Find the critical points of the function. For each critical point, determine, by the second derivative test, whether it corresponds to a relative maximum, to a relative minimum, or neither, or whether the test gives no information.
f(p,q) = pq - 1/p - 1/q
Answers
The critical points (1,1), (1,-1), and (-1,1) correspond to a relative minimum, a saddle point, and a saddle point, respectively, while the critical point (-1,-1) requires further investigation.
To find the critical points of the function f(p,q) = pq - 1/p - 1/q, we need to find where the partial derivatives of f with respect to p and q are equal to zero:
∂f/∂p = q + 1/p^2 = 0
∂f/∂q = p + 1/q^2 = 0
Solving for p and q, we get:
p = q = ±1
Therefore, the critical points of the function are (1,1), (1,-1), (-1,1), and (-1,-1).
To determine whether each critical point corresponds to a relative maximum, relative minimum, or neither, we need to use the second derivative test. Letting fpp, fpq, and fqq denote the second partial derivatives of f with respect to p and q, we have:
fpp = 2/p^3
fpq = 1
fqq = 2/q^3
At the critical point (1,1), we have fpp > 0 and fqq > 0, so this point corresponds to a relative minimum.
At the critical point (1,-1), we have fpp > 0 and fqq < 0, so this point corresponds to a saddle point.
At the critical point (-1,1), we have fpp < 0 and fqq > 0, so this point corresponds to a saddle point.
At the critical point (-1,-1), we have fpp < 0 and fqq < 0, so the second derivative test is inconclusive.
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Related Questions
please answer will give brainlist and a thanks <3
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Answer:
x=8
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
Please help me! Work out for me pleasee
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Prove whether the series converges or diverges. n=2∑[infinity] (−1)n+16+n5+n The series is diverges
Answers
Answer:
Diverges by A.S.T
Step-by-step explanation:
\(\displaystyle \sum^\infty_{n=2}(-1)^{n+1}\frac{5+n}{6+n}\) is an alternating series, so to test its convergence, we need to use the Alternating Series test.
Since \(\displaystyle \lim_{n\rightarrow\infty}\frac{5+n}{6+n}=1\neq0\), then the series is divergent.
which is the largest number
A. 7.51
B.7.5
C.7.501
D.7.5
Answers
Answer:
its A 7.51
Step-by-step explanation:
What is the value of the expression below when y=9 and z=3
10y-7z
Answers
Answer:
69
Step-by-step explanation:
10y - 7z = ? y=9 z=3
(10 x 9) - (7 x 3) = ?
90 - (7 x 3) = ?
90 - 21 = 69
HI HELP ME W MATH PLSS!!
Hannah drove her car 318.4km in 4h
a) Calculate her average speed=
b) At this speed, how far can she expect to travel in 5.5 h? =
Answers
Answer:
a) 79.6
b) 437.8
Step-by-step explanation:
First, you have to do 318.4/4 to find the rate she goes in the duration of an hour. The rate is 79.6, which means she travels at a rate of 79.6 kilometers per hour.
Then, you have to find the distance she takes to travel in 5.5 hours, so you have to do 5.5*79.6 which is 437.8.
So, Hannah travels 437.8 kilometers in 5.5 hours.
Charlie creates and sells jewelry. He has designed a triangular pendant with two 2-inch sides and one 1.5-inch side.Charlie will use wire to form the triangle. He wants to make several of these pendants to sell at his store. How many pendants can Charlie make using 5 feet of wire?
Answers
Answer:
Number of pendant made = 10
Step-by-step explanation:
Given:
Sides of triangle = 2 in , 2 in , 1.5 in
Total wire = 5 ft = 5 × 12 = 60 in
Find:
Number of pendant made.
Computation:
Perimeter of 1 pendant = 2 in + 2 in + 1.5 in
Perimeter of 1 pendant = 5.5 in
Number of pendant made = Total wire / Perimeter of 1 pendant
Number of pendant made = 60 / 5.5
Number of pendant made = 10.90
Number of pendant made = 10 and 1 pendant incomplete
how many perpendicular bisectors can be constructed for a line segment
Answers
Answer:
Infinite
Step-by-step explanation:
ANY line segment can have INFINITE bisectors crossing it
I need help!!!ASAP if you can help that would be great
Answers
Answer:
6^-6 and 1/6^6
Step-by-step explanation:
Note that (n^a)/(n^b) = n^(a-b) and n^-a = 1/n^a
Therefore, 6^-10/6^-4 = 6^(-10+4) = 6^-6 = 1/6^6
We have our answer: 6^-6 and 1/6^6
I hope this helps! :)
Could someone help me solve for this question? I have a hard time
Understanding. Thanks, the question is
Which statement describes the end behavior of the exponential equation y = 3^x?
A as x -> - ♾ , y -> - ♾
B as x -> - ♾ , y -> 0
C as x - > ♾ , y -> - ♾
Answers
Answer:
the answer is b ok understand
please help me ill put you as brainliest:)
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Using the following year-end information for Work-Fit calculate the acid-test ratio: Cash $ 40,000 Short-term investments 5,000 Accounts receivable (all current) 65,000 Inventory 340,000 Supplies 14,030 Accounts payable 111,500 Wages payable 33,000
Multiple Choice
0.26
0.35
0.46
0.67
0.76
Answers
pls help need it pls pls
Answers
Answer:thats map testing
Step-by-step explanation:
Answer:
C. 17
Step-by-step explanation:
Subtract 3 from 6 first in the parenthesis, then multiply that by 5.
3 x 5 = 15
Now add 2 to 15.
15+2=17
x y 3 12 5 20 6 24 8 32 The table shows a proportional relationship between x and y. What is the unit rate of y per x? A) 1 B) 2 C) 3 D) 4
Answers
Answer:
D.6
Step-by-step explanation:
Answer:d)4
Step-by-step explanation:
Some History teachers at Dayton High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Gruber bought 25 student tickets and 28 adult tickets, which cost a total of $984. Mr. Ellison spent $900, getting 25 student tickets and 25 adult tickets. What is the price for each type of ticket?
Answers
Answer:
Student Ticket: $8
Adult $28
Step-by-step explanation:
To find out the price of each ticket create 2 equations, then solve for x & y
x = student tickets
y = adult tickets
25x + 28y = 984
25x + 25y = 900
To do this first put x on one side of the equation
25x = 900 - 25y
x = 36 - y
Now substitute this equation in x for the first equation
25(36 - y) + 28y = 984
Now distribute 25 in 36 - y, 900 - 25y + 28y = 984
After this combine like term, then subtract 900 from each side, 3y = 84
Then divide 3 on each side, y = 28
Lastly substitute 28 for y in any equation to solve for x, x = 8
x & y are the price of each ticket
3. What are the lateral area and the surface area of the cone shown below? Round the answers
the nearest tenth. The figure is not drawn to scale.
12 ft
21 ft
LA = 452.4 ft?; SA = 2,598.8 ft?
LA = 452.4 ft?; SA = 1,244.1 ft2
LA=791.7 ft?; SA = 2,598.8 ft2
OLA = 791.7 ft2, SA = 1,244.1 ft2
Answers
Answer:
option 4
Step-by-step explanation:
LA = πrl
Here, l ----> slant height
l= 21 ft
r = 12 ft
LA = 3.14*12*21 = 791.7 square ft
SA = πr(l + r)
= 3.14*12 *(12+21)
=3.14* 12 * 33
= 1244.1 square ft
A company makes cell phones in two different factories, one abroad and one more local. At the factory abroad it takes 30 hours to produce the cellphone and at the local factory it takes 20 hours. The costs of producing these cell phones are $20 each at the factory abroad and $60 each at the local factory. The company's total labor force can provide 6000 hours of labor each week and total resources are $12,000 each week. How many cell phones should the company make at each factory to maximize the amount of phones produced?
Answers
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of phones produced abroad and y represent the number of phones produced locally.
The company can provide 6000 hours of labor each week and it takes 30 hours to produce the cellphone abroad and at the local factory it takes 20 hours, hence:
30x + 20y = 6000 (1)
Also, there is a total resource of $12000 each week, the cost of producing abroad is $20 and the cost of producing locally is $60. Hence:
20x + 60y = 12000 (2)
Multiply equation 1 by 3 and subtract equation 2 from the result. This gives:
70x = 6000
x = 600/7 ≈ 86
Put x = 86 in equation 1:
30(86) + 20 y = 6000
20y = 3420
y = 171
86 phones should be produced abroad and 171 phones locally
11) How many kilograms of How many kilograms of calcium are there
in 173 pounds of calcium? (1 lb = 454 g; 1
kg 1000 g)
A) 78.5 kg
B) 110 kg
C) 78500 kg D) 1.10 kg
Answers
Explanation. First, we must convert the lbs into grams, we can do this my multiplying 454 by 173 and get 78,500. Then convert it to kg, there are 1,000 g in a kg do divide 78,500 by 1,000 to get 78.5 kg. Let me know if it’s correct so others can use it. Brainliest would be appreciated.
Good luck :)
The kilogrammes of calcium found in 173 pounds of calcium is = 78.5 kg. That is option A.
First convert the 173 pounds of calcium to gramma
1 lb(pounds) = 454 g;
Therefore 173 pounds = 173 ×454
= 78,542g
But, 1000 g = 1kg
Therefore, 78542g = 78542 ÷1000
= 78.542
=78.5kg.
Therefore, the kilogrammes of calcium found in 173 pounds of calcium is = 78.5kg.
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A group of students was asked about the number of flights they have taken. The data is shown in the line plot. Which of the following best describes the spread of the data? Explain its meaning in this situation. The data has a range of 5, which is a wide spread. This means the greatest number of flights was 5. The data has a range of 15, which is a narrow spread. This means that there is not a large difference in the number of flights taken by the students. The data has a range of 5, which is a narrow spread. This means that most of the students have taken a similar number of flights. The data has a range of 15, which is a wide spread. This means that there is a difference of 15 flights between each of the students.
Answers
Answer:
In the case presented, the range is the difference between the maximum value and the minimum value of the data. The range describes the breadth of the data and how much they vary from the minimum value to the maximum value. Therefore, the range indicates the dispersion of the data.
The statement indicates that the range is 5, which means that the most flights made by students is 5. Since the data has a narrow dispersion, we can conclude that most students have taken a similar number of flights, implying that most students have flown an amount close to the maximum number observed.
Therefore, the option that best describes the dispersion of the data is: "The data has a range of 5, which is a narrow dispersion. This means that most students have taken a similar number of flights."
Step-by-step explanation:
Given that a * b = 4 * 6
Find the value of: -4 * 6
Answers
Answer:
-24
Step-by-step explanation:
Multiply -4 by 6
-$-4-3/-2
V
Which equation represents a circle with the same radius
as the circle shown but with a center at (-1, 1)?
O(x-1)²+(v + 1)² = 16
O(x-1)² + (y + 1)² = 4
O (x + 1)² + (v-1)² = 4
O(x + 1)² + (y-1)² = 16
Answers
The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1) is (x + 1)² + (y - 1)² = 16.
We know that, the center of a circle is (-1, 1).
We know that, the standard form for an equation of a circle is
(x - h)² + (y - k)² = r²
The (h, k) are co-ordinate of your Centre of circle, which in this case is (-1,1) and r is the radius of circle.
As we can see in the figure radius = 4units
From Centre (1,-2) to (1,-2)
Put these into the equation
(x + 1)² + (y - 1)² = 4²
(x + 1)² + (y - 1)² = 16
Therefore, option D is the correct answer.
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help ASAP pleaseeee...
Answers
Answer: let's try C ( sorry if i'm wrong)
Step-by-step explanation:
is the sum of the integers x and y a prime number? (1)x is an even prime number. (2)y is a prime number between 10 and 20.
Answers
Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.
So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.
Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.
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a fire truck is called to a scene. three minutes later, a second truck is called. the first truck averages only 30 miles per hour, but the second averages 60 miles per hour. the truckcs travel a total of 12 miles and arrive at the same time.
Answers
The trucks arrive 10 minutes after the first call. The first and the second truck travel for 5 miles and 8 miles respectively.
In a time difference of 3 minutes, two fire trucks are called.
The average speed of the first truck is 30 miles per hour.
The average speed of the second truck is 60 miles per hour.
The trucks totally travel for 12 miles and arrive at the same time.
Let d be the number of miles the first truck drove.
Let t be the number of minutes it took the first truck to travel.
Now, Convert 30 miles per hour to a half mile per minute and 60 miles per hour to a mile per minute as we are measuring time in minutes.
For the first truck:
d = 0.5t
The second truck traveled 12 - d miles if the first truck traveled d miles. In the event where the first truck traveled for t minutes and was called 3 minutes later, the second vehicle would have gone for t - 3 minutes.
For the second truck:
12 - d = t - 3
Therefore,
12 - 0.5t = t - 3
15 = 1.5t
t = 15 / 1.5
t = 10 minutes
The trucks arrive after 10 minutes after the first call.
Then,
d = 0.5t = 0.5(10) = 5 miles
And 12 - d = 12 - 5 = 8 miles.
Hence, the first truck traveled for 5 miles and the second truck traveled for 8 miles.
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The complete question is mentioned below:
A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel? We must first remember to change miles per hour to miles per minute.
In the U.S., shoe sizes are defined differently for men and women, but in Europe, both sexes use the same shoe size scale. The accompanying histogram shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. What might be the problem with either the mean or the median as a measure of center?
Answers
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them.
The problem with either the mean or the median as a measure of center in this case is that the data is not separated by gender, and the shoe size distributions for men and women are likely to be different. Therefore, computing the mean or median shoe size across all students may not accurately represent the typical shoe size for men or women separately.
For example, if the men in the sample have, on average, larger shoe sizes than the women, then the mean shoe size across all students may be biased towards the larger sizes, even though the majority of the students are women. On the other hand, if there are a few male students with very large shoe sizes, then the median shoe size across all students may be biased towards the larger sizes as well, even if most of the students are women with smaller shoe sizes.
To accurately represent the shoe sizes for men and women separately, it would be better to compute the mean or median shoe size for each group separately and compare them. Alternatively, a better measure of center might be to report the mode, which represents the most common shoe size in the data.
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What is the value of x? Enter your answer in the box. x =
Answers
Answer:
55°Step-by-step explanation:
the sum of the interior angles of a triangles is 180°
so
180 = 75 + 50 + x
x = 180 - 75 - 50
x = 55°
-----------------------
check
55 + 75 + 50 = 180°
the answer is good
If you know the answer to this question please help!! ASAP
7th grade Math
Answers
Answer:
22°
Step-by-step explanation:
a right angle have 90°
So
x+68°=90°
=>x=90-68
=22°
Solve the following quadratic by
completing the square.
y = x2 + 4x - 2
Answers
Answer:
x = √6 - 2 , -√6-2
Step-by-step explanation:
We have ,
=> y = x² + 4x - 2
Let y = 0=> x² + 4x - 2 = 0
=> x² + 2(2)(x) - 2 = 0
=> x² + 2(2)(x) +2² - 2² -2 = 0
=> x² + 2(2)(x) + 2² -4-2 = 0
=> ( x + 2 )² -6 = 0
=> ( x +2)² = 6
=> ( x + 2) = √6
=> x + 2 = ±√6
=> x = √6 - 2 , -√6-2
The solution for x in terms of y is x = √y - 2 + √6.
To solve the quadratic equation y = x² + 4x - 2 by completing the square, we need to follow a few steps:
Step 1: Move the constant term to the right side of the equation:
y + 2 = x² + 4x
Step 2: Take half of the coefficient of x and square it. Add the resulting value to both sides of the equation to create a perfect square trinomial on the left side:
y + 2 + (4/2)² = x² + 4x + (4/2)²
y + 2 + 4 = x² + 4x + 4
y + 6 = (x + 2)²
Step 3: Rewrite the equation in vertex form:
(y + 6) = (x + 2)²
The equation is now in the form y = (x - h)² + k, where (h, k) represents the vertex of the parabola.
Therefore, the vertex is (-2, -6), and the equation represents a parabola that opens upward.
To solve the equation (y + 6) = (x + 2)² for x, we need to isolate x. Here's how:
Start with the equation: (y + 6) = (x + 2)²
Subtract 6 from both sides of the equation: (y + 6) - 6 = (x + 2)² - 6
Simplify: y = (x + 2)² - 6
Take the square root of both sides of the equation: √y = √[(x + 2)² - 6]
Simplify: √y = x + 2 - √6
Subtract 2 from both sides of the equation: √y - 2 = x - √6
Rearrange the equation to solve for x: x = √y - 2 + √6
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What is the simplified form of the expression the quantity x squared minus 4x minus 21 end quantity divided by 4 times the quantity x minus 7 end quantity? the quantity x plus 3 end quantity divided by 4 the quantity x minus 3 end quantity divided by 4 the quantity x plus 3 end quantity divided by quantity x minus 7 end quantity the quantity x minus 3 end quantity divided by quantity x minus 7 end quantity.
Answers
The Simplified form of the given expression (x² - 4x - 21)/4(x - 7) is (x+3)/4 , the correct option is (a) .
In the question ,
it is given that ,
the algebraic expression is (x² - 4x - 21)/4(x - 7) ,
we need to find the simplified value of it .
we first simplify the numerator that is x² - 4x - 21 ,
By using the split the middle term method ,
we get ,
= x² - 7x \(+\) 3x - 21
= x(x - 7) \(+\) 3(x - 7)
= (x \(+\) 3)(x - 7)
Writing the simplified numerator in the expression ,
we get ,
= (x \(+\) 3)(x - 7)/4(x - 7)
cancelling out the common term (x-7) , we get
= (x \(+\) 3)/4
Therefore , the simplified form is (x + 3)/4 .
The given question is incomplete , the complete question is
What is the simplified form of the expression
(x² - 4x - 21)/4(x - 7) ?
(a) (x+3)/4
(b) (x-3)/4
(c) (x+3)/(x-7)
(d) (x-3)/(x-7)
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Pls help need to turn in soon
Answers
Answer:
the answer is 5 x +3 = 3 x - 1
Step-by-step explanation: