Group Work 2.6 Newton's Law of Cooling states that an object cools at a rate proportional to the difference between the temperature of the object and the room temperature. The temperature of the object at a time t is given by a function f(t)= alpha x^ prime prime +a where a = mc * pi temperature c = initial difference in temperature between the object and the room r = constant determined by data in the problem Suppose you make yourself a cup of tea. Initially the water has a temperature of 95 degrees * C ; 5 minutes later the tea has cooled to 65 degrees * C Problem: When will the tea reach a drinkable temperature of 40°C? Hint: Assume that the room temperature a = 22 degrees * C . First solve for r and then find tapplying the natural logarithm.
Answers
Answer:
ΔT = ΔT0 e^-K T
As I understand Newton's Law of Cooling
ΔT at any time is the difference between the temperature and the surroundings
Originally ΔT0 = 95 - 22 difference between 95 and room temperature
65 - 22 = 33 = 73 e^-KT where t is time to cool to 65 deg
ln (33/73) = -KT K = .794 / 5 = .159 where 5 is time to cool to 65 deg
40 - 22 = 73 e^-.159 T where t is time to cool to 40 deg
18 = 73 e^-.159 T
ln (18 / 73) = -.159 T
T = 8.8 min
It would take 8.8 min for the object to cool to 40 deg C
Suppose the object cooled from 95 to 90 deg, then
ln 68 / 73 = -.159 T and T = .45 min
Answer:
13.2 minutes
Step-by-step explanation:
We cannot tell what your equation is supposed to be. Usually, the equation will have the form ...
f(t) = c·e^(kt) +r
where c is the initial temperature difference (95 -22 = 73) and r is the room temperature (22). The value of k can be found from the given intermediate temperature and time.
f(5) = 65 = 73·e^(k·5) +22
43/73 = e^(5k)
Taking the natural log gives ...
5k = ln(43/73)
k = ln(43/73)/5 ≈ -0.105852
__
We want to find t for f(t) = 40. Then ...
f(t) = 40 = 73·e^(-0.105852t) +22
18/73 = e^(-0.105852t)
t = ln(18/73)/-0.105852 ≈ 13.227
The tea will be drinkable after 13.2 minutes.
__
In the attached, we have used exponential regression to find the equation of the temperature curve.
Related Questions
46 degrees and x
X =
Answers
Answer:
136° that's 90 plus 46.........
Answer:
x = 136°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle , then
x = 90° + 46° = 136°
please help!!!!!
Solve.
−4/9x+2.4=6
Enter your answer as a decimal or as a mixed number in simplest form in the box.
x =
Answers
-8.1
Step-by-step explanation:
[tex] \frac{ - 4}{9} x + 2.4 = 6[/tex]
Times all by 9 to get rid of fraction
[tex] - 4x + 21.6 = 54[/tex]
Take 21.6 away from both sides
[tex] - 4x = 32.4[/tex]
Divide by -4
[tex]x = - 8.1[/tex]
Answer: -8 1/10
Step-by-step explanation:
Can someone help me with these 2 problems I’ve been stuck on them for a very long time :’) tysm!!
Answers
Answer:
Christmas How many pouds this proportion to solve
Solve for m.
m+13<−214
m>−11112
m>−2712
m<−11112
m<−2712
Answers
Answer:
You cannot expect someone to type the "right" answer if you dont put the time to even spell it out correctly next time think abt it a bit more ^^
The correct answer is m<- 2 7/12
Step-by-step explanation:
This is for the k12 6.01 Quiz: One-Step Addition or Subtraction Inequalities
Good luck everyone of the rest !!!!
The solution for [m] belongs tot he set as : m ∈ (- ∞, -227).
What is inequality? What is a mathematical function, equation and expression? inequality : An inequality is used to compare two expressions or numbers.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the inequalities and it is asked to solve for [m].
The given inequalities are given as follows -
m + 13 < − 214
m > − 11112
m > − 2712
m < − 11112
m < − 2712
Now, we can write -
m + 13 < − 214
m < - 214 - 13
m < - 227
Remaining all inequalities are far far smaller than -227. So, we can say that the solution for m as : m ∈ (- ∞, -227)
Therefore, the solution for [m] belongs tot he set as : m ∈ (- ∞, -227).
To solve more questions on functions, expressions and polynomials, visit the link below -
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Ali is x years old Ali’s aunt is four times as old as Ali will be in 5 years Find the present age of Ali’s aunt
Answers
Answer:
Ali= x + 5
Aunt= 4x
Ralph has 9 cards, each with a number on it. What is the probability that the number chosen is a multiple of 4 ?
Answers
Answer:
2/9.
Step-by-step explanation:
There are 2 multiples of 4 in the 9 cards, 4 itself and 8.
So the required Probability is 2/9.
76 is 0.4% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 76. Slightly less than 76, slight greater than 76, or a lot greater than 76? Explain.
Answers
Answer:
Step-by-step explanation:
It's a lot greater. If you take 0.4% of some number and the answer is 76, you better be starting with something that is very large. The formula will make the solution automatic.
Formula
Let the number be x
0.4% x = 76
0.4% = 0.4/100
0.4 / 100 * x = 76 Multiply both sides of the equation by 100
0.4x = 76*100 Combine the right.
0.4x = 7600 Divide by 0.4
x = 7600/0.4
x = 19000 Which is quite a bit larger than 76
Answer:
greater than 76
Step-by-step explanation:
hope it will help goodbye
MARKING BRAINLIEST PLEASE HELP
Answers
So -15x = 90 - 210
-15x = -120
Divide both sides by -15 that equals 8 so the your answer is but if it’s the time before the draining began (I will assume at 0) then the answer would be 3 + 8, it will be 11 hours for it to reach 90
6x² = 7xy + 20y² where x ˃ 0 and y ˃ 0
Find the ratio x : y
Answers
More Icon
STEP
1
:
Equation at the end of step 1
((6 • (x2)) - 7xy) - (22•5y2)
STEP
2
:
Equation at the end of step
2
:
((2•3x2) - 7xy) - (22•5y2)
STEP
3
:
Trying to factor a multi variable polynomial
3.1 Factoring 6x2 - 7xy - 20y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (2x - 5y)•(3x + 4y)
Final result :
(2x - 5y) • (3x + 4y)
The winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles. He finished the race in 54 minutes. For the entire triathlon, what was his average speed in miles per hour?
Answers
Answer:
15 or 15.546
Step-by-step explanation:
you add all the numbers then divide by 54
Based on the information given, the speed is 20 miles per hour.
From the information given, the winner of the local triathlon swam 0.5 miles, biked 15 miles and ran 2.5 miles and he finished the race in 54 minutes.
Note that 54 minutes = 0.9 hour.
The speed will be:
= (0.5 + 15 + 2.5) / 0.9
= 18/0.9
= 20 miles per hour.
Learn more about speed on:
https://brainly.com/question/4931057
if the restaurant donated $690 to the soup kitchen what we’re the total sales for the day
Answers
Answer:
Total sales = x + $690
Step-by-step explanation:
x = amount of sales in a day
Donated amount = $690
Total sales = amount of sales in a day + Donated amount
Total sales = x + $690
What is the length of the mid segment AB??
Answers
Answer:
14.5
Step-by-step explanation:
AB is halfway between MN and PO. this means it would be the distance halfway between 9 units (length of MN) and 20 units (length of PO). to find this, find the average of 20 and 9. 20+9= 29. 29/2= 14.5
Amelie read 12 pages of her book each day for 4 days. Matthew read 12 pages of the same book each day for 8 days.
Answers
Answer:
if u are asking how many more pages Matthew read then it's 48 pages. If u are asking how many they read all together then it's 144 pages.
HELP PLEASE!!!A 2-column table with 5 rows. Column 1 has entries 25 percent, 25 percent, 25 percent, 25 percent, Total 100 percent. Column 2 has entries 12 dollars, 12 dollars, 12 dollars, 12 dollars, Total 48 dollars.
Which of the following scenarios could be accurately modeled using this diagram?
Juan Victor gave a gratuity of $25 on a bill that was $48.
Juan Victor gave a 25% gratuity of $12 on a bill that was $48.
Juan Victor gave a gratuity of $12 on a bill that was $100.
Juan Victor gave a 12% gratuity on a bill that was $25.
Answers
B) Juan Victor gave a 25% gratuity of $12 on a bill that was $48.
hope this is helpful!
ASAP HELP PLEASE SHOW ALL WORK
*Find the value of x. Show all the work
Answers
The line of length 48 is passing through the midpoint of traingle so it's half of base
[tex]\\ \sf\longmapsto \dfrac{3x}{2}=48[/tex]
[tex]\\ \sf\longmapsto 3x=96[/tex]
[tex]\\ \sf\longmapsto x=32[/tex]
Logan and his sister, Tessa, are baking oatmeal raisin cookies. Logan uses 1.25-ounce scoops
of dough to form his cookies, and Tessa uses 1 12 -ounce scoops for hers.
Who is making bigger cookies?
Answers
Answer:
Logan is making bigger cookies
Step-by-step explanation:
1.25 > 1.12
please help i need this rn!! ( please tell me how much boxes I color)
Answers
the output is two more than the input
Answers
help with this pleased
Answers
Answer:
Kite A ascends to a height of 36 feet
Step-by-step explanation:
21 + 15 = 36
Answer:
Kite A is now at 36 feet.
Step-by-step explanation:
Ascend means go up, so adding 15 to 21 gives you your answer.
Enter the value of :
Answers
Answer:49
Step-by-step explanation: The square root of a number is a number that, when multiplied by itself, equals the desired value. So, for example, the square root of 49 is 7 (7x7=49). The process of multiplying a number times itself is called squaring.
Which of the following represents the zeros of f(x) = 6x3 − 31x2 + 4x + 5? (1 point)
Answers
Did this question before and I have many study guide websites
Tell whether each graph is a function and justify your answer. Which graph is not a good representation of a real-world situation? Explain.
Answers
Using the function concept, it is found that:
Graph B is a function because each value of x corresponds to exactly one y-value.In a function, one value of the input can be related to only one value of the output.
In a graph, it means that for each value of x(horizontal axis), there can be only one respective value of y(vertical axis).In this problem, at Graph A, when x = 5, for example a vertical line crosses the function 3 times, hence there are 3 respective values of y for x = 5, and the same is valid for other values of x, hence it is not a function.
At Graph B, for each value of x, there is only one value of y, hence it is a function.
Hence:
Graph B is a function because each value of x corresponds to exactly one y-value.
To learn more about the function concept, you can take a look at https://brainly.com/question/12463448
9. Determine whether the parallelogram is a rectangle, square, or rhombus. G(-4,3), D(2,1) F(-5, 0) and E(1, -2)
Answers
Answer:
rectangle
Step-by-step explanation:
Answer:
Rectangle
Step-by-step explanation:
FG's slope is the opposite reciprocal of GD's, so they are perpendicular. The same with the other sides.
The opposite sides have the same length.
Select the correct answer.
Which equation represents the line that is perpendicular to y = 1/5 and passes through (-4,-3)?
A.X=-4
B.X=-3
C. y=-5
D. y=-3
Answers
Step-by-step explanation:
The answer is b for sure.
Find f(2) and f(3).
f(1) = 3
f(n) = 7f(n = 1)
Answers
Answer:
do it got a picture
on the edge2020
Step-by-step explanation:
Can anyone help me convert these??
What is 76ml of milk in cups, tablespoons, or teaspoons?
What is 38g of Egg yolk in cups, tablespoons, or teaspoons?
What is 78g of Egg white in cups, tablespoons, or teaspoons?
I'm trying to make something that is Japanese but they don't use cups, tablespoons, or teaspoons. My math keeps going wrong and my PC wont convert them for me
Answers
Answer:
0.321233-cups, 0.321233-tablespoon, 0.321233-teaspoon
Step-by-step explanation:
the next 2 questions I can't convert because I don't have grams
Answer:
76ml= 0.321233 cups
76ml = 5.13973 tablespoons
76ml = 15.4192 teaspoons
38g = 0.139 cups
38g = 2.224 tablespoons
38g = 6.672 teaspoons
78g = 0.349 cups
78g = 5.584 tablespoons
78g = 16.752 teaspoons
Step-by-step explanation:
I think thats right
Which is the graph of the ordered pairs from the table below?
X Y
3 5
5 7
7 9
9 11
Answers
Answer:
It is the second
Step-by-step explanation:
Answer: number 2 ᕙ(＠°▽°＠)ᕗ
Step-by-step explanation:
The diagonal of a square is 8 cm.
What is the length of the side of this square?
Give your answer as an exact surd in its simplest form
Answers
the length of the side of this square is [tex]4\sqrt{2} \:or \:5.65[/tex]cm
Answer:
Solutions Given:
let diagonal of square be AC: 8 cm
let each side be a.
As diagonal bisect square.
let it forms right angled triangle ABC .
Where diagonal AC is hypotenuse and a is their opposite side and base.
By using Pythagoras law
hypotenuse ²=opposite side²+base side²
8²=a²+a²
64=2a²
a²=[tex]\frac{64}{2}[/tex]
a²=32
doing square root on both side
[tex]\sqrt{a²}=\sqrt{32}[/tex]
a=±[tex]\sqrt{2*2*2*2*2}[/tex]
a=±2*2[tex]\sqrt{2}[/tex]
Since side of square is always positive so
a=4[tex]\sqrt{2}[/tex] or 5.65 cm
Answer:
Given :
↠ The diagonal of a square is 8 cm.
To Find :
↠ The length of the side of square.
Using Formula :
Here is the formula to find the side of square if diagonal is given :
[tex]\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}} [/tex]
Where :
➺ a = side of square ➺ d = diagonal of squareSolution :
Substituting the given value in the required formula :
[tex]{\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}[/tex]
Hence, the length of the side of square is 5.6 cm.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
there are nine children and Kenneth preschool class three of them chose to play at the sand table based on past data is 12 preschoolers are at school today how many should you expect to play at the sand table
Answers
Answer:
4 are playing at the sand table
Step-by-step explanation:
There were 9 kids at Kenneth's preschool and 3 were playing, thats one third of the kids(3x3=9). One third of 12 is 4(3x4=12) Basically since there were 9 total kids, and 3 at the sand table, they are divided equally in groups of three so you just divide 12 by 3 too and thats how you get 4
Select the statement that is true.
0.969 < 0.967
0.967 > 0.969
0.967 = 0.969
0.967 < 0.969
Answers
Answer:
d option
Step-by-step explanation:
(d) option is true, as 0.969 is greater than 0.967.
Rest all options are false.
Hope it helps :)