Answer:
a) True. The differential equation is [tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex], where [tex]T[/tex] is measured in Celsius.
b) The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.
Step-by-step explanation:
a) The object is heated up by convection and radiation, from First Law of Thermodynamics we get that energy interactions on the object are represented by:
[tex]-\dot Q_{out} + \dot W_{in} = \frac{dU_{sys}}{dt}[/tex] (Eq. 1)
Where:
[tex]\dot Q_{in}[/tex] - Heat transfer rate to the object, measured in watts.
[tex]\dot W_{in}[/tex] - Electric power given by the microwave owen, measured in watts.
[tex]U_{sys}[/tex] - Internal energy of the object, measured in watts.
Then, we expand the expression by means of definition from Heat Transfer and Thermodynamics:
[tex]-h_{c}\cdot A_{s}\cdot (T-T_{\infty})+\dot W_{in} = m\cdot c\cdot \frac{dT}{dt}[/tex]
Where:
[tex]h_{c}[/tex] - Heat transfer coefficient, measured in watts per square meter-Celsius.
[tex]A_{s}[/tex] - Surface area of the object, measured in square meters.
[tex]T[/tex] - Temperature of the object, measured in Celsius.
[tex]T_{\infty}[/tex] - Internal temperature of the microwave oven, measured in Celsius.
[tex]m[/tex] - Mass of the object, measured in kilograms.
[tex]c[/tex] - Specific heat of the object, measured in joules per kilogram-Celsius.
After some algebraic handling, we get this non-homogeneous first order differential equation:
[tex]\frac{dT}{dt} = -\frac{h_{c}\cdot A_{s}}{m\cdot c} \cdot (T-T_{\infty}) + \frac{\dot W_{in}}{m\cdot c}[/tex]
[tex]\frac{dT}{dt}+\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T =\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T_{\infty}+\frac{\dot W_{in}}{m\cdot c}[/tex] (Ec. 2)
If we know that [tex]h_{c} = 40\,\frac{W}{m^{2}\cdot ^{\circ}C}[/tex], [tex]A_{s} = 0.01\,m^{2}[/tex], [tex]m = 1\,kg[/tex], [tex]c = 1000\,\frac{J}{kg\cdot ^{\circ}C}[/tex], [tex]T_{\infty} = 25\,^{\circ}C[/tex] and [tex]\dot W_{in} = 50\,W[/tex], the differential equation is:
[tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex]
b) The solution of this differential equation is:
[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+ \frac{0.06}{0.0004}\cdot (1-e^{-0.0004\cdot t})[/tex]
Where [tex]T_{o}[/tex] is the initial temperature of the object, measured in Celsius.
[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+150\cdot (1-e^{-0.0004\cdot t})[/tex]
[tex]T(t) = 150+(T_{o}-150)\cdot e^{-0.0004\cdot t}[/tex]
Where [tex]t[/tex] is the time, measured in seconds.
If we know that [tex]T_{o} = 25\,^{\circ}C[/tex], then:
[tex]T(t) = 150-125\cdot e^{-0.0004\cdot t}[/tex] (Ec. 3)
For [tex]t = 200\,s[/tex], we get that temperature of the object is:
[tex]T(200) = 150-125\cdot e^{-0.0004\times 200}[/tex]
[tex]T(200) \approx 34.611\,^{\circ}C[/tex]
The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.
What’s 890,000,090 in scientific notation
Answer:
[See Below]
Step-by-step explanation:
[tex]Hey~There![/tex]
________________________
➜ Turn into scientific notation :
[tex]890,000,090=8.9000009*10^{8}[/tex]________________________
So the answer is [tex]\bold8\bold.\bold9\bold0\bold0\bold0\bold0\bold0\bold9\bold*\bold1\bold0^{\bold8}[/tex].
________________________
[tex]Hope~this~helps~Mate!\\-Your~Friendly~Answerer,~Shane[/tex] ヅ
Answer:
The number 890000090 can be written as 8.90 × 10^8 in scientific notation.
I need help with these questions
Answer:
29. D
30. A
31. 15
32. -34
33. -241
34. -36
Step-by-step explanation:
Shelly found that the coefficient of determination between the age of a runner x and the runner’s finishing position y was about 0.728. What can she conclude?
72.8% of the variation in the runner’s finishing position is explained by the runner’s age.
0.728% of the variation in the runner’s finishing position is explained by the runner’s age.
53% of the variation in the runner’s finishing position is explained by the runner’s age.
0.728 more variation in the runner’s finishing position is caused by the runner’s age.
Answer:
72.8% of the variation in and the runner’s finishing position is explained by the runner’s ageStep-by-step explanation:
The number 0.728 is converted to percentage
0.728*100% = 72.8%Correct option is the first one
Answer:
72.8% of the variations in the runner's finihsing position is explained by the runner's age
explanation:
Ralph wants to show 13/20
Answer:
why won't Ralph show 13/20 then?
Your statement balance is $433.97. You have an outstanding check for $46.78 and an
outstanding deposit for $235.00. What is your adjusted balance?
A) S245.75
B) $387.19
C) $622.19
D) $668.97
X+Y+3=0 en grafica
Answer:
x=-y-3
Step-by-step explanation:
hope to get a brainliest thank u
A 1-unit by 4-unit rectangle is shown below
Order from least to greatest
I’m just rlly dumb and rlly tried srry:/
Answer:
The answer is D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
yawn
help me please somebody
Answer:
I am pretty sure that it would be a A whole number
If you spent 15 minutes exercising everyday, for a year nonstop,
¿how many minutes of exercise would you do?
An auto parts manufacturer throws out gaskets with weights that are not within 0.06 pound of the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Which gasket(s) should be thrown out?
Answer:
0.53 will not chosen
Step-by-step explanation:
Given weights:
0.58, 0.63, 0.65, 0.53, and 0.61.
Computation:
Mean weight X = [0.58+0.63+0.65+0.53+0.61] / 5
Mean weight X = [3] / 5
Mean weight X = 0.60
Acceptable weight = l x-X l < 0.06
l x-0.60 l < 0.06
So solving inequality
0.54 < x < 0.66
So, 0.53 will not chosen.
Simplify 83.63 -2.89 x (4.9 - 2.9) squared.
If the population proportion p = 0.63, what is the probability of getting correct answers on less than 60% of the questions?
Complete question:
An exam consists of 50 multiple choice questions. Based on how much you studied, for any given question, you think you have a probability of 0.63 of getting the correct answer. Consider the sampling distribution of the sample proportion of correct questions out of 50.
If the population proportion p = 0.63, what is the probability of getting correct answers on less than 60% of the questions?
Answer:
the probability of getting correct answers on less than 60% of the questions is 0.33
Step-by-step explanation:
Given;
number of samples, n = 50
population proportion, P = 0.63
For normal distribution;
np ≤ 60 and n(1-p) ≤ 60
(50 x 0.63) ≤ 60 and (1-0.63) ≤ 60
31.5 ≤ 60 and 22.2 ≤ 60
The condition is satisfied, then mean of the distribution is given by;
x = p = 0.63
The standard deviation is given by;
[tex]\sigma_p =\sqrt{\frac{P(1-P)}{n} }\\\\ \sigma_p =\sqrt{\frac{0.63*0.37}{50} }\\\\ \sigma_p = 0.068[/tex]
For a correct answers on less than 60% of the questions
Upper boundary = 0.6
lower boundary = 0
Thus, the probability is given by;
P (p' < 0.6) = 0.33
Therefore, the probability of getting correct answers on less than 60% of the questions is 0.33
Same set up as the problem
to the left. Fill in the blanks.
25
39
Answer:
In a quiz, positive marks are given for correct answers and negative marks are ... a − (−b) = 21 − (−18) = 21 + 18 = 39 ... (i) He jumps 3 steps down and then jumps back 2 steps up.
Step-by-step explanation:
make me as brain liest
Can someone help with the picture please?
Answer:-12 degrees ferenheight
Step-by-step explanation:
Just add 13 to -25 to find the temp change.
Thus, 13-25= -12 degrees F
Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. Complete the table to show the distance traveled in 1 minute at this speed
Answer:
4 miles in 1 min
Step-by-step explanation:
What is the solution to 5(2x−2)=30? Enter your answer in the box.
Answer:
x=4
Step-by-step explanation:
5(2x-2)=30
10x - 10 = 30
10x = 40
x = 4
The football team at a high school wants to conduct a survey of student opinion. The coaches want to begin with a simple random sample of 200 students. Which of the following survey methods will produce a simple random sample?
Survey the first 200 students to arrive at school in the morning
Survey every 20th student entering the school gym until 200 students are surveyed
Number the students on the school roster. Use a table of random numbers to choose 200 students from this roster for the survey.
Use random numbers to choose 50 each of freshmen, sophomores, juniors, and seniors
Number the gym seats. Use a table of random numbers to choose seats and interview the students until 200 have been interviewed.
Answer: Number the students on the school roster. Use a table of random numbers to choose 200 students from this roster for the survey.
Step-by-step explanation:
A truly random sample would be one that gave every member of the population the same chance to be represented. This is why the method that will produce a simple random sample is one where the official school rooster is used and 200 students are selected randomly. This way every student in the school gets an equal chance of representation.
The first option is not random as it excludes students arriving after the first 200.
The second and last options will not be representative nor will it be random because it does not account for students who do not use the gym.
The fourth option limits the number of people that may be picked per class so reduces the chance of simple random selection across the school. This is stratified instead.
crystal has played the piano for 15 years. jared has played for 3 years. how many times longer has crystal played the paino?
Answer:
5
Step-by-step explanation:
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where , , , and . Do the results make sense? (a) The mean phenotype code is 2.6. (Round to the nearest tenth as needed.) (b) The median phenotype code is 2.5. (Type an integer or a decimal.) (c) Select the correct choice below and fill in any answer boxes within your choice. A. The mode phenotype code is 4. (Use a comma to separate answers as needed.) B. There is no mode. (d) The midrange of the phenotype codes is 2.5. (Type an integer or a decimal.) Do the measures of center make sense? A. Only the mean, median, and midrange make sense since the data is nominal. B. Only the mode makes sense since the data is nominal. C. Only the mean, median, and mode make sense since the data is numerical. D. All the measures of center make sense since the data is numerical.
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the (a) mean. (b) median. (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4= wrinkled-green. Do the results make sense?
Given the phenotype code as 4, 3, 3, 1, 3, 4, 1, 1, 1, 4, 2, 3, 1, 1
a) Mean is the average of the number. It is gotten by taking of the ratio of the variables to the sample size.
Sum of variables = 4+3+3+1+3+4+1+1+1+4+2+3+1+1
Sum of variables = 32
Sample size = 14
Mean = 32/14
Mean = 2.29
The mean phenotype is 2.29
B) median is the value at the middle after rearrangement either in ascendng or descending order.
On rearranging:
1,1,1,1,1,1),2,3,(3,3,3,4,4,4
It can be seen that there are two values at the middle. To get the actual median, we will take the median of the values.
Median = 2+3/2
Median = 5/2
Median = 2.5
Hecke the median phenotype is 2.5
c) The mode is the vale that is occurring the most in the data. It can be seen from the data that 1 is the only value occurring the most (6 times), hence the phenotype mode of the data is 1.
d) Midrange = Highest value + Lowest value/2
Midrange = 1+4/2
Midrange = 5/2
Mid range = 2.5
Hence the midrange of the phenotypic code is 2.5
e) Yes, the measures of center make sense since the data is numerical. Since all our values are numerical and measurable, hence we can conclude that the measure of centres make sense
PLEASE HELP!! Are triangles A,B,C and D acute obtuse or right angles?
Answer:
right angle
Step-by-step explanation:
it has a 90 degree angle so its a right angle
What’s the y-intercept of this graph
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
Finding the slope:
So first it'll help to find the slope. You could do that by finding two perfect points, which in my case I chose (3,4) and (4,2). Then you tell what the rise over run is....you go down 2 and right 1 to get from (3,4) to (4,2). So the slope would be -2, since we went down it'll become a negative.
Finding the y-intercept:
Then after we found the slope we could easily make an equation and solve it for the y-intercept, but first we'll need to get a point. Let's choose (4,2). So after you got your point you will plug it into the slope formula like this....
[tex]y=mx+b\\\\\\2=-2(4)+b[/tex]
Then we solve it to get....
[tex]2=-2(4)+b\\2=-8+b\\b=10[/tex]
So the y-intercept is 10.
please helpppp I will give you a brainleist !!!!!!
Answer:
Hope this helps
Step-by-step explanation:
4. 10^2
5. 64 / 14 * 9 + 8
64/126+8
8 64/126
8 4/9
6. 1.762 x 10^3
Answer:
I am confused with #5 but the rest are solid and checked
Step-by-step explanation:
#4 (A)
10*10=100
#5 (97)
64+4*4+3*3+2*2*2=
64+16+9+8=97
#6 (1.762 × 103)
#7 1070
find the value 3x^2+2x+5, if x=-7
Answer:
432
Step-by-step explanation:
Original Equation:
3x^2 + 2x + 5
x = -7
3 multiplied by -7 = -21
Equation:
-21^2 + 2x + 5
-21 multiplied to the second power is 441
(two negatives cancel each other out making the number positive)
Equation:
441 + 2x + 5
2 multiplied by -7 is -14
441 + -14 + 5
441 + -14 = 427
427 + 5 = 432
Answer: 432
Hope I helped :)
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Read Edward Corsi’s quotation from the book Immigrant Kids by Russell Freedman. The writer Angelo Pellegrini has recalled his own family’s detention at Ellis Island: We lived there for three days - Mother and we five children, the youngest of whom was three years old. Because of the rigorous physical examination that we had to submit to, particularly of the eyes, there was this terrible anxiety that one of us might be rejected. And if one of us was, what would the rest of the family do? This quotation adds credibility to the text because his mother lived on Ellis Island with her children, and their experience agrees with Freedman’s statement that families were separated. he lived at Ellis Island for three days, and his experience agrees with Freedman’s statement that families were afraid of the health examinations. he was a writer who wrote about Ellis Island and described the feelings an immigrant might have during the physical exams. he lived at Ellis Island for three days, a
Answer:
he lived at Ellis Island for three days, and his experience agrees with Freedman’s statement that families were afraid of the health examinations
Step-by-step explanation:
In the book immigrant kids, freeman gives readers a glimpse of what it was like to be new and young America. It talked about the journey and what life is like as soon as they arrive.
Pallegrini's experience about rigorous physical examination and the anxiety that followed agrees with freedman's statement about people being afraid of health examinations.
Answer:
he lived at Ellis Island for three days, and his experience agrees with Freedman’s statement that families were afraid of the health examinations
Step-by-step explanation:
i know all that touches the sunlight
Dos automóviles son puestos a prueba uno es de color rojo y recorre 9 vueltas y otro es de color azul que recorre 3139°, ambos a una velocidad constante de 240 km/h.
Answer:
what in the world
Step-by-step explanation:
the first two common multiples of 3, 4, and 6
Answer:
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36
Multiples of 6 6, 12, 18 , 24 , 30, 36 , 42 , 48, 54, 60
but the first two common multiples of 3, 4, and 6 are
3: 6, 9
4 : 8,12
6 : 12, 18
Find the midpoint of AB if a (-1,7) and B (11,-1)
Answer:
(5, 3)Step-by-step explanation:
Given Points A(-1,7) and B (11,-1)To findMidpoint of ABSolutionUsing midpoint formula
x = (-1 + 11)/2 = 10/2 = 5y = (7 -1)/2 = 6/2 = 3Midpoint is (5, 3)
Answer:
mid point = 5, 3Step-by-step explanation:
A(-1, 7) B(11, 1)
use the midpoint formula:
mid point = (x₁ + x₂) , (y₁ + y₂)
2 2
= (-1 + 11) , (7 - 1)
2 2
mid point = 5, 3
A regular piece of ice has a temperature of 32ºF. A piece of dry ice has a temperature of -109ºF. Which is the true statement?
The regular ice is colder than the dry ice.
The difference in temperature is less than 100ºF.
The dry ice is colder than the regular ice.
The dry ice has a greater temperature
Answer:
C
Step-by-step explanation:
The Dry Ice Is Colder Then the Regular Ice. By 77°F.
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A rope for zip lining is tied between two parallel trees. The rope is taut, forming a straight line. What is m<2?
Answer:
72°.
Consecutive interior angle
Step-by-step explanation:
The complete question is shown below
The consecutive interior angle theorem states that if two parallel lines are cut by a transversal line, the pair of interior angles formed are supplementary (that is they sum up to 180°).
Hence since the two trees are parallel and the rope forms a transversal hence they form an interior angle:
m∠2 + 72° = 180° (consecutive interior angles)
Add -72 to both sides and then simplify:
m∠2 + 72 -72 = 180 - 72
m∠2 = 108°