What is the percent change if a shirt that cost $36 goes on sale for $24? Round your answer to the nearest tenth. Please solve in the "show your work box" below. You may use the pen tool, or you can use the text tool and type your answer. Then select the correct answer. You MUST show work to get full credit.
Answers
Answer:
33.3%
Step-by-step explanation:
Take the original price and subtract the new price
36-24=12
Divide this by the original price
12/36 = 1/3 = .33333repeating
Multiply by 100 % to get to percent form
.3333 repeating * 100%
33.3333%
Round to the nearest tenth
33.3%
Related Questions
Incorrect Question 1 0/10 pts Which of the following statements can be proved true using a constructive proof of existence? Select all applicable statements. There exists a false statement. vxEZ =(x > 0 -> x < 0) V = x + 2x > 0 -> x = 0 There does not exist an even integer which is the sum of three primes. ncorrect Question 6 0/10 pts Select all of the proof techniques (from Ch 4 of Epp) that could NOT be a plausible first step in proving the following statement: One of the cards in the middle three rows is the one the user selected at the start of the trick. Constructive or non-constructive proofs of existence Exhaustive proof of universals Proof by contrapositive. Direct proof for existential statement Incorrect Question 7 0/10 pts Select all of the proof techniques (from Ch 4 of Epp) that could NOT be a plausible first step in proving the following statement. (You likely will not understand the statement. Nonetheless, you should be able to answer correctly.) Please note that by "direct proof for universal statements" we mean any proof that starts from the premises (of a universally quantified statement) and derives the conclusion based on these premises and other known facts. aceR, ano e Zt, vne Zt, T(n) >c*2". Constructive or non-constructive proofs of existence Exhaustive proof of universals Direct proof for universal statement Direct proof for existential statement
Answers
Multiple questions are included, and the answers vary for each question.
Which proof techniques are applicable for constructive proofs of existence?The given paragraph consists of multiple questions related to proof techniques and statements.
The questions ask for selecting the applicable proof techniques or true statements based on constructive proof of existence, plausible first steps in proving a statement, and different proof techniques mentioned in Epp's book.
Each question requires careful reading and understanding of the provided options and statements in order to determine the correct answers.
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what does X equal? giving 50 points
Answers
Square both sides
1) 27 is 3 times as many as what number?
Answers
Answer:
9
Step-by-step explanation
Its like saying 3 nine times so
3, 6, 9, 12, 15, 18, 21, 24, 27
So that is 3 nine times
Hope this help ;)
What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12?
(–6, 0), (2,0)
(–2, –16), (0, –12)
(–6, 0), (–2, –16), (2, 0)
(0, –12), (–6, 0), (2, 0)
Answers
Answer:
The x intercepts would be (-6; 0) and (2; 0).
Step-by-step explanation:
Take a look at the picture.
Calculate it replacing f(x) with 0. The result will be: x1 = -6, x2 = 2 (consequently, both y's equal 0).
Answer:
(-6,0),(2,0)
Step-by-step explanation:
x-intercept
at x-intercept y=0
f(x)=x^2+4x-12
x^2+4x-12=0
by using factorisation method
product=-12
sum=4
factors=6,-2
(x^2 -2x)+(6x-12)=0
x(x-2)+6(x-2)=0
(x+6)(x-2)=0
x+6=0, x-2=0
x= -6,x=2
Question 5.
In the third month of a study, a sugar maple tree is 86 inches tall. In the seventh month, the tree is 92 inches tall. Assuming the tree grows at a constant rate every month, what is the rule for the height of the tree during the nth month?
an = 83 + 1.5(n – 1)
an = 83 + 1.5(n + 1)
an = 86 + 2(n – 1)
an = 86 + 2(n + 1)
Answers
Answer:
an= 86 + 2(n+1)
Step-by-step explanation:
The rule for the height of the tree during the nth month can be determined by finding the common difference, d, between consecutive terms in the sequence. To do this, we subtract the height of the tree in the third month from the height of the tree in the seventh month:
92 - 86 = 6
The common difference is 6, so the height of the tree in the nth month can be represented by the equation:
an = a3 + 6(n - 3)
We know that a3 = 86, so we can substitute this value into the equation:
an = 86 + 6(n - 3) = an+ 86 + 2(n+1)
This equation represents the height of the sugar maple tree during the nth month, where n represents the number of months after the third month.
Answer:
an= 86 + 2(n+1)
Step-by-step explanation:
The lengths of two sides of a triangle are shown.
Side 1: 8x2 − 5x − 2
Side 2: 7x − x2 + 3
The perimeter of the triangle is 4x3 − 3x2 + 2x − 6.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work. (4 points)
Part B: What is the length of the third side of the triangle? Show your work. (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answers
Answer:
To find the total length of the two sides, we simply add them together:
Total length = Side 1 + Side 2
Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)
Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3
Total length = 7x^2 + 2x + 1
Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.
Step-by-step explanation:
To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:
Perimeter = Side 1 + Side 2 + Side 3
We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:
4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3
Simplifying the right-hand side:
4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3
Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1
Simplifying further:
Side 3 = 4x^3 - 7x^2 - x - 7
Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.
Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.
Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.
Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.
Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.
The difference between the roots of a quadratic is 4i. The sum of the roots is 12. Write the equation.
Answers
The equation whose difference between the roots of a quadratic is 4i and The sum of the roots is 12 is; x² -12x + 40 = 0
According to the question;
The difference between the roots of a quadratic is 4i. The sum of the roots is 12.In essence,
f - g = 4if + g = 12By solving simultaneously;
f = 6 + 2i. and. g = 6 - 2iThe equation can therefore be written as follows;
(x - 6 -2i) (x -6 +2i) = 0The equation is therefore;
x² -12x + 40 = 0
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Q.2) A jar contains three balls numbered 1,2, and 3. If two balls are drawn: a) Write the probability space? b) what is the probability that the sum of the numbers is 4 ? c) what is the probability that the sum of the numbers is at least 4 ?
Answers
a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).
b) The probability that the sum of the numbers drawn is 4 is 2/9.
c) The probability that the sum of the numbers is at least 4 is 2/3.
a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:
P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)
Hence, the probability space can be written as a set, S = {1,2,3}.
b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:
P = 2/9
c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:
(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)
Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3
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Last week a certain pet store had 52, 72, 96, 21, 58, 40, and 75 paying customers. Which data value(s) are outliers? Select all that apply.
Answers
There is one value greater than 148.25, which is 96. the value of 96 is considered an outlier in this Dataset.
To identify outliers in a dataset, we need to first calculate the interquartile range (IQR) and then use the following rule:Any data value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.
To find Q1 and Q3, we first need to order the data:
21, 40, 52, 58, 72, 75, 96
The median of the entire dataset is (58 + 72)/2 = 65, so Q2 (the second quartile) is 65.
The lower quartile Q1 is the median of the lower half of the data, which is:
21, 40, 52, 58
The median of this data is (40 + 52)/2 = 46, so Q1 is 46.
The upper quartile Q3 is the median of the upper half of the data, which is:
72, 75, 96
The median of this data is (75 + 96)/2 = 85.5, so Q3 is 85.5.
Now we can calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 85.5 - 46 = 39.5
Using the rule for outliers, any data value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.
Q1 - 1.5 * IQR = 46 - 1.5 x 39.5 = -23.25
Q3 + 1.5 * IQR = 85.5 + 1.5 x 39.5 = 148.25
Therefore, any data value less than -23.25 or greater than 148.25 is an outlier.
In this case, there are no values less than -23.25, but there is one value greater than 148.25, which is 96. Therefore, the value of 96 is considered an outlier in this dataset.
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the points A (- 3, - 2 ),B(-3, 3) and C (5, 3) are 3 points
what type of triangle is ABC
Answers
Answer:
right triangle
Step-by-step explanation:
P=(x,y)
point=(number on x-axis, number on y-axis)
90° angle=right triangle
Answer:
Step-by-step explanation:
It is a right triangle.
Segment AB is a vertical line,
Segment BC is a horizontal line.
They meet at a right angle.
Note that the Unicode for character A is 65. The expression "A" + 1 evaluates to ________.
A. 66
B. B
C. A1
D. Illegal expression
Answers
Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".
The terms you mentioned are related to the Unicode character encoding standard and the concept of evaluating expressions. When discussing the expression "A" + 1, it's essential to note that the Unicode value for the character "A" is 65.
The expression "A" + 1 is attempting to add a numerical value (1) to a character ("A"). In many programming languages, this operation is allowed, and the result would be based on the Unicode values of the characters involved. Since the Unicode value for "A" is 65, adding 1 to it would result in a new Unicode value of 66. Consequently, the evaluated expression would correspond to the character with the Unicode value of 66, which is the letter "B". Therefore, the correct answer to this question is option B: "B".
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the pie chart shows the age distribution in a village of 120 people
Answers
Answer:
you must pls pls post full question
Answer:
a) 60 villagers
b) 5%
Step-by-step explanation:
Find the Perimeter and Area of the rhombus.
Answers
Find f^-1(x) where
f(x) = 3x+2/x
Answers
Given:
Consider the function is
\(f(x)=\dfrac{3x+2}{x}\)
To find:
The inverse of the function, .i.e., \(f^{-1}(x)\).
Solution:
We have,
\(f(x)=\dfrac{3x+2}{x}\)
Putting f(x)=y, we get
\(x=\dfrac{3y+2}{y}\)
Isolate the variable y.
\(xy=3y+2\)
\(xy-3y=2\)
\(y(x-3)=2\)
\(y=\dfrac{2}{x-3}\)
Putting \(y=f^{-1}(x)\), we get
\(f^{-1}(x)=\dfrac{2}{x-3}\)
Therefore, the inverse function is \(f^{-1}(x)=\dfrac{2}{x-3}\).
A large water bottle holds 25 litres of water correct to the nearest liter. A drinking glass holds 0.3 litres correct to the nearest 0.1 litres Calculate the lower bound for the number of glasses of water which can be filled from the bottle
Answers
This question is solved using rounding and proportion concepts.
Using this, we find that: the lower bound for the number of glasses of water which can be filled from the bottle is 100.A drinking glass holds 0.3 litres correct to the nearest 0.1 litres
This means that, with 2 decimal places, the drinking glass holds between 0.25 litres and 0.34 litres.
-------------------------------------
Calculate the lower bound for the number of glasses of water which can be filled from the bottle
For the lower bound, we consider that 1 glass holds 0.25 litres, and want to find how many glasses are needed for 25 litres. So
1 glass - 0.25 litres
x glasses - 25 litres
Applying cross multiplication:
\(0.25x = 25\)
\(x = \frac{25}{0.25} = 100\)
Thus, the lower bound for the number of glasses of water which can be filled from the bottle is 100.
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(3,0) (7,16) Write a slope intercept equation for these numbers.
Answers
Answer:
y=4x-12
Step-by-step explanation:
leana has left a mug of hot tea on the counter to cool off so she can drink it safely. She watches the steam rising up out of the tea. Which type of thermal energy transfer is occurring as the steam rises into the surrounding air?
Group of answer choices
conduction
sublimation
convection
radiation
Answers
The type of energy transfer that Leana is seeing as a result of steam rising is radiation.
Radiation is:
A method of energy transfer Works best in gas or open space between materialsThe steam rising from the tea is energy and it shows energy moving from the tea to the air. There is space between the tea and the air which means that it is radiation that the energy transfer is using as a conduit.
In conclusion, this statement describes radiation.
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The equation below describes a parabola of a is positive which way does the parabola open? X=ay2
Answers
Answer:
If a is positive, the parabola will open to the right, so the answer is C
Step-by-step explanation:
Find y
0
(t), the zero-input response of the response for an LTIC system described by (c) the complex-root system (D
2
+4D+40)y(t)=(D+2)x(t) with initial conditions y
0
(0)=2 and
y
˙
0
(0)=16.78.
Answers
The transform ,D2Y(s) + 4DY(s) + 40Y(s) = (D+2)X(s) Therefore, the zero-input response of the system y0(t) is given asy0(t) = (e -2t) - 2(cos6t + sin6t) + 6/5
Given that, LTIC system described by the complex-root system is given below.(D2+4D+40)y(t)=(D+2)x(t)
The zero-input response of the response for an LTIC system is given by the initial conditions. The initial condition for the given system is given below.y0(0)=2 and y˙0(0)=16.78.
Using the Laplace transform method, find the transfer function of the given system .
1: Finding the Laplace Transform for the given system(D2+4D+40)y(t)=(D+2)x(t). First, we need to take the Laplace transform of both sides of the given equation. We know that the Laplace transform of y(t) and x(t) are Y(s) and X(s) respectively. Therefore, we get,D2Y(s) + 4DY(s) + 40Y(s) = (D+2)X(s)
2: Solving for the Transfer Function. We know that transfer function is H(s)=Y(s)/X(s). Therefore, we getH(s)= (D+2)/(D2+4D+40)Taking the Laplace inverse of H(s) gives the zero-input response of the given system y0(t).
3: Finding the Zero-Input Response of the given system. We need to find the partial fraction of the transfer function. For that, solve the following equation.D2+4D+40 = 0. Using the quadratic formula, we get,D = -2 ± 6iTherefore, we get the partial fraction of the transfer function as, H(s)=1/(D+2) - 2/D + 3/5 + (3/5s)
Therefore, the zero-input response of the system y0(t) is given asy0(t) = (e -2t) - 2(cos6t + sin6t) + 6/5
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Bridget says that when a standard number cube is rolled getting an even number is an outcome. Uma says that getting an even number is an event. Who is correct? Explain
Answers
Uma is correct, because getting an even number is an event.
What is Probability?The term probability refers to the likelihood of an event occurring.
Given that;
Bridget says that when a standard number cube is rolled getting an even number is an outcome.
And, Uma says that getting an even number is an event.
Now,
We know that;
When a standard number cube is rolled then getting an even number is an event.
Hence, Uma statement is correct.
Thus, Uma is correct, because getting an even number is an event.
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Simplify 4 to the power of 6 ÷ 4 to the power of 2
Answers
Answer: 4 to the power of 4
Step-by-step explanation:
When we divide two numbers with powers, we subtract the powers from each other.
6 - 2 = 4
I hope it helped!
Answer:
256
Step-by-step explanation:
4^6 = 4 x 4 x 4 x 4 x 4 x 4 = 4096
4^2 = 4 x 4 = 16
4096/256 = 256
Hope this helped!
PLEASE HELP VERY IMPORTANT
Answers
HELP
33
-
88
in simplest form
Answers
Answer:
55
Step-by-step explanation:
33-88 =
-55
Say whether the given function has limit at the point (0,0). If the limit exists, then find it. (a) f(x, y) = 5ry² 3x² + y² (Hint: the parabola z = - y²); (b) f2(x, y) = Vel+V sin(y). (Hint: [√x + √] × [√ √U] ...). [2,3]
Answers
(a) The function f(x, y) does not have a limit at (0,0). (b) No information is provided to determine the limit for f2(x, y).
(a) For the function f(x, y) = 5ry²/(3x² + y²), we can analyze the behavior as (x, y) approaches (0,0). Since the denominator 3x² + y² becomes zero as (x, y) approaches (0,0), we cannot directly evaluate the function at this point. However, by considering the parabola z = -y², we can observe that the function does not approach a specific value and thus does not have a limit at (0,0).
(b) The function f2(x, y) = Vel + Vsin(y) is not well-defined as no information or context is provided for the variables Vel, V, and U. Without this information, it is not possible to determine the limit of the function at (0,0) or any other point.
Therefore, for (a), the function f(x, y) does not have a limit at (0,0), and for (b), no information is given to determine the limit for f2(x, y).
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QUESTION1 Round 3,500 to the nearest ten thousand. QUESTION 2 Round 462,183.5062749 to the nearest tenth. QUESTION 3 Evalutate 8^8
QUESTION 4 6+(−3)−5 equals
Answers
1) 3,500 rounded to the nearest ten thousand is 0.
2) 462,183.5062749 rounded to the nearest tenth is 462,183.5.
3) 6 + (-3) - 5 is equal to -2.
QUESTION 1:The given number is 3,500. To round it to the nearest ten thousand, we need to see which ten thousand is closest to the number. In this case, 3,500 is between 0 and 10,000. Since 0 is closer, we round down to 0. So, 3,500 rounded to the nearest ten thousand is 0.
QUESTION 2: To round the given number, 462,183.5062749, to the nearest tenth, we need to look at the digit in the hundredths place (the second digit after the decimal point), which is 0. Since 0 is less than 5, we round down the digit in the tenths place to 3.
Therefore, 462,183.5062749 rounded to the nearest tenth is 462,183.5.
QUESTION 3:We have to evaluate 8 to the 8th power. That means we have to multiply 8 by itself 8 times. Using a calculator, we can find that 8^8 is equal to 16,777,216.
QUESTION 4:When solving the expression 6 + (-3) - 5, we should follow the order of operations, which is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Since there are no parentheses or exponents in this expression, we can simply perform addition and subtraction from left to right.
6 + (-3) = 3, then 3 - 5 = -2.
Therefore, 6 + (-3) - 5 is equal to -2.
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Which data type is used to store real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42?
Answers
The float type of data stores real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42.
What is data- type?A data type, in programming, is a classification that specifies which type of value a variable has and what type of mathematical, relational or logical operations can be applied to it without causing an error.
All number types that allow for the possibility of a fractional component, such as 42.7 or pi, are known as floating point types.
The precision of various floating point data types varies depending on how many bits are utilized to represent the digits, which is directly proportional to the total number of bits in the number. In the IEEE standard, for instance:
Single precision floats have a range of around 10-38 to 1038 with a precision of about 7 decimal digits using a total of 32 bits and 24 bits for the digits.Double precision floats, commonly referred to as doubles, have a precision of about 16 decimal digits and a range of roughly 10^-308 to 10^308. They require 64 total bits and 53 bits for digits.Quadruple precision floats, Quad doubles, sometimes known as double doubles, have a precision of about 34 decimal digits and a range of roughly 10^-4932 to 10^4932 using 128 total bits and 113 bits for the digits.Hence, the type of data is floating point.
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Sarah is sitting blindfolded before a plate holding 3 apples and 1 pear. What is the probability that Sarah will select the pear? Write your answer as a fraction.
Answers
Answer:
3/1
Step-by-step explanation:
3/1 the ratio is 3:1
Let u (1, 2, 3), v (4, 4,-2), and w (2, 0,-2). Find 4u 5v w. STEP 1: Multiply each vector by a scalar. 4u = _____
5v = _____
-w = _____
STEP 2: Add the results from Step 4u + 5v - w = _____
Answers
STEP 1: To multiply a vector by a scalar, we simply multiply each component of the vector by the scalar.
4u = 4(1, 2, 3) = (4, 8, 12)
5v = 5(4, 4, -2) = (20, 20, -10)
-w = -1(2, 0, -2) = (-2, 0, 2)
STEP 2:
To add vectors, we simply add their corresponding components.
4u + 5v - w = (4, 8, 12) + (20, 20, -10) + (-2, 0, 2)
= (4+20-2, 8+20+0, 12-10+2)
= (22, 28, 4)
Therefore, 4u + 5v - w = (22, 28, 4).
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hi! please help in math!
i need the solution/explanation on how you got the answer
(y + 3) = -8(x - 4)
what is the slope?
Answers
Answer:
slope m = - 8
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y + 3 = - 8(x - 4) ← is in point- slope form
with slope m = - 8
The slope is :
↬ -8Solution:
Given: \(\bf{y+3=-8(x-4)}\)
To determine the slope, it's important to know the form of the equation first.
There are 3 forms that you should be familiar with.
The three forms of equations of a straight line are:
Slope Intercept (y = mx + b)Point slope (y-y₁) = m(x - x₁)Standard form (ax + by = c)This equation matches point slope perfectly.
The question becomes, how do you work with point slope to find slope?
Point slopeIn point slope, m is the slope and (x₁, y₁) is a point on the line.
Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.
Hence, the slope is -8.∂²p/∂r² + 1/r ∂p/∂r = ϕμC/k ∂p/∂t
derivation of equations
1-partial derivative diffusivity equation spherical flow
2- partial derivative diffusivity equation hemi- spherical flow
Answers
The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.
1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.
2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.
1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.
2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.
In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.
These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.
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