A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. The total rate of heat rejection to the environment is 298.4458 kJ/min.
What is a Heat Engine?A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. It accomplishes this by transferring a functioning ingredient from a higher to a lower state temperature.
For the following condition, the diagram can be made as shown below. Also, the Heat Engine Sink temperature, [tex]T_H[/tex] = 900 K
Heat Engine surrounding temperature, [tex]T_L[/tex] = 300 K
Refrigerator surrounding temperature, [tex]T'_C[/tex] = 215 C + 273 = 488 K
Refrigerator sink temperature, [tex]T'_H[/tex] = 300 K
The heat removed by the refrigerator, [tex]Q'_{in}[/tex] = 250 kJ/min
A.) For a Carnot refrigerator, the COP or the coefficient of performance is given by,
[tex]COP = \dfrac{T'_C}{T'_H-T'C}[/tex]
COP = (488)/(488-300)
COP = 2.596
The COP is also the ratio of the Heat input and the work output.
[tex]COP = \dfrac{Q'_{in}}{W}[/tex]
2.596 = 250/W
W = 96.302 kJ/min
The Carnot engine efficiency is expressed as,
[tex]\eta = 1- \dfrac{T_C}{T_H}[/tex]
η = 1 - (300/900)
η = 0.6667
Also, the Carnot engine efficiency is defined as,
[tex]\eta = \dfrac{W}{Q_{in}}\\\\[/tex]
[tex]0.6667 = \dfrac{96.302}{Q_{in}}\\\\Q_{in} = \rm 144.4458\ kJ/min[/tex]
Hence, the rate of heat supplied to the heat engine is 144.4458 kJ/min.
B.) The total work done by the engine is 96.302 kJ/min, while the heat input is 144.4458 kJ/min. Therefore, the heat output of the system is,
[tex]W = Q_{in} - Q_{out}\\\\Q_{out} = 48.1438\rm\ kJ/min[/tex]
Thus, the total rate of heat rejection to the environment,
[tex]\text{Total Heat rejection} = Q_{out}+Q'_{in}\\[/tex]
= 48.4458 kJ/min + 250 kJ/min
= 298.4458 kJ/min
Hence, the total rate of heat rejection to the environment is 298.4458 kJ/min.
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-5(-1) ≤ 55
and
8-y< 12
Step 2 of 4: Solve the second inequality and express your answer in interval notation. Use decimal form for numerical values.
The solution to the inequality is (-4, ∞)
How to solve the inequality?The second inequality is given as:
8 - y < 12
Subtract 8 from both sides
-y < 4
Rewrite as:
y > -4
In interval form, we have:
y = (-4, ∞)
Hence, the solution to the inequality is (-4, ∞)
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Type your answer into the box. 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres, the length is 7.3 metres and the height is 4.2 metres. Dulce Livramento 4.2 m What is the volume of the cuboid? Type your answer into the box . 7.3 m 6 m cm³ Q The width of a cuboid is 6 metres , the length is 7.3 metres and the height is 4.2 metres . Dulce Livramento 4.2 m What is the volume of the cuboid ?
The volume of the cuboid is 183.96 m³
What is the volume of a cuboid?A cuboid is a plane shape with a six-faced solid called a hexahedron. The volume of a cuboid is Length × width × height
From the information given:
The length of a cuboid is = 7.3 metresThe width = 6 metresThe height = 4.2 metresThe volume of the cuboid is;
= (7.3 × 6 × 4.2) m³
= 183.96 m³
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(a) Using the digits 0 to 7 exactly once each, form a collection of positive integers whose sum is 100.
(b) Find a second solution to (a) which has a different number of integers in the sum.
(c)Show that in any solution (a), the sum of the digits in the units places is 20.
(d)Find, with reasons, the smallest possible value of the largest integer in a solution to (a).
A) The collection of positive integers whose sum is 100 are: 23, 17, 6, 54, 0.
B) Another collection of positive integers whose sum is 100 are: 13, 27, 4, 56, 0.
C) Due to the fact that the units can be commuted, their sum is always equal to 20.
D) The smallest possible value is 0 and the largest is 57.
What is the sequence of positive integers?A) The formation of a collection of positive integers can be done by trial and error. For example, only using the digits {0, 1, 2, 3, 4, 5, 6, 7}.
For example, we can have;
23 + 17 + 6 + 54 + 0 = 100
Where the numbers used are: 23, 17, 6, 54, 0.
B) Another example is;
13 + 27 + 4 + 56 + 0 = 100
C) If we add the units digits of these 5 numbers, we get:
3 + 7 + 6 + 4 + 0 = 20
Now, if we compute the units digits between the different numbers, to get for example: 27, 13, 6, 54, 0
The sum is still equal to 100, and the units digits are the same ones, so we still have that the sum of the units digits is equal to 20.
d) The smallest integer that we use is 0.
For the largest we just commute the tens and units digits so we make the larger integer possible, which is:57.
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what is the constant of variation?
Answer:
constant (unchanged) ratio of two variable quantities
Step-by-step explanation:
y = k x ( or y = k x )
y = 15 when x = 24, find x when y = 25. find the constant of variation.
Super confused new topic please help
Answer:
1960cm squared
Step-by-step explanation:
in case you're still confused ask where you're still confused and I'll offer my assistance.good day.
What was the percent increase of China's
population from 1970 to 1995?
56.25%
45%
156.25%
9.405%
China's Population
Population
(billions)
0.7
Year
1965
1970
1975
1980
1985
1990
1995
2000
0.8
0.92
0.98
1.08
1.14
1.25
1.26
The percentage increase China's population from 1970 to 1995 is: 56.25%.
How to Calculate Percentage Increase?Percentage increase = (Final Value - Original Value)/Original value × 100.
Given the following:
Original value = 0.8 billion
Final Value = 1.25 billion
Final Value - Original Value = 1.25 - 0.8
Final Value - Original Value = 0.45
Percentage increase = 0.45/0.8 × 100 = 56.25%.
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the diameter of a baseball is appromately 3 inches. What is its volume?Round your answer to the nearest whole number.
The volume of the baseball roundibg off to nearest whole number is 14 cube inches.
If radius of a sphere is r and the volume of that spherical figure is given by V then,
[tex]V=\frac{4}{3}\pi r^3[/tex]
So in the problem the object is a baseball which is a sphere for sure.
Given that the diameter of that baseball is 3 inches.
So the radius of that baseball is given by = 3/2 = 1.5 inches.
Hence the volume of that base ball is
[tex]=\frac{4}{3}\pi\times(1.5)^3 \approx 14.1372 \approx 14[/tex]
Thus the volume of the baseball rounding off to nearest whole number is given by 14 cube inches.
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help me help me help help help me
Answer:
b. 0
c. 4
d. 2
e. [tex]\frac{76}{35}[/tex]
Step-by-step explanation:
b.) When translated it will become this expression 10 - [(2x15)/3] = 0
c.) It will become [tex]\frac{4(12-7)}{5}[/tex]
d.) This will transform to [tex]\frac{(\frac{78-13}{5}) + 5}{9}[/tex]
e.) The first eq is [tex]\frac{4(7+3)}{8}[/tex], then after the changes it becomes [tex]\frac{4[\frac{(7+3)+9}{7}]}{5}[/tex]
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
Does order matter when casting the 3 young Cosettes? (In other words, are young Cosette 1, young Cosette 2, and young Cosette 3 different parts?)
No, all three girls will play the same part.
Yes, even though they will all be playing the same part, it will be on different nights.
No, all three girls will get paid the same amount.
Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
What is an inference?It should be noted that a inference simply means the conclusion that can be deduced based on the information given.
In this case, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette.
Hence, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts. Therefore, ordering matters.
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What is the value of f(x) when x = 4 in the piecewise function f(x) =
2x² when x>4 …….. 4x when x < 4
The question asks the value of f(x) when x = 4 in the equation
x = 4 is less than or equal to 4, so we use the first equation in the piecewise functions => {4x when x≤4}
Solving for f(x):
4(4)=16
16 is the answer!
Hope it helps!
complete the flow chart to prove
someone pls help me pls pls asap
The attached figure represents the complete flowchart.
How to complete the flowchart?The given statement is:
∠1 ≅ ∠2
To prove
∠3 ≅ ∠4
By vertical angle theorem, we have:
∠2 ≅ ∠4
By transitive property of congruence, we have:
∠2 ≅ ∠3
By transitive property of congruence, we have:
∠1 ≅ ∠3
By vertical angle theorem, we have:
∠3 ≅ ∠4
See attachment for the complete flowchart.
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In a catalog, movies are identified by an ID number—2 letters followed by 3 digits.Repetitions are permitted. How many catalog numbers can be made?What is the probability that the ID number is divisible by 5? (Include the 2 letters in the ID number.)
Using the Fundamental Counting Theorem, it is found that:
676,000 catalog numbers can be made.There is a 0.2 = 20% probability that the ID number is divisible by 5.What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For the 2 letters(26 outcomes each), and 3 numbers(10 outcomes each), we have that the parameters are:
[tex]n_1 = 26, n_2 = 26, n_3 = 10, n_4 = 10, n_5 = 10[/tex]
Hence the number of catalog numbers is:
[tex]N = 26^2 \times 10^3 = 676000[/tex]
The ID number is divisible by 5 if the last digit is either 5 or 0, hence [tex]n_5 = 0[/tex] and the probability is:
[tex]p = \frac{26^2 \times 10^2 \times 2}{26^2 \times 10^3} = 0.2[/tex]
There is a 0.2 = 20% probability that the ID number is divisible by 5.
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Explain what the slope and y-intercept of the equation represents in this situation y=14x+9
Answer:
slope: 14
y intercept: (0,9)
Step-by-step explanation:
in the form y = mx + b, the slope is m: 14
to solve for the y intercept, we set x as 0: 14 * 0 + 9 = y interecept is 9.
Evaluating an exponential function
Using the given exponential function, we have that:
The initial amount is of 523 grams.The amount after 50 years will be of 165 grams.What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem, the function is:
[tex]A(t) = 523(0.5)^{\frac{t}{30}}[/tex]
Hence the initial amount is of 523 grams.
The amount after 50 years will be given by:
[tex]A(50) = 523(0.5)^{\frac{50}{30}} = 165[/tex]
The amount after 50 years will be of 165 grams.
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I need help asap. ive tired a lot and cant get it
San is currently three times Harry's age. Sam's age is also 10 more than twice Harry's age. the following systems of equation models this scenario. x=3y, x=10+2y
Step-by-step explanation:
so, what do we need to do ?
just solve these equations and find Sam's age (and Harry's) ?
x = 3y
x = 10 + 2y
so, we simply use the first equation in the second :
3y = 10 + 2y
y = 10
x = 3y = 3×10 = 30
Sam is currently 30 years old, Harry is 10.
Why is it most logical to let x represent Dianna’s current age?
Answer:
In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?
Choose the most logical value for the variable to represent.
x= Diana's age now
This question is impossible to fully answer without further context. (Who is Dianna? Why do we need her age?)
However, it can be noted that [tex]x[/tex] is easily the most common variable name whenever you have a missing value in an equation. Generally, it is understood by mathematicians that [tex]x[/tex] and most other letters denote an unknown value, something to either use in solving the equation or something to find on its own.
Elsa sold 24 drawings for $12 each at the art fair. She is going to use ‡ of the money to buy books. The rest of the money is going into her savings account. How much money will she put into her savings account?
The amount going to her savings accounts is $192
How to determine the amount saved?The given parameters are:
Drawings = 24
Rate = $12
The total amount earned from selling the drawings is:
Total = 24 * $12
Evaluate
Total = $288
She buys books with 1/3.
This means that she saved 2/3
So, we have:
Savings = 2/3 * $288
Evaluate
Savings = $192
Hence, the amount going to her savings accounts is $192
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I am a 3-digit odd number.
The sum of my digits is 9.
My tens digit is twice that if my hundreds digit.
What am I?
Answer:
Step-by-step explanation:
let the number at unit place=x
ten's place=y
hundred's place=z
x,y,z are integers.
x+y+z=9
also digit=100z+10y+x
y=2z
x+2z+z=9
x+3z=9
x=1,3,5,7,9
for x=1
1+3z=9
3z=9-1=8
z=8/3 (rejected as z is an integer.)
when x=3
3+3z=9
3z=9-3=6
z=6/3=2
z=2
y=2z=2×2=4
so number=100×2+10×4+3=200+40+3=243
f(x) = x/2 - 3 and g(x) = 3x² + x − 6, find (f+ g)(x)
Answer:
3x^2+3x/2-9
Step-by-step explanation:
collect like term
A printer designs a tag in the shape of a circle with a smaller circle cut out. She cuts her prototype from a 5 in. by a 7 in. index card. The cut edges of the tag will be printed with gold leaf. What is the approximate amount of gold leaf on a tag?
The circumference of the larger circle is about ____ inches. The circumference of the smaller circle is about ____ inches. So, the total length of gold leaf on a tag is approximately
____ inches.
The circumference of the larger circle is about 12.57 inches. The circumference of the smaller circle is about 3.14 inches. So, the total length of gold leaf on a tag is approximately 15.71 inches.
How to illustrate the circle?The circumference will be:
= 2πr
= 2 × 3.14 × 2
= 12.57 inches.
The circumference of the smaller circle will be:
= 2πr
= 2 × 3.14 × 0.5
= 3.14
The total length will be:
= 12.57 + 3.14
= 15.71 inches.
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The number of goals the Blue Jay hockey team scored in each game last year are: 3, 2, 1, 3, 0, 3, 1, 1, 2, 3, 3 What is the mode?
Answer:
3 is the mode
Step-by-step explanation:
if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places.
x y
2 73
3 77
4 85
5 101
6 133
A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706
The regression equation is (d) log(y) = 0.064x + 1.706
How to determine the regression equation?The table of values is given as:
x 2 3 4 5 6
y 73 77 85 101 133
Calculate the logarithm of the y values.
So, we have:
x 2 3 4 5 6
log(y) 1.86 1.89 1.93 2 2.12
Next, we enter the above values in a regression calculator.
From the calculator, we have the following summary:
Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63The regression equation is then represented as:
log(y) = bx + a
Where:
b = SP/SSX = 0.64/10 = 0.064
a = MY - bMX = 1.96 - (0.064*4) = 1.706
So, we have:
log(y) = 0.064x + 1.706
Hence, the regression equation is (d) log(y) = 0.064x + 1.706
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Answer: D. log(y) = 0.064x + 1.706
Step-by-step explanation: I got it right on my test
Justin‘s gas tank is 3/10 full after he buys 14 gallons of gas it is 4/5 full how many gallons can Justin‘s tank hold
Answer:
I can help, its 45
a line of best fit was drawn for 15 data points. what is the maximum number of these data points that may not actually be on the line?
The maximum number of the data points that may not actually be on the line is 15
How to determine the number of data points?The number of points is given as:
Points = 15
A line of best fit implies that the model is a regression model
In a regression model, all the data points may not pass through the line of best fit.
This means that the maximum number of the data points that may not actually be on the line is 15
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please solve it?
1. 3q4 × 2q5 ÷q3
2. 4-²
3. 16^1/2
4.4°
Ibsan want to buy a chicken from one of two supermarkets around his house. the two supermarkets contain 20 local and 25 imported chickens respectively. how many possible chickens are there to choose from
Answer:
Since there are 20 chickens in one supermarket, and 25 chickens in the other supermarket, there are 45 chickens to choose from.
Jeff places a 13 ft ladder against a wall. The base of the ladder is 5 ft from the wall. How high on the wall does the ladder reach?
Work Shown:
[tex]a^2+b^2 = c^2\\\\5^2+b^2 = 13^2\\\\25+b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12\\\\[/tex]
I used the pythagorean theorem.
(3.125) + (-3.9) - (2.46)
Answer:
-3.235Step-by-step explanation:
First, let's start by removing the parentheses and simplifying the expression.
3.125 + - 3.9 - 2.46
Adding a negative number is the same as subtracting it, so we can remove the + sign.
3.125 - 3.9 - 2.46
From there, we can do simple subtraction and get:
-3.235
here is a gauge for the fuel tank of a car the fuel tank hols 52 litres of fuel when the tank is full the tank is 1/4 full of fuel
work out how many more litres of fuel are needed to fill the tank