/ 4 of this area. How would you correctly calculate the size of this new area? A. the total area multiplied by 4 divided by 3 B. the total area divided by 3 C. the total area divided by 4 D. the total area multiplied by 3 divided by 4 math

Answers

Answer:your answer is D.

Step-by-step explanation:

When dividing fractions you must flip the numerator and denominator so that would leave you with 6/1 divided by 3/4, solve this and then you have an improper fraction so after you multiply by 3 you must divide because of the improper fraction and you will divide by 4.

Answer:

d .the total area multiplied by 3 divided by 4

Step-by-step explanation:

.

the total area multiplied by 3 divided by 4

3.
a) Find the HCF of 45 and 60
b) Find the LCM of 45 and 60
c) Multiply your answers to parts a and b together.
d) Multiply 45 and 60.

Answers

Answer:

a- 15

Step-by-step explanation:

Answer:

a.) 15

b.) 180

c.) 2700

d.) 2700

The width of a rectangle is (5x + 2) inches and the length is (6x − 7) inches. Find the area of the rectangle.

Answers

Answer:

30x² − 23x − 14

Explanation:

Area = Length · Width

Length: (6x - 7)

Width: (5x + 2)

Create An Equation

(6x - 7) (5x + 2)

= (6x + −7)(5x + 2)

(6x)(5x) + (6x)(2) + (−7)(5x) + (−7)(2)

= 30x² + 12x − 35x − 14

30x² − 23x − 14

- PNW

Please help with my question

Answers

Answer:

Your answer is "C"

Step-by-step explanation:

Dont ask me how I know, I just know

No clue why but brainly said I had inappropriate words in my answer so here's a picture

The elevation of a bird was 23 m. The bird flew over to a branch to rest. It's elevation changed by -14.5 m. What is it's new elevation? Label​

Answers

Answer:

8.5m

Step-by-step explanation:

PUT THE NUMBERS IN ORDER FROM LEAST TO GREATEST.

-29/5^2
(1, 2.5)
4,21
5.5
6
9

DONT SKIP ILL GIVE 40 POINTS.!!!

Answers

Answer:

boop

Step-by-step explanation:

-29/5^2,1,2.5,4,5.5,6,9,21

homework 1 relations domain range and functions 3-8

Answers

Answer:

Step-by-step explanation:

Domain - Set of x-values

Range - Set of y-values

3). Since, x values vary from x = -6 to x = 5,

    Domain of the graph = [-6, 5]

    Since, y-values vary from y = -2 to y = 3

    Range of the graph = [-2, 3]

4). Domain of the graph = [-3, 3]

    Range of the graph = [-6, 5]

5). Domain of the graph = (-∞, ∞)

    Range of the graph = (-∞, ∞)

6). Domain of the graph = (-∞, 4]

    Range of the graph = (-∞, ∞)

7). Domain of the graph = (-∞, ∞)

    Range of the graph = [-1, 5]

8) Domain of the graph = [-1, 5)

    Range of the graph = [-3, 3)

Answer:

Step-by-step explanation:

Is 15/16 bigger than less than or equal to 1/2

Answers

Answer:15/16 > 1/2

Step-by-step explanation:

Answer:

15/16 is greater

Step-by-step explanation:

The square pyramid shown below has a base with sides of 101010 units. The slant height of the pyramid is 888 units.

Answers

Answer:6.12

Step-by-step explanation:

got the answer right

Answer:

on khan the answer is 6.12

(a) Write the ratio 32 : 80 in its simplest form​

Answers

Answer:

Therefore, 32/80 simplified to lowest terms is 2/5.

Solve the following equation.
4x - 2 = 22-8x

Answers

Answer:

x = 2

Step-by-step explanation:

4x - 2 = 22 - 8x

Move all variables to a single side by adding 8x to both sides of the equation.

4x + 8x - 2 = 22 - 8x + 8x

12x - 2 = 22

Add 2 to both sides to move the constants to one side.

12x - 2 + 2 = 22 + 2

12x = 24

Divide both sides by 12 to isolate the x.

12x / 12 = 24 / 12

x = 2

Answer:

x = 2

Step-by-step explanation:

Add 2 to both sides.

4x - 2 +2 = 22 - 8x + 2

Simplify.

4x=-8+24

Add 8x to both sides.

4x+8x= -8x + 24 + 8x

Simplify.

12x = 24

Divide both sides by 12.

12x/12 = 24/12

Simplfy.

x = 2

hope this helps! :)

Two rectangles are similar the sides of the larger rectangle have lengths of 24 and 30 inches the perimeter of the smaller rectangle is 27 inches find the length of the shorter side of the smaller rectangle

Answers

Answer:

small rectangle sides are 7.5 and 6

Step-by-step explanation:

Large rectangle perimeter=30+30+24+24=108

Small rectangle perimeter=27

27 is one fourth of 108 so:

small rectangle sides are 30/4 and 24/4

small rectangle sides are 7.5 and 6

Answer:

i have no clue

Step-by-step explanation:

it is really hard and i need help with it myself

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