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.
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In the attached, we have used exponential regression to find the equation of the temperature curve.
Related Questions
Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a light
source. The relationship in intensities for subjects at different distances from the same source can
be likewise seen as a ratio or proportional relationship.
I x
A proportional relationship can be mathematically expressed as follows for light intensity (I) in
lumens when a subject is at the light source.
Lumens at current distance
Lumens at origin or source
So, if a light intensity (I) is 516 lumens at the source and 4 lumens at a specific distance from the
source, what is that distance?
Round the value to the nearest tenth if necessary. You do not need to include a label for distance.
Only the number, rounded to the tenth, will be necessary.
Answers
The required distance is 11.4 rounded to the tenth
If light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a light source, this is expressed as:
l = ka/dk is the variation constant
If a light intensity (I) is 516 lumens at the source and 4 lumens at a specific distance from the source, the distance is calculated as:
l = a/d²
d² = a/l
d² = 516/4
d = √129
d = 11.4
Hence the required distance is 11.4 rounded to the tenth
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FIND THE PROBABILITY OF EACH EVENT. MAKE SURE YOUR PROBABILITY IS IN SIMPLEST FORM (NOT KEYWORDS)
M&M BAG HAS 5 BLUE, 6 GREEN, 10 YELLOW, 2 RED, AND 3 BROWN.
blue________
yellow_________
brown and red_________
not blue or brown________
purple____________
not red____________
skittles_____________
M&M__________
FIRST TWO ANSWERS HAVE A CHANCE OF GETTING BRAINLIEAST
Answers
Answer:
(a) The probability that at least 5 of the first 10 sites contain the given keyword is 0.0328.
(b) The probability that the search engine had to visit at least 5 sites in order to find the first occurrence of a keyword is 0.4096.
Step-by-step explanation:
Mark as brainliest if correct
Can someone plz help Me?
Answers
Answer:
A and C
Step-by-step explanation:
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
<
Step-by-step explanation:
4.
ind
home
Julio won a contest. His cash prize is given to him in the following way:
On the first day, Julio will receive $0.25.
For each successive day, the amount of money Julio receives doubles.
a. Write an explicit formula to represent the amount of money, f (d), in dollars, Julio receives d days after the first day.
b. How much money will Julio receive on the tenth day?
Answers
Julio will receive $ 128 on the tenth day.
Given that Julio won a contest, and his cash prize is given to him in the following way: On the first day, Julio will receive $ 0.25, and for each successive day, the amount of money Julio receives doubles, to determine an explicit formula to represent the amount of money, f (d), in dollars, Julio receives d days after the first day, and determine how much money will Julio receive on the tenth day, the following calculations must be performed:
0.25 x 2 ^ D = F 0.25 x 2 ^ 9 = F 0.25 x 512 = F 128 = F
Therefore, Julio will receive $ 128 on the tenth day.
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please help!! i don’t know how to do this please help asap.
Answers
Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time
Answers
Answer:
We consider:
T1 = 2s
T2 = 3s
T3 = 5s
We calculate the least common multiple of the Ts:
Ttot = 30 s.
During a seven minute dance the lights will come on at the same time:
7*60 s / 30 = 14 times.
In a span of 7 minutes, the lights will blink together 14 times.
What is LCM?LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.
Given, Joe was in charge of lights for a dance.
The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds.
∴ LCM of 2, 3, and 5 is 30 so the lights blink together after every 30 seconds.
So, in 7 minutes or (7×60) = 420 seconds the lights will blink together
(420/30) = (42/3) = 14 times.
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in the figure given alongside if X=3y find the sizes of angles represented by a and b
Answers
Answer:
Step-by-step explanation:
x = 3y
x + y = 180°
3y + y = 180° ⇒ y = 45° = a
x = 3( 45° ) ⇒ x = 135° = b
The sizes of angles represented by a and b are 45 and 135 degrees.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on.
We are given that
x = 3y
Since we know that the linear pair is
x + y = 180°
Therefore, 3y + y = 180°
y = 45° = a
x = 3( 45° )
x = 135° = b
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If x=9 and y=- -2 evaluate the following expression:
x+y
Answers
Answer:
x + y = 11
Step-by-step explanation:
You would need to substitute the numbers into the expression.
Evaluate means that we need to work out what the answer would be.
x + y is equivalent to 9 - - 2.
- - is equivalent to +.
Therefore you would do 9 + 2, which equals 11.
Hope this helps :)
5. You purchase a bicycle with a retail (pre-tax) price of $760. The local sales tax rate is
7.6%. What is the final cost?
Answers
Answer:
Final cost is 817.76
Step-by-step explanation:
First find the amount of the tax
760 * 7.6%
760 * .076
75.76
Add this to the cost of the bike
760+57.76
817.76
How far will the snail be from the rock after 9 minutes?
Answers
Answer:
27 inches <3
Step-by-step explanation:
What is the area of a rectangle with the following measurements:
Answers
Answer:
24x^5
Step-by-step explanation:
3 x 8 = 24
x multiplied by x^4 = x^5
(the exponents add to each other when multiplied)
Find the value of c that makes x^2+ 9x + c a perfect square trinomial. Write the expression as the square of a binomial. The expression is
Answers
Answer:
[tex]c=\frac{81}{4}[/tex]
I hope this is the right answer and I hope this helps
The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.
What is a perfect square trinomial?A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.
The expression is given below.
⇒ x² + 9x + c
The value of the variable 'c' to convert the expression as the square of a binomial will be given as,
c = (9/2)²
c = 81 / 4
The value of the variable 'c' to convert the expression as the square of a binomial will be 81 / 4.
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X = 8 find the slope
Answers
Answer:
the slope is 8
Step-by-step explanation:
since , x = 8 is a vertical line ,so the slope is undefined
please help.
with the steps.
just b, please
Answers
Answer:
x² +3x -50 = 0
Step-by-step explanation:
The area expression you got in part (a) is ...
A = (x +8)(x -5) = x² +3x -40
If the area is to be 10, then x must satisfy the equation ...
10 = x² +3x -40
x² +3x -50 = 0 . . . . . . subtract 10 and put in standard form
what is 110/12- 28/12 as an improper fraction
Answers
Answer:
82/12
Step-by-step explanation:
Can someone help me make sense of the problem. Provide an explanation and answer if at all possible
Answers
Answer:
1.728×10¹⁵
Step-by-step explanation:
You may recall from 3rd grade that multiplying by 10 adds a zero to the right of a number (moves the decimal point 1 place to the right).
An exponent is used to signify repeated multiplication. These facts together are used to translate to/from scientific notation.
10 = 1 × 10
100 = 1 × 10 × 10 = 1 × 10²
__
Continuing in like fashion, 5.4×10⁸ represents 5.4 × (1 followed by 8 zeros).
Similarly, 3.2×10⁶ = 3.2 × (1 followed by 6 zeros)
The product will be ...
(5.4×10⁸)×(3.2×10⁶) = (5.4×3.2) × (1 followed by 8+6 = 14 zeros)
= 17.28 × 10¹⁴
= (1.728 × 10) × 10¹⁴ . . . moving the decimal point so there's 1 digit to its left
Adding that extra zero into the count we already have, this becomes ...
= 1.728×10¹⁵
_____
Additional comment
Your scientific or graphing calculator will have a mode for showing numbers in scientific notation. You can enter these numbers directly into your calculator and have it show you the result in scientific notation.
Or, you can use a spreadsheet with appropriate output cell formatting.
Answer:
1.728×10¹⁵ is the answer
f(-3)
f(x)= 3 to the power of x
Answers
See attached picture
When a stone is dropped from a height, the time taken to fall, t, is proportional to the square root of the distance fallen, d.
Write down a formula, using k, connecting the time taken to fall and the distance traveled.
Answers
Step-by-step explanation:
We know that in kinematics we can write the formula for uniformly accelerated bodies:
s = 1/2 a t^2 + v0 t + s0
In our case s0 (initial deployment) = 0m and v0 (initial velocity) = 0
So:
s = 1/2 a t^2
Now we isolate t:
t = [tex]\sqrt[2]{\frac{2s}{a} }[/tex]
All proportionalities are obvious.
Note: I forgot to say that a, the acceleration, is the gravitational acceleration. It can be g or -g depending on how you'll choose the reference system.
if a is more than b, what is the equation for an ellipse with a centre at the origin and a horizontal major axis?
Answers
Answer:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
HELP!!! WILL MARK BRAINLIEST!!! +15 POINTS!! REAL ANSWERS ONLY PLEASE!
Answers
Answer:
3rd option
Step-by-step explanation:
Answer:
it's the first option (x ≥ -4)
Step-by-step explanation:
Domain refers to the x range, which is the horizontal line. As we can that the point last touches from the left is -4 and it is a colored circle so that means that there is a line underneath. Then, it goes right so that means that x is larger and/or equal to -4.
x ≥ -4
Triangle ABC has coordinates A(−6,2), B(−3,6), and C(5,0). Find the perimeter of the triangle. Round your answer to the hundredths place (2 decimal places) I will give brainliest
Answers
Answer:
26.18 units
Step-by-step explanation:
You could use distance formula three times to calculate the length of each side. Add the three lengths to find the perimeter. However, (see image) if you look at a graph of these points, two of the sides are the hypotenuse of a right triangle that have known, integer values--Pythagorean triples. The sides are 3-4-5 and the other is 6-8-10. We use the Pythagorean theorem to find the third side. See image.
11.18 + 5 + 10
= 26.18 units
The perimeter of triangle is 26.18.
What is triangle?A triangle is 2-dimensional closed curve. which has 3 sides, 3 angles and 3 vertices.
According to the question,
Triangle ABC has coordinates A(-6,2), B(-3,6), C(5,0).
Distance formula: √(x₂-x₁)² + (y₂-y₁)².
Points A and B are (-6,2) and (-3,6)
= √(-3-(-6))² + (6-2)²
= √9+16
= √25
=5.
Thus, point A and B has distance, S₁ = 5.
Points B and C are (-3,6) and (5,0)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(5-(-3))² + (0-6)²
= √(8)² + (-6)²
= √(64+36)
=√100
=10.
Thus, point B and C has distance, S₂ = 10.
Points C and A are (5,0) and (-6,2)
Distance formula: √(x₂-x₁)² + (y₂-y₁)²
= √(-6-(5))² + (2-0)²
= √((-11)² + (2)²)
=√(121+4)
=√125
=5√5
Thus, point C and A has distance, S₃= 5√5.
Perimeter of triangle = S₁ + S₂+S₃
= 5 + 10 + 5√5
=15+5√5
=15+5(2.23606)
=15+11.1803
=26.1803 ≈ 26.18
Hence, the perimeter of triangle is 26.18.
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A dollar bill is about 0.00011 meter thick. What is this thickness in scientific notation?
Answers
Answer:
1.1 * 10 ^ -3Step-by-step explanation:
Given the value of the thickness of a dollar bill to be 0.00011 metre .
The standard scientific Notation is expressed as A * 10 ^ n
A is any value between 1 and 10 where n is any Integer .
0.00011 = 11 / 100000
0.00011 = 11 / 10000
0.00011 = 11 *1 / 1000
0.00011 = 11 * 0.0001
0.00011 = 1.1 * 0.001
0.0011 = 1.1 * 10 ^ -3
Hope this helps you !!Hello could someone help me I don’t get this? Will name brainliest :D if correct answer please no links
Answers
Answer:
A -- only
Step-by-step explanation:
A segment bisector intersects a segment at its midpoint.
S is the midpoint of segment PQ, so ST is a segment bisector. (It intersects PQ at its midpoint, S.)
No other midpoints are shown in this drawing.
__
A perpendicular bisector is perpendicular to the segment it bisects. None are shown in this drawing.
__
An angle bisector divides an angle into two congruent parts. None are shown in this drawing.
__
The vertex of a right angle is often marked with a small square. Only point P is the vertex of a right angle in this drawing. (We cannot assume OPQR is a square.)
Solve the system by substitution
8x + y = 4
-2x - 8 =y
(answer as an ordered pair)
Answers
8 less than the sum of u and 2
Answers
Answer: u < 6
Step-by-step explanation: 2 + u < 8
u < (8-2)
u < 6
What is the domain and range of this? Is it a function yes or no?
Answers
Yes it is a function
You know when it’s a function when the left side (x/domain) does not repeat itself (Y/range) is allowed to repeat
in a dilation, what is preserved and what is altered?
Answers
Answer:
Preserve angles
Step-by-step explanation:
i think sorry if its wrong
Answer:
to preserve angles
Step-by-step explanation:
Write the formula for the volume of a cone V=1/3 π r^2 h in terms of h. Find the height h of a cone with volume V= 32π cm^3 and a radius r= 4cm
Answers
Answer:
Step-by-step explanation:
h≈1.91cm
Pls help. I need it asap
Answers
Answer:
18
Step-by-step explanation:
since the equation of AC is y=x-4 then the length of CB and AB must be the same. therefor its (6*6)/2