To confirm that the inverse of a square matrix A has been found correctly, it should be verified that AA⁻¹ = I (identity matrix) .
The Inverse of a square matrix A (denoted by A⁻¹) , is a matrix that satisfies the equation AA⁻¹ = AA⁻¹ = I, where I is the identity matrix.
The identity matrix is a square matrix of size n×n with ones on the main diagonal and zeros everywhere else.
If A⁻¹ has been computed correctly, multiplying it by A should result in the identity matrix. That is, AA⁻¹ = I. This confirms that the inverse has been found correctly and that the inverse property holds for the matrix A.
The given question is incomplete , the complete question is
let A be an n×n matrix. if A⁻¹ = (1/detA)×adjA is computed, what should AA⁻¹ be equal to in order to confirm that A⁻¹ has been found correctly ?
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Consider the following linear programming problem:Max Z = $300x1 + $100x2 s.t. 30X1 + 70x2 ≤ 210 20x1 + 10x2 ≤ 100 X1, X2 ≥ 0 What is maximum Z and the value of X1 and X2 at the optimal solution? a. Z = 1500; X1 = 5; and X2 = 0b. Z = 300; X1 = 0; and X2 = 3;c. Z = 1250: X1 = 3; and X2 = 3.5; d. Z=3000, X=-10, and X2 = 0: e. None of the above
Answer:none of the above
Step-by-step explanation:
The maximum Z is 1800 and the value of X₁ and X₂ at the optimal solution : X₁ = 5 and X₂ = 3.
The constraints for the linear programming problem:
30X₁ + 70X₂ ≤ 210
20X₁ + 10X₂ ≤ 100
X₁, X₂ ≥ 0
First we draw the graph for equations 30X₁ + 70X₂ = 210 and 20X₁ + 10X₂ = 100
Consider equation 30X₁ + 70X₂ = 210
For X₁ = 0,
70X₂ = 210
X₂ = 3
For X₂ = 0,
30X₁ = 210
X₁ = 7
This means, the line 30X₁ + 70X₂ = 210 passes through (0, 3) and (7, 0) as shown in the following graph.
So, 30X₁ + 70X₂ ≤ 210 includes the region below the line.
Consider equation 20X₁ + 10X₂ = 100
For X₁ = 0,
10X₂ = 100
X₂ = 10
For X₂ = 0,
20X₁ = 100
X₁ = 5
This means, the line 20X₁ + 10X₂ = 100 passes through points (0, 10) and (5, 0) as shown in the following graph.
so, an inequality 20X₁ + 10X₂ ≤ 100 includes the region below the line.
From the figure, (0, 3) and (5,0) are feasible corner points.
Thus the optimal solution is: X₁ = 5 and X₂ = 3
For X₁ = 5 and X₂ = 3,
Z = 300X₁ + 100X₂
Z = 300(5) + 100(3)
Z = 1500 + 300
Z = 1800
Therefore, the maximum value of Z is 1800
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Joey drive a golf cart when he need to monitor ecurity of hi neighborhood. He can cove over the 40 mile of treet in hi neighborhood in 2 hour. What unit rate expree the peed of Joey golf cart per hour?
20 miles/hours best express the speed of Joey's golf cart.
speed = time + distance
That is, speed = time + distance. To put it another way, distance divided by speed equals time.
You can figure out the third input if you know the first two.
For example, if a car drives 120 miles in two hours,
Then the speed is 120/2 = 60 miles per hour.
As per the data given,
We have,
So, the value of the speed of Joey's golf cart can be expressed as a unit rate by dividing the total distance he covers by the time it takes him to cover that distance.
So, the value of the unit rate will be
=40 miles/2 hours = 20 miles/hour.
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Find the smallest whole number taht is divisible by both 112 and 525
Answer:
8400
Step-by-step explanation:
The smallest whole number that is divisible by both 112 and 525 is their LCM.
112 = 2 × 2 × 2 × 2 × 7
525 = 3 × 5 × 5 × 7
Therefore, LCM = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 8400
So it is 8400.
Hope it helps.
If you have any query, feel free to ask.
problem 3 complex arithmetic: perform the following complex arithmetic (make sure to show your steps or how you used matlab or a calculator to help you in computation)
a. 3+j(5j/2+3j)
b. (4+2j)(3e^j.2π/4)+1/3+2j+5e^j0.5
The solution of the complex numbers are
a. 3+j(5j/2+3j) = j * (3 + 8i)
b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5[tex]e^{j0.5}[/tex] = 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)
Complex arithmetic involves working with complex numbers, which are numbers that have both real and imaginary parts.
a. 3+j(5j/2+3j)
To perform this operation, we first need to simplify the expression inside the parentheses: 5j/2 + 3j. We can simplify this expression by adding the two imaginary parts together:
5j/2 + 3j = (5 + 3)j = 8j
Next, we substitute this result back into the original equation:
3 + j(8j) = 3 + j(8 * j) = 3 + j * 8i
Now we can simplify this expression by multiplying the real part 3 with j, and adding it to the real part of the expression:
3 + j * 8i = 3j + j * 8i = j * (3 + 8i)
So the final result is: j * (3 + 8i)
Next, let's look at the second part of the problem:
b. (4+2j)([tex]3e^{j.2\pi/4}[/tex])+1/3+2j+5e^j0.5
We can simplify this expression by using the properties of complex numbers and exponential functions:
(4 + 2j) * ([tex]3e^{j.2\pi/4}[/tex]) = (4 + 2j) * (3 * (cos(2π/4) + j * sin(2π/4)))
= (4 + 2j) * (3 * (cos(π/2) + j * sin(π/2)))
= (4 + 2j) * (3 * j)
= (4 + 2j) * 3j
= 12j² + 6j³ * 2j
= 12j² + 12j³
Next, we substitute this result back into the original equation:
12j² + 12j³ + 1/3 + 2j + [tex]5e^{j0.5}[/tex]
Next, we simplify the remaining terms:
=> 3 + 2j + [tex]5e^{j0.5}[/tex] = 1/3 + 2j + 5 * (cos(0.5) + j * sin(0.5))
=> 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)
So the final result is: 12j² + 12j³ + 1/3 + 2j + 5 * cos(0.5) + 5 * j * sin(0.5)
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Which list shows the units of measure in order from smallest to largest?
A) kilometer, meter, centimeter
B) centimeter, kilometer, meter
C) kilometer, centimeter, meter
D) centimeter, meter, kilometer
Answer: D
Step-by-step explanation:
____ 13. Use Scenario 3-2. If heart disease death rate were expressed as deaths per 1,000 people instead of as deaths
per 100,000 people, how would the correlation r between wine consumption and heart disease death rate
r would not change
The correlation between two variables is an important measure that helps us understand the relationship between them. In Scenario 3-2, if the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would not change the correlation (r) between wine consumption and heart disease death rate.
The correlation coefficient (r) measures the strength and direction of the relationship between two variables. If the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would change the units in which the death rate is expressed, but it would not change the underlying relationship between wine consumption and heart disease death rate.
In other words, regardless of the units in which the death rate is expressed, the correlation between wine consumption and heart disease death rate would remain the same. This is because the correlation measures the relationship between two variables, not the units in which they are expressed. It is important to note that expressing the death rate in different units may make it easier or more difficult to understand the relationship between two variables, but it does not change the underlying correlation.
In conclusion, the correlation (r) between wine consumption and heart disease death rate would not change if the death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people.
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Two students expanded the expression (2 - 3x)²
One student got the answer 4 – 12 x + 9x² and the other student got the answer 4 + 9x². Which student is correct? Explain your reasoning.
Based on the expanded the expression (2 - 3x)², the student who got the answer 4 – 12 x + 9x² is the first student.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two (2).
In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.
By applying the following binomial expression to the given quadratic function, we have:
(a - b)² = a² - 2ab + b²
(2 - 3x)² = 4 - 2(2)(3x) + 3x²
4 - 2(2)(3x) + 3x² = 4 - 12x + 9x².
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Randy purchae 7/12 of a box of grape. Detiny bought 1/6 of the ame box. Kev bought 1/4 of the box. How much of the box wa left over for melanie?
Answer:
None
Step-by-step explanation:
[tex]1-\frac{7}{12}-\frac{1}{6}-\frac{1}{4}=1-\frac{7}{12}-\frac{2}{12}-\frac{3}{12}=1-\frac{12}{12}=0[/tex]
Answer:
Step-by-step explanation:
an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?
What is the area of a circle with a diameter of 12 meters? Leave the answer in terms of π. 6π square meters 12π square meters 36π square meters 144π square meters
The area of the given circle is 36π square meters.
What is the area of a circle?
The region encircled by a circle is known as the area of a circle in geometry. The area of a circle is π multiplied by the square of the radius r. Here, the Greek letter π stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
Given,
Diameter of the circle = 12 metres
Radius of the circle = Diameter/2 =12/2 = 6 metres
Area of circle = πr² = π ×6² = 36 π square meters
Therefore the area of the given circle is 36π square meters.
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suppose you repeatedly and independently roll a pair of fair dice and each time record the sum of the dice. what is the probability that an outcome of 5 appears before an outcome of 7?
The probability that an outcome of 5 appears before an outcome of 7 is 1.
Probability of 5 Before 7The probability of getting a 5 or a 7 in one roll of two fair dice is 6/36 = 1/6. The probability of getting a 5 before a 7 is equal to the sum of the infinite geometric series with the first term being 1/6 and common ratio 5/6:
1/6 + (5/6) * (1/6) + (5/6)² * (1/6) + ... = 1/6 / (1 - (5/6)) = 1/6 / (1/6) = 1.
So, the answer is 1.
The method used here is called the Geometric Series formula. It is used to calculate the sum of an infinite geometric series, which is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. The formula for the sum of an infinite geometric series is:
S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
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A class of pre-schoolers were asked if they liked the colors blue and green. 17 liked blue and 16 liked green. If 12 liked both and 5 liked neither, how many students were in the class?
A. 24
B. 50
C. 26
D. 48
The number of students were in the class is 26
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Let's call the total number of students "n".
Then:
n - 5 students liked either blue or green or both,
12 students liked both blue and green,
17 - 12 = 5 students liked only blue,
16 - 12 = 4 students liked only green.
So:
n - 5 = 5 + 4 + 12
n = 26
There were 26 students in the class.
Therefore, The number of students were in the class is 26
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Find the value of each variable urgentttt
The values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
sin 45° = √2/2 and cos 45° = √2/2
considering the right triangle;
sin 45° = x/6 {opposite/hypotenuse}
√2/2 = x/6
x = 6 × √2/2
x = 3√2
cos 45° = y/6 {adjacent/hypotenuse}
√2/2 = y/6
y = 6 × √2/2
y = 3√2
Therefore, the values of x and y are the same with x = 3√2 and y = 3√2 derived using the trigonometric ratio of sine and cosine of the angle 45.
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what is the circumference of a circle with an area of 200.96cm use 3.14 for pi
Answer:
50.25
C= 2πA= 2·π·200.96 ≈50.25274
Answer: 50.25
C=2πA=2·π·200.96≈50.25274
Four buses were filled with children and 20 children rode in cars for a field trip. Write an expression for how many children went on the field trip.
Answer:
4c+20
Step-by-step explanation:
Gabby and their four sisters combine the money their parents gave them.What is the maximum number of pizzas they can order to stay within their budget
The four sequential sides of a quadrilateral have
lengths a = 5.3, b = 7.4, c = 10.5, and d = 11.2 (all
measured in yards). The angle between the two
= 95°.
smallest sides is a =
What is the area of this figure?
area=yd^2
On solving the provided question we can say that this figure is a quadrilateral and area will be = A = 38.5199475951548 units
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
x = √(a2 + b2 - 2ab cos X) = √(3.62 + 5.12 - 2*3.6*5.1 cos 108°) = 7.09345501384537
Then, we can get the area of the second triangle either by solving for one of the angles using the cosine law and using 1/2 ab sin C or use Abel's law.
Abel's law for variety.
p=(8,5 + 10.2+ 7.09345501384537)/2
A =√((p(p-a)(p-b)p-c) = 29.7892487755653
A = 8.73069881958951 + 29.7892487755653 = 38.5199475951548
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Ron has a bag of marbles that contains blue, orange, and green marbles. The ratio of blue to orange to green is 4:2:1. If the bag contains 8 blue
marbles,
marbles are green.
Answer:
2 green
Step-by-step explanation:
The ratio of blue to green is 4 to 1 <===== there is 1/4th asmany green as blue.... so if there are 8 blue, there are only 2 green
Mark lives 5,000
5
,
000
feet from school. He walks to school at a steady rate of 250
250
feet per minute. Use that information and the diagram to complete the table below.
The required complete table regarding the distance traveled has been shown.
From the given condition, let y be the distance left and x be the time,
According to the question an equation model is given as,
Distance traveled = 5x
Distance remaining to travel = y = 5000 - 250x
Now,
Put x = 5
Distance traveled = 250x
= 250(5) = 1250
Distance remaining to travel = y
y = 5000 - 1250
y = 3750 ft
Similarly,
At
x = 20
Distance traveled = 5000
X = 10
Distance remaining = 2500
Thus, the required complete table has been shown.
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joseph and nichole are comparing student grade performances between their two class sections. based on the histograms of their grades, which class section has a larger standard deviation?
The class section with the larger standard deviation will be the one with the larger variance.
The standard deviation is a measure of how much variation exists in a set of data. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. To calculate the standard deviation for Joseph and Nichole's class sections, we need to first calculate the variance for each class. To do this, we need to subtract the mean of each class from each data point, square the result, and then average the squared differences. The larger the variance, the larger the standard deviation will be. Therefore, the class section with the larger standard deviation will be the one with the larger variance.
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A $145 scooter is on sale at 20% off. Find the sale price.
The discount amount is $29. The sale price of the scooter is $116.
What is the percentage?
A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.
Given that, the market price of a scooter is $145.
The discount on the scooter is 20%.
The discount amount is $145×20%
= 145 × (20/100)
= 145 × (1/5)
= 29
The sale price is Marke price - discount
= $(145 - 29)
=$116
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Solve using the quadratic formula
The value of x in the equation is x = -1 and x = -4.67
How to solve using the quadratic formulaFrom the question, we have the following parameters that can be used in our computation:
3x^2 + 13x + 4 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 3, b = 13, c = 4
So, we have
x = (-13 ± √(13² - 4 * 3 * 4)) / 2 * 3
x = (-17 ± √(169 +- 48)) /6
x = (-17 ± 11) /6
Expand
x = (-17 + 11)/6 and x = (-17 - 11)/6
Evaluate
x = -1 and x = -4.67
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A model boat is 4 inches long. The scale factor is 24:1 How long is the actual boat?
According to the problem statement the actual boat is 96 inches long.
What is boat?Boat in math is a geometric shape that is formed when two perpendicular lines intersect at two points, forming two pairs of equal-length sides that cross each other in the middle. It looks like the bottom of a boat with two sides meeting at the center. In mathematics, the boat shape is often used to represent an equation or a function. It is also used to illustrate the concept of a mathematical set, or group of related objects. The boat shape can also be used to graphically represent relationships between two or more variables.
The actual boat is 96 inches long. The scale factor of 24:1 means that for every 1 inch on the model, there are 24 inches on the actual boat. Therefore, for the 4 inch model boat, there are 4 × 24 = 96 inches on the actual boat.
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show (separately) how the integral and differential forms of the continuity equation can be simplified for application to fluid problems involving: (a) steady flow, (b) steady, incompressible flow,
A two-dimensional reducing bend has a linear velocity profile at section The flow is uniform at sections The fluid is incompressible and the flow is steady.
As given in the problem statement,flow is in compressible and flow is internal flow
Re=5*10^5
Using equation
V=Re/density*diameter of pipe
Maximum velocity=98.98 m/s
why are the Navier-stokes equations difficult to solve?
Being nonlinear makes the Navier-Stokes equation challenging to solve. Although it's frequently used, this word has a specific meaning in this context. A linear equation can have multiple simple solutions, all of which combined can yield a complex answer.
The Navier-Stokes equations lack an additional equation to determine the pressure levels at various locations. A partial differential equation used to model the flow of incompressible fluids is the Navier-Stokes equation in fluid mechanics.
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how big is the aperture in a 35-mm lens set to a stop of f/2?
The diameter of the aperture in a 35-mm lens set to a stop of f/2 is 17.5mm.
In this question, we are asked to determine the size of the aperture or we can say Diameter of aperture
Given the focal length of lens (f) = 35 mm
The lens is set to a stop f/2
We need to find the size of the aperture
Let d be the diameter of the aperture.
So, d = f/2 --(1)
Putting the value of f = 35 mm in equation (1). We get,
d = (35 mm)/2
d = 17.5 mm
Hence, the Size (diameter) of the aperture is 17.5 mm
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Find the compound interest and the total amount after 4 years and 6 months if the interest is compounded annually.
Principal = ₹1{,}00{,}000=₹1,00,000equals, ₹, 1, comma, 00, comma, 000
Rate of interest = 10 \%=10%equals, 10, percent per annum
Total amount ==equals ₹ Compound interest ==equals ₹
The compound interest is ₹46,148.68 and the total amount after 4 years and 6 months is ₹1,46,148.68.
How to Find Compound Interest?The formula to calculate compound interest is:
A = P * (1 + r/n)^(nt)
Where:
A is the total amount after t years
P is the principal amount
r is the interest rate per annum
n is the number of times the interest is compounded per year
t is the number of years
In this case:
P = ₹1,00,000
r = 10% per annum = 0.10
n = 1 (since the interest is compounded annually)
t = 4 years and 6 months = 4.5 years
A = ₹1,00,000 * (1 + 0.10/1)^(1 * 4.5) = ₹1,00,000 * 1.461486788
A = ₹1,46,148.68
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a newspaper kiosk sells 10 varieties of newspapers from around the world. the average daily sales for some of the varieties are as follows:english language newspapers eight papers, sells 25 of each paper each dayfrench language newspapers two papers, sells one of each paper each daykorean language newspapers one paper, sells 16 each dayjapanese language newspapers eight papers, sells 16 of each paper each day russian language newspapers one paper, sells 22 each day how many of these newspapers are sold each day?
The total number of newspapers sold each day is: 200 + 2 + 16 + 128 + 22 = 368.
To find the total number of newspapers sold each day, we need to find the sum of the daily sales of each variety:
English language newspapers: 25 * 8 = 200
French language newspapers: 1 * 2 = 2
Korean language newspapers: 16 * 1 = 16
Japanese language newspapers: 16 * 8 = 128
Russian language newspapers: 22 * 1 = 22
Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
In mathematics, addition is the process of joining two or more integers. The numbers being added are known as addends, and the result or final response obtained after the procedure is known as the total.
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A fish tank holds at most 125 gallons of water. The tank already has 20 gallons of water in it when Ian begins to fill it at a rate of 8 gallons per minute. What is the longest time that Ian has to wait to fill the tank? You will get a decimal answer.
Step-by-step explanation:
To find the longest time that Ian has to wait to fill the tank, we need to find the total time it takes to fill the tank from its current level of 20 gallons to its maximum level of 125 gallons.
First, we need to find the amount of water that needs to be added to the tank by subtracting the current water level from the maximum water level:
125 gallons - 20 gallons = 105 gallons
Next, we need to divide the amount of water that needs to be added by the rate at which Ian is filling the tank to find the time it will take:
105 gallons / 8 gallons per minute = 13.125 minutes
So the longest time that Ian has to wait to fill the tank is 13.125 minutes.
it is required to reduce a pipe diameter of 8 inches to a minimum diameter
The required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.
To maintain a constant flow rate in a pipe with changing diameter, the velocity of the fluid must remain constant. This is known as the principle of continuity, which states that the product of the velocity and the cross-sectional area of a pipe must remain constant.
Given that the diameter of the pipe is reduced from 8 inches to 4 inches, the cross-sectional area of the pipe is also reduced by a factor of 4. Hence, to maintain the same flow rate, the velocity of the fluid must increase by a factor of 4.
Since the fluid is incompressible and Newtonian, the pressure drop can be calculated using the continuity equation and motion equation (Bernoulli's equation).
ΔP = ρ * v² / 2
where ΔP is the change in pressure, ρ is the density of the fluid, and v is the velocity of the fluid.
Plugging in the values, we get:
ΔP = ρ * (v / 4)² / 2 = ρ * v² / 16
So, the required change in pressure to maintain the flow rate in a pipe with a reducing diameter is ρ * v² / 16.
Complete Question:
'It is required to reduce a pipe diameter of 8 inches to a minimum diameter of 4 inches while maintaining a constant flow rate. Assuming the pipe is circular and the fluid is incompressible and Newtonian, what is the required change in pressure to maintain the flow rate?'
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suppose we have two people in the market: a, b. their utility functions are ua=min{x1,x2}, ub=min{x1,x22}. solve their optimal choices and then find market demand.
Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.
In order to find the optimal choices of person A and person B, we need to find the values of x1 and x2 that maximize their respective utility functions.
For person A, their utility function is ua = min{x1,x2}, which means their satisfaction is equal to the minimum value of x1 and x2. The optimal choice for x1 and x2 would be the values that make x1 = x2, because if one value is higher, the minimum will always be the lower value. Hence, person A's optimal choices are x1 = x2.
For person B, their utility function is ub = min{x1,x22}, which means their satisfaction is equal to the minimum value of x1 and x22. The optimal choice for x1 and x2 would be the values that make x1 = x22, because if x1 is higher, x22 will be even higher and the minimum will always be x1. Hence, person B's optimal choices are x1 = x22.
To find the market demand, we need to find the aggregate demand of both person A and person B. The aggregate demand is the sum of the individual demands. The demand for x1 and x2 can be found by adding the individual demands.
Person A's demand for x1 and x2 is the same, x1 = x2, hence the total demand for x1 and x2 is 2x1.
Person B's demand for x1 and x2 is x1 = x22, hence the total demand for x1 and x2 is x1 + x22.
The aggregate demand for x1 and x2 is the sum of both individual demands:
Demand(x1,x2) = 2x1 + x1 + x22
This represents the market demand for x1 and x2.
Therefore, Person A's optimal choices are x1 = x2 and person B's optimal choices are x1 = x22. Also Demand(x1,x2) = 2x1 + x1 + x22 represents the market demand for x1 and x2.
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Find the area of this circle. Use 3 for pi
Step-by-step explanation:
what do you not understand here ?
you got the formula, the numbers for the formula.
since you should use 3 for pi, this is a very simple calculation :
3×15² = 3×225 = 675 ft²
that's it.
