compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = log(x − y)
Answers
The second partial derivatives of the function are:
∂²f/∂x² = -1/(x - y)²
∂²f/∂x∂y = ∂²f/∂y∂x = 1/(x - y)²
∂²f/∂y² = 1/(x - y)²
What are the second partial derivatives of the function f(x, y) = log(x - y)?To compute the second partial derivatives of the function f(x, y) = log(x - y), we'll differentiate the function twice with respect to each variable. Let's begin:
First, we differentiate f(x, y) = log(x - y) with respect to x:
∂f/∂x = 1/(x - y)
Now, we differentiate ∂f/∂x with respect to x:
∂²f/∂x² = -1/(x - y)²
Next, we differentiate f(x, y) = log(x - y) with respect to y:
∂f/∂y = -1/(x - y)
Now, we differentiate ∂f/∂y with respect to y:
∂²f/∂y² = 1/(x - y)²
Finally, we compute the mixed partial derivatives:
∂²f/∂x∂y = ∂²f/∂y∂x = 1/(x - y)²
Therefore, the second partial derivatives of the function f(x, y) = log(x - y) are:
∂²f/∂x² = -1/(x - y)²
∂²f/∂x∂y = ∂²f/∂y∂x = 1/(x - y)²
∂²f/∂y² = 1/(x - y)²
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Related Questions
Given the system of equations below. Use the Inverse of the matrix method to solve. x+2y+3z=11
2x+4y+5z=21
3x+5y+6z=27
Answers
The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.
The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.
Here, we will solve this system of equations using inverse of the matrix method as follows:
We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].
The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33] where,
d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,
d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,
d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,
d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,
d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,
d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,
d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,
d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,
d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.
We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]
Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]
Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.
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Help please thank you !
Answers
Answer:
3
Step-by-step explanation:
2/36=x/54
Cross multiply and find x
Answer:
it is 3 cups!
Step-by-step explanation:
36+18=54
2 cups were used for 36, 3 cups were used for 54 :)
HELLPPPPPLSSSS SOMSE
Answers
Answer:
Option F
Step-by-step explanation:
F). x + y = 3 -------(1)
x - 3y = -2 --------(2)
Equation (1) minus equation (2)
(x + y) - (x - 3y) = 3 - (-2)
4y = 5
y = 1.25
Hence, y is positive.
G). x + y = 3 --------(1)
x + y = -2 --------(2)
Both the equations represent parallel lines.
There are no solutions of the given equations.
H). x - 3y = -2 -------(1)
x + y = -2 -------(2)
Equation (2) minus equation (1)
(x + y) - (x - 3y) = -2 - (-2)
4y = 0
y = 0
Since, 0 is neither positive nor negative, y will be neither positive nor negative.
J). x + y = 3 -------(1)
x - y = 3 --------(2)
Equation (1) - Equation (2)
(x + y) - (x - y) = 3 - 3
2y = 0
Hence, y is neither negative nor positive.
Therefore, Option F is the answer.
Use the drawing tool(s) to form the correct answers on the provided number line.
Yeast, a key ingredient in bread, thrives within the temperature range of 90°F to 95°FWrite and graph an inequality that represents the temperatures where yeast will NOT thrive.
Answers
The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F
Writing an inequality of the temperatures where yeast will NOT thrive.from the question, we have the following parameters that can be used in our computation:
Yeast thrives between 90°F to 95°F
For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range
Using the above as a guide, we have the following:
T < 90°F or T > 95°F.
Where
T = Temperature
Hence, the inequality is T < 90°F or T > 95°F.
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Use the number line to answer the following 2 22 questions. How many groups of 5 3 3 5 start fraction, 5, divided by, 3, end fraction are in 1 11? groups Evaluate. 9 ÷ 5 3 = 9÷ 3 5 =9, divided by, start fraction, 5, divided by, 3, end fraction, equals
Answers
The value of 9 ÷ 5 3 (9 divided by 5 divided by 3) is 1 remainder 1.To determine how many groups of 5 3 3 5 (5 divided by 3) are in 1 11, we can use the number line to visualize the division.
Starting at 0 on the number line, we can count in increments of 5 3 3 5 (5 divided by 3) until we reach or exceed 1 11.
On the number line, we can observe that there are two groups of 5 3 3 5 (5 divided by 3) that fit into 1 11. This means that 1 11 can be divided into two groups of 5 3 3 5.
Therefore, the answer to the question "How many groups of 5 3 3 5 (5 divided by 3) are in 1 11?" is 2.
Now, evaluating the expression 9 ÷ 5 3 (9 divided by 5 divided by 3), we perform the division from left to right:
9 ÷ 5 = 1 remainder 4
Then, taking the remainder 4 and dividing by 3:
4 ÷ 3 = 1 remainder 1.
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what does x times y plus x equal?
Answers
x times y plus x is equal to
xy + x
= x(y + 1)
Hope it helps...Answer:
x (y + 1)
Step-by-step explanation:
x times y plus x
= x × y + x
= xy + x
= x (y + 1)
Hope it helps ⚜
it’s cut off but it says “about how many of them would you expect to be marked with a white dot.”
Answers
Answer:
Assuming that the person does not account for probability changes when counters are not replaced, the answer is 20 counters.
Step-by-step explanation:
Please refer to the picture above.
Disclaimer: Probability is not used to deduce the question. The knowledge of fraction is used instead to avoid excess complexity.
Assuming the number of dabbed counters follow the ratio of 1/4 as deduced from the number of dabbed counters in 200 counters, you would expect the number of dabbed counters in 80 counters to follow the same ratio of 1/4. Hence the answer is 20.
Please help!!
Joanne earns £7.25 an hour plus £2 per mile she has had to drive to work.
Write a formula for how much Joanne earns (E) in terms of hours (h) and miles (m).
Answers
Answer:
E=(7.25h)+2m
Step-by-step explanation:
h is the number of hours worked and we know Joanne earned 7.25 per hour so we have 7.25h, every hour she earns 7.25. M is the number of miles She drives and we know she is paid 2 for every mile so 2m. E is the total amount she earns so it is equal to everything else
help me pleaseeeeeeEEEEEE
Answers
16. 23=3+4*5
Arjun begins the calendar year with $4000 in his bank account. he earns 9% simple interest annually. after how many years will the valance of the account be $6500?
Answers
The number of years that it will take for the Valence of the account to be $6500 = 6.9 years
What is annual simple interest?Annual simple interest is defined as the amount of money that is being paid to an individual who invested a specific amount of money for a period of time.
The principal amount = $4000
The rate for earnings= 9%
The simple interest= $6500 - 4000 = 2500
Time = X
Using the formula:
Simple interest = P ×T×R/100
Make T the subject of formula;
T = Simple interest × 100/ P × R
T = 2500 × 100/ 4000× 9
T = 250000/36000
T = 6.9 years
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find the missing side of the triangle
Answers
Answer:
x= 8 km
Step-by-step explanation:
measurement used:
When getting measurement the missing side occupies 1 more than a half of 15km
Answer:
x = 8km
Step-by-step explanation:
Use Pythagorean Theorem:
c2 = a2 + b2
In the diagram given, the hypotenuse (c) is 17 so substitute these values into the equation
17^2 = x^2 + 15^2
Take 15 to the power 2, to the other side.
17^2 - 15^2 = x^2
Solve to get
64 = x2
Square root both sides so
x = 8
In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither.
Find probability that a student chosen at random has a cat or a dog.
Answers
The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.
Main body:
According to the question, the total number of students is; 25.
15 of them have a cat
16 of them have a dog
while, 3 of them have neither
where, x = number if students who own a cat and a dog.
Consequently, the total number of students who own a cat, a dog, both or neither is as follows;
15-x + x + 16-x + 3 = 25.
-x = 25 - 34
In essence, x = 9
the number of students who own a cat and a dog is 9.
Therefore, probability that a student chosen at random has a cat and a dog is therefore;
P(cat and dog) = 9/25.
Therefore probability that a student chosen at random has a cat or a dog is 22/25.
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Urgent please help, will give brainliest
Answers
Answer:
the answer is x=9
Step-by-step explanation:
Step-by-step explanation:
the answer was x=9 wish you luck on your homework and tests
math help pls!!
i have no clue how to do this
Answers
Answer:
I THINK it's A
Step-by-step explanation:
Natalie can bike 10 kilometers per hour faster than Aaron. By the time
Natalie travels 60 kilometers, Aaron has gone 40 kilometers. Find the speed
of Natalie and Aaron.
Answers
Mary wants to fence in a RECTANGULAR part of her backyard. In order to determine the amount of fencing that she should purchase, Mary should calculate the ___________ of this part.
A) area
B) volume
C) capacity
D) perimeter
Answers
Answer:
D
Step-by-step explanation:
cause Mary needs to know how much fencing to get.
A student observes the phases of the moon over the course of 3 months and records observations with pictures each day.
Which option best explains whether or not this approach is an authentic scientific investigation?
This is an authentic investigation because the phases of the moon are changing each day.
This is not an authentic investigation because science requires that you follow the scientific method correctly.
This is an authentic investigation because science does not always have to follow the scientific method.
This is not an authentic investigation because it does not change any variables.
^_____^ (～￣▽￣)～ Please HeLp
Answers
That's great! Observing and recording the phases of the moon over several months can be an interesting project.
Capture the moon's image: Using a camera or smartphone, take a picture of the moon on a daily basis. Aim for clear and focused shots that capture the moon's details.
Present the findings: The student can create a report or presentation summarizing their project, including the methodology, observations, and conclusions. They may also include a selection of the most representative pictures to showcase the changes in the moon's appearance.
Remember, this project requires patience and consistency in taking pictures each day. By documenting the moon's phases over three months, the student will gain a deeper understanding of this celestial phenomenon and its cyclical nature.
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A locker measurement at the bottom as 2 one by 6 ft 2, side as 1 and a half ft, and length as 2 2 by 3 ft.
*Picture not drawn to scale
What is the volume of the file cabinet?
Answers
The volume of file cabinet is equal to 26 / 3 cubic feet.
How to determine the volume of the file cabinet
The statement let us infer that file cabinet has the form of right prism with rectangular base, whose formula is shown below:
V = b · h · l
Where:
V - Volume, in cubic feet.b - Base width, in feet.h - Height, in feet.l - Base length, in feet.If we know that b = 2 1 / 6 ft (13 / 6 ft), h = 1 1 / 2 ft (3 / 2 ft) and l = 2 2 / 3 ft (8 / 3 ft), then the volume of the file cabinet is:
V = (13 / 6 ft) · (3 / 2 ft) · (8 / 3 ft)
V = 26 / 3 ft³
RemarkStatement present an anomalous character "2", correct statement is introduced below:
A locker measurement at the bottom as 2 1 / 6 ft wide, 1 1 / 2 ft high and 2 2 / 3 ft long.
Picture is missing but question can be solved by inferential approach.
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PLSSS HELP ILL GIVE BRAINLIEST TO THE RIGHT ANSWER
Answers
Answer:
56
Step-by-step explanation:
The simplest way to do this is to divide 3 by 21 to get 7. This means that it takes $7 to buy one T-shirt. If you multiple 8 X 7, you get 56. This mean that the correct answer is A. $56.00
Hope it helped and have a great day :)
Charlotte wants to know which website gains more new subscribers per amount of content. 1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A Number of new subscribers divided by number of writers (Choice B) B Number of new subscribers divided by number of likes (Choice C) C Number of new subscribers divided by number of posts (Choice D) D Number of new subscribers divided by number of words 2) Determine which website gains more new subscribers per amount of content according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, website A gains more subscribers per amount of content. (Choice B) B Yes. According to both definitions, website B gains more subscribers per amount of content. (Choice C) C No. The definitions have opposite results.
Answers
Answer:
1)
Number of new subscribers divided by number of posts.
Number of new subscribers divided by number of words.
2)
No. The definition have opposite results
Step-by-step explanation:
Khan academy said it was right tehee
Answer:
Step-by-step explanation:
number of new subscribers divided by posts
number of new subscribers divided by the number of words
no the definitions have opposite results.
Which of these triangles are translations of Triangle A?
Select all that apply.
А
E
D
B
F
С
please help
Answers
Answer:
B and D
Step-by-step explanation:
A translation of a triangle is moving it up down or side to-side on the axis, not changing the shape flipping it or the orientation,so the translations of a would be B and D!
Hoped this helped, have a good one!
Answer:
B, D
Step-by-step explanation:
Fill in the gaps to factorise this expression.
x²
x +5x – 14 = (x− _)(x + _)
Answers
Answer:
the answer is
x +5x – 14 = (x− 2 )(x + 7)
In 1992, the moose population in a park was measured to be 3590. By 1999, the population was measured again to be 4500. If the population continues to change linearly
A.) Find a formula for the moose population, P, in terms of t, the years since 1990.
P(t)= ____
B.) What does your model predict the moose population to be in 2006?
Answers
Answer:
A.) P(t) = 130t +3330
B.) P(16) = 5410
Step-by-step explanation:
Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear modelWe can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be ...
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find ...
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) PredictionThe value of P(16) will be ...
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
__
Additional comment
The value of t is years since 1990, so the relevant values are ...
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
Values of moose population by linear model A.) P(t) = 130t +3330 B.) P(16) = 5410
What does the term "linear model" mean?
In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. A linear model is not just a straight line or its higher dimensional equivalent.Given the ordered pairs (t, P(t)) = (2, 3590) and (9, 4500), you want a linear model that describes the relation. You also want the value of P(16).
A.) Linear model
We can write the formula for P(t) starting with the point-slope equation for P in terms of t. To do that, we need the slope:
m = (P2 -P1)/(t2 -t1)
m = (4500 -3590)/(9 -2) = 910/7 = 130
The point-slope equation will be
P -P1 = m(t -t1)
P -3590 = 130(t -2)
Solving for P, we find
P = 130t -260 +3590 . . . . . eliminate parentheses, add 3590
P(t) = 130t +3330
B.) Prediction
The value of P(16) will be
P(16) = 130(16) +3330 = 2080 +3330 = 5410
The moose population is predicted to be 5410 in 2006.
(B) The value of t is years since 1990, so the relevant values are
1992: t = 1992 -1990 = 2
1999: t = 1999 -1990 = 9
2006: t = 2006 -1990 = 16
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Some students washed 24 cars in 2 hours.
How many cars can they wash in 15 hours?
a 12
b 48
c 180
d 360
Answers
Answer:
option C. 180 cars
Step-by-step explanation:
24 = 2
x = 15
cross multiply
2x = 24 × 15
2x = 360
x = 360/2
x = 180
Answer:
180
Step-by-step explanation:
What is the equation of the line from the graph?
Answers
Answer:
y=3
Step-by-step explanation:
All points have the same y coordinate. Or
A line parallel to the x axis has slope 0, so it's y= 0x +3 that becomes y=3
Answer: Y=3
Step-by-step explanation:
Dr.Marks is studying 3 blacktop sharks and 4 tiger sharks. What is the total lenght of the 7 Sharks show your stategty
Answers
I'm not sure,, is there a paper or written length of the sharks,, or is it going off of searching it on the internet?
You haven't given the length of each shark so we can't really calculate the total length of the 7 sharks but I'll just give a strategy to find it.
let \(x\) be the length of the blacktop sharks and let \(y\) be the length of the tiger sharks. In order to figure out their total length, you can use this formula:
\(3x\ +\ 4y\ =total\ length\ of\ sharks\)
cuál es el valor total de 9?
Answers
Answer:
(0.98768834,0.15643446)
Step-by-step explanation:
yo creo
Question 5(Multiple Choice Worth 2 points)
(Real-World Proportional Problems MC)
A small business that makes candles uses a proportional amount of essential oil and wax. For 132 ounces of wax, they use 11 ounces of essential oil.
How many ounces of essential oil is needed for 648 ounces of wax?
54 ounces
58.9 ounces
121 ounces
15.9 ounces
Answers
Based on the amount of essential oil and wax that is needed for the business to make candles, the ounces of essential oil needed for 648 ounces of wax is 54 ounces
How to find the ounces needed?The ounces needed to make candles between essential oils and wax are proportional. This means that they can be expressed in ratio form.
The ratio would be:
132 ounces of wax : 11 ounces of essential oils
If there are 648 ounces of wax, the number of ounces of essential oil needed is:
= (648 x 11) / 132
= 7,128 / 132
= 54 ounces of essential oils
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Pt.2 Please show your work
Find the slope when given the following points
(-3, 2) and (1, 0)
Answers
Answer:
slope is = -1/2
Step-by-step explanation:
y2-y1= 2-0= 2
x2-x1= -3-1= -4
2/-4= -1/2
m=___
x-x
it would be 2-0 OVER (fraction formula shown above) -3-1
so your end fraction would be 2/-4 which would be -0.5
so, your slope would be -0.5
when the increase in demand is greater than the decrease in supply, the equilibrium price _____ and the equilibrium quantity _____.
Answers
Answer:
increasedeacreasesWhen the increase in demand is greater than the decrease in supply, the equilibrium price rises and the equilibrium quantity increases.
What is economic equilibrium?
Economic equilibrium, as used in economics, is a state in which forces such as supply and demand are in balance and where, in the absence of external influences, the values of economic variables will remain constant.
The equilibrium quantity rises if the rise in demand outweighs the fall in supply. The equilibrium quantity falls if the rise in demand is smaller than the fall in supply. Equilibrium price rises in each scenario.
The supply and demand curves move in opposition to one another. However, the supply curve shifted to the left while the demand curve shifted to the right (signalling a rise in demand) (indicating a decrease in supply).
In the case increase in demand > decrease in supply
In this instance, the supply curve's leftward movement is proportionally less than the rightward change of the demand curve. So, the price and the equilibrium quantity both increase.
Therefore, the equilibrium price and quantity increases.
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