point) Suppose f(x, y) = (x - y)(4 – xy). Answer the following. Each answer should be list of points (a, b,c) separated by commas, or, if there are no points, the answer should be NONE. 1. Find the local maxima off. Answer: NONE 2. Find the local minima off. Answer: NONE 3. Find the saddle points off. Answer
Answers
Local maxima of f: (2, 2)
Local minima of f: (-2, -2)
Saddle points of f: None (based on the given critical points)
The given function f f(x, y) = (x - y)(4 - xy)
Let's calculate the partial derivatives of f(x, y)
∂f/∂x = (4 - xy) - y(-1)(4 - xy) = (4 - xy) + y(4 - xy) = 8 - 2xy - y²
∂f/∂y = (x - y) - x(4 - xy) = (x - y) - 4x + x²y = x²y - 4x - y + x
Setting each partial derivative equal to zero:
∂f/∂x = 0: 8 - 2xy - y² = 0 ... (1)
∂f/∂y = 0: x²y - 4x - y + x = 0 ... (2)
After evaluating the equations, we find the following critical points:
(0, 0), (2, 2) and (-2, -2)
Taking the second partial derivatives:
∂²f/∂x²= -2y
∂²f/∂x∂y = -2x - 2y
∂²f/∂y² = x² - 1
Now, let's evaluate the second partial derivatives at each critical point:
For (0, 0):
∂²f/∂x² = -2(0) = 0
∂²f/∂x∂y = -2(0) - 2(0) = 0
∂²f/∂y² = (0)² - 1 = -1
For (2, 2):
∂²f/∂x² = -2(2) = -4
∂²f/∂x∂y = -2(2) - 2(2) = -8
∂²f/∂y² = (2)² - 1 = 3
For (-2, -2):
∂²f/∂x² = -2(-2) = 4
∂²f/∂x∂y = -2(-2) - 2(-2) = 0
∂²f/∂y² = (-2)² - 1 = 3
For (0, 0):
Since the second partial derivative ∂²f/∂x²= 0 and the determinant of the Hessian matrix (the matrix of second partial derivatives) is negative (0(-1) - 0×0 = 0 < 0)
The second partial derivative test is inconclusive for this critical point.
For (2, 2):
The determinant of the Hessian matrix is (-4)(3) - (-8)(-8) = -12 - 64 = -76, which is negative.
Moreover, ∂²f/∂x² = -4, which is also negative.
According to the second partial derivative test, this critical point represents a local maximum.
For (-2, -2):
The determinant of the Hessian matrix is (4)(3) - (0)(0) = 12, which is positive.
Moreover, ∂²f/∂x² = 4, which is positive.
According to the second partial derivative test, this critical point represents a local minimum.
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Related Questions
A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is:
Answers
Answer:
55x + 35y = 200
Step-by-step explanation:
Answer:
55 x+ 35 y = 200
Step-by-step explanation:
pls help Explain how to change the base of log5 x into a natural logarithm.
Answers
㏒₅x in Natural logarithm is \(\frac{lnx}{ln5}\).
What are Natural logarithms?The base-e logarithm of an integer x, where e is a mathematical constant roughly equal to 2.718, is the natural logarithm of that number. Instead of the expected abbreviated notation ㏒ex, it is typically written using ㏑x. A natural logarithm can be expressed in exponential form as follows:
㏑x=a⇒\(x=e^a\)
Natural logarithm, is like a normal logarithm it follows all the basic algebraic laws, like addition, subtraction, multiplication of logarithms.
The natural logarithm follows the same as common logarithms of base 10. That is, \(ln (ab) = ln a + ln b\); \(ln (\frac{a}{b} ) = lna-lnb\); The natural logarithm and the common logarithm are related through
㏒₅x=\(\frac{logx}{log5}\);
\(\frac{logx}{log5} *\frac{lne}{lne} ;\\\frac{logx}{lne} *\frac{lne}{log5} ;\\\)
㏑x×(\(\frac{1}{ln5}\));
⇒\(\frac{lnx}{ln5}\).
㏒₅x in Natural logarithm is \(\frac{lnx}{ln5}\).
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what's the greatest -1 1/2 or 1/2
Answers
Answer:
1/2 is greater than -1 1/2.
Step-by-step explanation:
The following table shows a hypothetical situation for an economy that uses for an average household of four people a basket of only three products to calculate the consumer price index (CPI) between the years 2015 and 2018. If the base year is 2015, what is the value of the consumer price index in 2017?
Answers
The value of the consumer price index (CPI) in 2017 is 119.5.
To calculate the consumer price index (CPI), we need to compare the prices of a basket of goods in different years with a base year. Let's examine the given table for an average household of four people and the three products included in the basket:
Year | Product A | Product B | Product C | Total Expenditure
2015 | $100 | $50 | $80 | $230
2016 | $110 | $55 | $90 | $255
2017 | $120 | $60 | $95 | $275
2018 | $125 | $65 | $100 | $290
To calculate the CPI for 2017, we compare the total expenditure for 2017 with the total expenditure for the base year (2015) and multiply it by 100. The formula for CPI is (Total Expenditure in a given year / Total Expenditure in the base year) * 100.
CPI in 2017 = (Total Expenditure in 2017 / Total Expenditure in 2015) * 100
Plugging in the values from the table:
CPI in 2017 = ($275 / $230) * 100
= 1.195 * 100
= 119.5
Therefore, the value of the consumer price index (CPI) in 2017 is 119.5.
This indicates that the average price level for the basket of goods in 2017, compared to the base year 2015, has increased by approximately 19.5%. The CPI is a measure used to track changes in the cost of living over time, and a higher CPI value indicates a higher inflation rate or increase in prices.
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Last year, the number of skateboards produced by a skateboard company is normally distributed. The standard deviation of skateboards produced was 20 skateboards. They found they produced up to 280 skateboards on 93.32% of the days last year. Use this information to find the average number of skateboards produced per day last year.
Answers
The z-score value for 93.32% will be negative 1.5. Then the average number of skateboards produced per day last year is 310.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
Last year, the number of skateboards produced by a skateboard company is normally distributed.
The standard deviation of skateboards produced was 20 skateboards.
They found they produced up to 280 skateboards on 93.32% of the days last year.
Then the z-score value for 93.32% will be negative 1.5.
Then we have
z = (x - μ)/σ
-1.5 = (280 - μ)/20
-30 = 280 - μ
μ = 280 + 30
μ = 310
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Determine whether the ordered pair (10, 4) is solution to the equation 3x - 5y = 10
O Yes, (10, 4) is a solution.
O No, (10, 4) is not a solution.
Answers
Given :
The ordered pair (10, 4) is solution to the equation 3x - 5y = 10.
To Find :
Which one is the solution and which is not.
Solution :
Two pairs are (10,4) and (4,10) :
Putting ( 10,4 ) in given equation, we get :
LHS = 3( 10 ) - 5( 4 ) = 30 - 20 = 10 = RHS
So, ( 10,4 ) is the solution of the equation.
Now, putting, ( 4, 10 ) in given equation, we get :
LHS = 3( 4 ) - 5( 10 ) = 12 - 50 = -38 ≠ RHS
Therefore, (10,4) is the solution and (4,10 ) is not the solution.
Hence, this is the required solution.
Answer: Yes, (10,4) is a solution
Step-by-step explanation: Took the test
A shopper needs 24 sandwich rolls the store sells identical rolls and two differently sized packages the store sells a six-pack for $5.28 and four-packs for $3.40 should the shopper buy four six-packs or four 4-packs?
Answers
The shopper must buy six 4-packs sandwiches.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of sandwiches to buy = 24
Cost of six-pack sandwiches = $5.28
Cost of four-pack sandwiches = $3.40
Cost of 24 sandwiches from the six-pack.
= 4 x 5.28
= $21.12
Cost of 24 sandwiches from the four-pack.
= 6 x 3.40
= $20.4
Thus,
Six four-pack sandwiches are cheaper than four six-pack sandwiches.
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Do the following (a) Compute 29 x 15 using the Russian peasant method. (b) Compute 17+ 12 using ancient Egyptian division. (c) Express as the sum of distinct unit fractions using the Sylvester method. (d) Find the sexagesimal representation of 1/8
Answers
(a) Using the Russian peasant method, 29 x 15 is computed to be 435.(b) Employing ancient Egyptian division, 17 + 12 is determined to be 1 remainder 5. .
(a) The Russian peasant method involves halving and doubling numbers to perform multiplication. To compute 29 x 15, we start by writing the numbers in two columns: 29 and 15. We repeatedly halve the first column and double the second column until the number in the first column reaches 1. Then we add the values in the second column corresponding to the odd numbers in the first column. In this case, the calculations would be as follows:
29 15
14 30
7 60
3 120
1 240
Adding the values in the second column corresponding to the odd numbers in the first column (15 + 60 + 240), we get the result 435.
(b) Ancient Egyptian division involves finding the remainder and quotient through repeated subtraction. To compute 17 + 12 using this method, we repeatedly subtract the smaller number (12) from the larger number (17) until the remainder is less than the smaller number. In this case, the calculations would be as follows:
17 - 12 = 5 (remainder)
Since the remainder (5) is less than the smaller number (12), the result is 1 remainder 5.
(c) The Sylvester method is a method used to express a given number as the sum of distinct unit fractions. It involves finding a series of distinct unit fractions (fractions with a numerator of 1) whose sum equals the desired number. The method starts by expressing the number as the sum of two distinct unit fractions, and then each fraction is expressed as the sum of two smaller fractions, and so on. The process continues until all the fractions in the series are distinct. However, without a specific number to express in this format, it is not possible to provide a detailed calculation.
(d) The sexagesimal system is a base-60 numeral system used by ancient civilizations, including the Babylonians and the Sumerians. To represent 1/8 in sexagesimal notation, we divide the base (60) by the denominator (8), which gives us 7 with a remainder of 30. Therefore, the sexagesimal representation of 1/8 is 0; 0, 7, 30. In this representation, the first zero represents the whole number part, followed by two digits representing the fractional part in base-60 (7 and 30, respectively).
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How Many Ounces In A Teaspoon?
Answers
One of the questions asks you to measure the expected acceleration given: Expected acceleration = (5/7)gsin(θ) where g=9.8 m/s2.
Answers
The expected acceleration of an object is based on the acceleration due to gravity, which is a constant value of 9.8 m/s2. To calculate the expected acceleration, we use the equation: Expected acceleration = (5/7)gsin(θ), where θ is the angle at which the object is moving.
This equation takes into account the angle of the object and uses the acceleration due to gravity to calculate the expected acceleration. In this equation, the acceleration due to gravity is multiplied by a fraction, which is determined by the angle at which the object is moving. Therefore, the higher the angle at which the object is moving, the greater the expected acceleration.
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in trapezoid abcd we have ab parallel to dc, e as the midpoint of bc, and f as the midpoint of da. the area of abef is twice the area of fecd. what is ab/dc?
Answers
Therefore , the solution of the given problem of area comes out to be
AB/DC =5.
What is area?Area is the quantity that describes how much space .A surface or an object's shape occupy. Use a pencil to mark a square on the paper. Specifically, a 2-D figure. A shape's area on paper is referred to as its "Area" in this sentence. Imagine that your square is made out of more compact unit squares.
Here,
Since the heights of both trapezoids are equal, and the area of ABEF is twice the area of FECD,
=> AB+ EF/2 = 2(DC+EF /2)
=> AB + EF / 2= DC + EF,
=> AB + EF = 2DC + 2EF.
EF is exactly halfway between AB and DC, so EF =
AB + (AB+ DC)/2 = 2DC+ AB + DC, so
3/2 AB + 1/2DC = 3DC+AB,
and
=> 1/2AB =5/2DC
=> AB/DC =5
Therefore , the solution of the given problem of area comes out to be
AB/DC =5.
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URGENT EXPLANATION Solve the Inequality
Answers
Answer:
3) a<5
5) z≤2
Step-by-step explanation:
3) a/5<1
a<1x5
a<5
5) 5(z+6)≤40
5z+30≤40
5z≤40-30
5z≤10
z≤10÷5
z≤2
12) Which is a value for h that makes the following true?
Answers
Answer:-7
Step-by-step explanation:
-3(-7)+6>=24
21+6>=24
27>=24
Answer:
-7
Step-by-step explanation:
-3h + 6 is greater than or equal to 24.
Solve by simplifying the equation to get h standing alone
1. Subtract the 6 on both sides. -3h \(\geq\) 18
2. Divide by -3 on both sides. h \(\leq\) -6 (You swap the sign when you divide by a negative.
3. Choose the value less than -6. -7
what is 2 hrs and 20 min to 40 min as a fraction?
Answers
Answer:
7/2
Step-by-step explanation:
2 hours= 120 mins
120 mins+20=140
140/40=7/2
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2. If lime juice has a pH of 1.7, what is the concentration of hydrogen
ions (in mol/L) in lime juice, to the nearest hundredth? Use the
formula pH = -log[H +].
Answers
Answer:0.02 mol/L
Step-by-step explanation:
Given: pH = 1.7
Required: [H+]
Equation: pH = -log [H+]
Solution:
Take the antilog of both sides
[H+] = antilog(-pH)
Antilog(-pH) is equal to 10^-pH. Therefore
[H+] = 10^-pH
Solve for [H+]
[H+] = 10^-1.7
Answer: [H+] = 0.02 mol/L
someone please help!
Answers
LK = 3.6
LM = 8.8
What two numbers multiply to give you 16 and add up to give you negative 8
Answers
Answer:
-4 and -4
Step-by-step explanation:
how could I use inverse operations to help solve 52 divided by 4
Answers
13
Explanation:
Given: 52 divided by 4
There should be an equal to sign in order to perform an inverse operation.
Let the answer we get after dividing 52 by 4 = x
52/4 = x
52 divided by 4 becomes:
52 = 4x
x is multiplied by 4. The inverse operation of multiplication is division.
So, we will divide 4 on both sides of the equation:
52/4 = 4x/4
13 = x
x = 13
The answer is 13
Which expression is equivalent to
Square root of 80 ?
Answers
Answer:
4i√5
Step-by-step explanation:
Measures of center and variation can be used to describe data sets. Choose ALL statements about these measures that are true.
The mean, or average is a measure of center
The range of data set is a measure of center
The median of a data set is a measure of variability.
Measures of variability describe how the values in a data set vary.
Measures of Center describe all values in a data set with a single number
Answers
Answer:
These are the answers:
A) The mean, or average, is a measure of center.
D) Measures of variability describe how the values in a data set vary.
E) Measures of center describe all values in a data set with a single number.
The mean, or average is a measure of center
Measures of variability describe how the values in a data set vary.
Measures of Center describe all values in a data set with a single number
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
The following statements about measures of center and variation are true:
The mean, or average, is a measure of center.
Measures of variability describe how the values in a data set vary.
Measures of center describe all values in a data set with a single number.
The statement "The range of data set is a measure of center" is false. The range is a measure of variability, not center.
The statement "The median of a data set is a measure of variability" is also false. The median is a measure of center, not variability
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If there is 0.1337 of a cubic foot in 1 gallon, how many gallons of water will it take to fill Myron's swimming pool completely?
Answers
Answer:
149,610 gallons
Step-by-step explanation:
To answer this question, we need to know the volume of Myron's swimming pool in cubic feet. Let's assume that the volume of Myron's swimming pool is 20,000 cubic feet.
Now we can use the given conversion factor to convert from cubic feet to gallons:
1 cubic foot = 7.48052 gallons
Therefore, the number of gallons of water needed to fill Myron's swimming pool is:
20,000 cubic feet x 7.48052 gallons/cubic foot = 149,610.4 gallons
So it will take approximately 149,610 gallons of water to fill Myron's swimming pool completely.
Simplify 7-5x-(3+5x)
Answers
Answer:
4-10x
Step-by-step explanation:
Hey there!
7 - 5x - (3 + 5x)
= 7 - 5x - 1(3 + 5x)
= 7 - 5x -1(3) - 1(5x)
= 7 - 5x - 3 - 5x
COMBINE the LIKE TERMS
= (-5x - 5x) + (7 - 3)
= -10x + 4
Therefore, your answer should be: -10x + 4
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Kaelyn was one of four hundred eighty people who waited in line for a chance to appear on a reality television show. If 30 people were selected at random, what is the probability that Kaelyn was selected?
Answers
Answer:
To calculate the probability that Kaelyn was selected out of 30 people chosen at random from a group of 480 people, we can use the concept of probability.
Given:
Total number of people in the group (N) = 480
Number of people chosen (n) = 30
We want to find the probability of Kaelyn being selected, which is the probability of selecting 1 person out of 480 people, or 1/480.
So, the probability that Kaelyn was selected is:
P(Kaelyn) = 1/480
This is the final answer, as it represents the probability of Kaelyn being selected out of 30 people chosen at random from a group of 480 people.
Step-by-step explanation:
Answer:
To calculate the probability that Kaelyn was selected out of 30 people chosen
Step-by-step explanation:
Just need the solution set, for some reason my calculator will not compute it
Answers
ANSWER:
\(x=\frac{6\ln5-5\ln7}{2\ln7-\ln5}\)The value of x is equal to -8.49
STEP-BY-STEP EXPLANATION:
We have the following equation:
\(7^{2x+5}=5^{x-6}\)We solve for x:
\(\begin{gathered} (2x+5)\cdot\ln (7)=(x-6)\ln (5) \\ \ln 7\cdot2x+5\ln 7=\ln 5\cdot x-6\ln 5 \\ \ln 7\cdot2x-\ln 5\cdot x=-6\ln 5-5\ln 7 \\ x(2\ln 7-\ln 5)=-6\ln 5-5\ln 7 \\ x=\frac{6\ln 5-5\ln 7}{2\ln 7-\ln 5} \\ x\cong-8.49 \end{gathered}\)The value of x is equal to -8.49
I need ur help please be right
Answers
Answer: the third choice
Step-by-step explanation:
What is the solution to the linear equation? 4b 6 = 2 – b 4
Answers
On solving the provide question, we can say that - the given linear equation can be written as following = \(4b^6 = 2 - b^4\)
What is linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Ax+By=C is the typical form for linear equations with two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts (x and y) for an equation of this type is not too difficult. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
The given linear equation -
\(4b^6 = 2 - b^4\)
\(4b^6 + b^4 = 2\\\\b^4(4b^2 + 1)=2\\b^4/2 = b^2 + 1\\\\b = \sqrt{(b^4/2) - 1}\)
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Can someone please help me
Answers
Answer:-2.4+3.2t
Step-by-step explanation:
-3.6+1.2-1.9t+5.1t
= -2.4+3.2t
How do I commplete this ratio of
3 17
6
9
12 68
15 85
Answers
The following ratio can be completed as;
3 17
6 34
9 51
12 68
15 85
How to solve ratio?Let
The unknown number = x
3 : 17 = 6 : x
3/17 = 6/x
cross product
3 × x = 6 × 17
3x = 102
divide both sides by 3
x = 102/3
x = 34
So,
3 : 17 = 6 : 34
6 : 34 = 9 : x
6/34 = 9/x
cross product
6 × x = 9 × 34
6x = 306
divide both sides by 6
x = 306/6
x = 51
Therefore, ratio is the comparison between two or more numbers.
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what is the answer to this fraction 2/6+5/6
Answers
Answer:
1 1/6
Step-by-step explanation:
2+5/6=7/6 but it is an improper fraction so you turn it into a mixed fraction which is one whole number one over six
Answer:
7/6
Step-by-step explanation:
because the denominator are the same we add the numerator
Round 4.77527806851 to the nearest millionth
Answers
Answer:
4.775278.
Step-by-step explanation:
4.77527806851, when rounded to nearest millionth results in 4.775278.
Answer: 4.775278
Step-by-step explanation:
The place values go tenth, hundredth, thousandth, ten thousandth, hundred thousandth, and millionth. The place value after that is zero, so it stays as eight.