Find the local maxima, local minima, and saddle points, if any, for the function z = 5x3 + 5x²y + 4y2. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *,*), (*, *, *)... Enter DNE if the points do not exist.)
Answers
The local maxima, local minima, and saddle points for the function z = 5x^3 + 5x^2y + 4y^2 need to be calculated.
To find the local maxima, local minima, and saddle points of the function z = 5x^3 + 5x^2y + 4y^2, we need to calculate the critical points and examine the nature of these points.
To find the critical points, we take the partial derivatives of z with respect to x and y and set them equal to zero:∂z/∂x = 15x^2 + 10xy = 0
∂z/∂y = 5x^2 + 8y = 0
Solving these equations, we find two critical points: (0, 0) and (-2/5, 0).
Next, we evaluate the second partial derivatives at these critical points to determine the nature of these points. Using the second partial derivative test, we examine the determinant and the sign of the second partial derivative.The determinant at (0, 0) is zero, indicating no conclusive information about the nature of the critical point. Further analysis is required to determine whether it is a local maxima, local minima, or saddle point.
At (-2/5, 0), the determinant is positive, and the second partial derivative with respect to x is negative. This indicates a local maximum.
Therefore, the points are as follows: (0, 0, DNE), (-2/5, 0, local maxima).
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Related Questions
Which absolute value expression represents the distance between 3 and
9 /2
on a number line?
A) |3 −
9
2
|
B) |3 − (−
9
2
)|
C) |−3 + (−
9
2
)|
D) |−3 −
9
2
)|
Answers
Given the diagram above and bd= 12 and ac= x+ 23, find ac
Answers
The value of AC when BD= 12 and AC = x+ 23 is 28
What is a line segment?A line segment can be defined as the part of a straight line that is being bounded by two different end points, and also contains all the points on the line between its endpoints.
From the information given, we have that line AD is a line with segments, line AB, line BC, line CD with B and C as the midpoints.
Given the points as;
AC = x + 23BD = 12BC = 14 + xAD = 26 + xWe have that;
AC + BC = AD
But line BD = 14 + x, we have;
Line AC = x + 23 - 14 + x
Line AC = 2x + 9
substitute the values into the equation
2x + 9 +12 = 26 + x
collect like terms
2x - x = 26 - 21
Add or subtract like terms
x = 5
But, we have that;
Line AC = x + 23
Line AC = 5 + 23
Add the values
Line AC = 28
Hence, the value is 28
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what is the summation notation for 8+4+2+1+1/2
Answers
Answer:
15 1/2
Step-by-step explanation:
hope this helped
Among all unbiased estimators that are weighted averages of Y1 ,..., Yn, the sample mean as an estimator of the population means is:
Select one alternative:
An estimator with lower sampling variances.
An estimator with a higher sampling variance.
The only consistent estimator.
The most unbiased estimator.
Answers
Among all unbiased estimators which are weighted averages of Y₁, ..., Yₙ, the sample mean as an estimator of population mean is an estimator with lower sampling variances.
The sample mean is known to be an unbiased estimator of the population mean.
Which means that on average, it provides an estimate that is equal to the true population mean.
However, when considering estimators that are weighted averages of the observations.
The sample mean tends to have lower sampling variances compared to other unbiased estimators.
Lower sampling variance is desirable because it indicates less variability in the estimates obtained from different samples.
A lower sampling variance implies that the sample mean is likely to be closer to the population mean, providing a more precise estimate.
Therefore, among unbiased estimators that are weighted averages, sample mean stands out as having a lower sampling variance.
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what is a residual? for a given set of data (paired observations of x and y), how many residuals are there?
Answers
A residual is the difference between the observed value of y and the predicted value of y (y-hat) based on the regression equation.
In other words, it is the amount of variation in the data that is not explained by the regression model. For a given set of data with paired observations of x and y, there is one residual for each observation. These residuals are used to assess the accuracy of the regression model and can help identify outliers or areas where the model may need to be improved.
A residual is the difference between an observed value of a dependent variable (y) and its predicted value, based on a regression model. In a given set of data with paired observations of x and y, the number of residuals will be equal to the number of observations. So, if you have n paired observations, there will be n residuals.
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Select all the correct answers.
Which two surfaces need NOT be sanitized between the two tasks?
a cutting board used to first slice bananas and then dice them
a grater used to first grate carrots and then cheese
a prep table used to first cut meat and then make sandwiches
a cup used first to measure sugar and then flour
a knife used to first filet fish and then slice ham
Answers
The two surfaces that need NOT be sanitized between the two tasks are:
A cup used first to measure sugar and then flour.
A knife used to first filet fish and then slice ham.
In both cases, there is no risk of cross-contamination between allergens or harmful bacteria.
The two surfaces that need NOT be sanitized between the two tasks are:
A cup used first to measure sugar and then flour.
A knife used to first filet fish and then slice ham.
In both cases, there is no risk of cross-contamination between allergens or harmful bacteria. The cup is being used for dry ingredients (sugar and flour), which pose a minimal risk of contamination. Similarly, the knife is being used on two different types of proteins (fish and ham), but as long as it is properly cleaned after use, there is no immediate risk of cross-contamination.
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Help ASAP please
347 divided by 7 I need to find the quotient and remainder
Answers
when 347 is divided by 7 it's gives:
Quotient:
Reminder:
Answer:
quotient is 49
and remainder is
Step-by-step explanation:first step is divide 347 by the divisor 7 you will get the quotient 49 and 4will remain as remainder because t can not be divided by divisor.
Show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)]
δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ
Answers
By using Dirac delta function, δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ.
Here's how to show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)]
To show that δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)],
we can use the definition of Dirac delta function.
Dirac delta function is defined as follows:∫δ(x)dx=1and 0 if x≠0
In order to solve the given expression, we have to take the integral of both sides from negative infinity to infinity, which is given below:∫δ(x^2-a^2)dx=∫1/2a[δ(x-a)+ δ(x+a)]dx
To compute the left-hand side, we use a substitution u=x^2-a^2 du=2xdxWhen x=-a, u=a^2-a^2=0 and when x=a, u=a^2-a^2=0.
Therefore,-∞∫∞δ(x^2-a^2)dx=-∞∫∞δ(u)1/2adx=1/2a
Similarly, the right-hand side becomes:∫1/2a[δ(x-a)+ δ(x+a)]dx=1/2a∫δ(x-a)dx +1/2a∫δ(x+a)dx=1/2a + 1/2a=1/2a
Therefore,∫δ(x^2-a^2)dx=∫1/2a[δ(x-a)+ δ(x+a)]dxHence, δ(x^2-a^2)=1/2a[δ(x-a)+ δ(x+a)].
Next, we can show that δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ as follows:We know that cosθ = cosθ' which implies θ=θ'+2nπ or θ=-θ'-2nπ.
Therefore, c0sθ-cosθ'=c0s(θ'-2nπ)-cosθ'=c0sθ'-cosθ' = sinθ'c0sθ-sinθ'cosθ'.
We can use the following identity to simplify the above expression:c0sA-B= c0sAcosB-sinAsinB
Therefore,c0sθ-cosθ' =sinθ'c0sθ-sinθ'cosθ'=sinθ'[c0sθ-sinθ'cosθ']/sinθ' =δ(θ-θ')/sinθ'
Hence,δ(c0sθ- cosθ)= δ(θ-θ’)/sin θ’= δ (θ- θ’)/ sin θ.
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A maple syrup producer has a booth at a Sunday farmer's market. The producer sells organic maple syrup by the pint. To get customers to start buying more pints of organic maple syrup, the producer is trying out a new discount system. Customers buying more than two pint bottles will get a discount per pint, beginning with the third pint bottle. For these customers, the expression shown represents the total price, in dollars, of buying p pints of organic maple syrup. 29.50 + 13.50(p – 2)
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
\(Price = 29.50 + 13.50(p - 2)\)
The question has missing details. However, I will solve on a general term.
A possible question could be to find the cost of purchasing (say 10 bottles).
To do this, we simply substitute 10 for p.
So:
\(Price = 29.50 + 13.50(p - 2)\)
\(Price = 29.50 + 13.50(10 - 2)\)
\(Price = 29.50 + 13.50 * 8\)
\(Price = 29.50 + 108\)
\(Price = 137.50\)
i.e. $137.50 for 10 pint bottles
Another possible question is to calculate the number of pint bottles that amount to (say $70).
To do this, we simply substitute 70 for Price.
So:
\(Price = 29.50 + 13.50(p - 2)\)
\(70 = 29.50 + 13.50(p - 2)\)
Collect like terms
\(70 - 29.50 = 13.50(p - 2)\)
\(40.5= 13.50(p - 2)\)
Divide both sides by 13.50
\(3= p - 2\)
Add 2 to both sides
\(3 + 2 = p - 2 + 2\)
\(5 = p\)
\(p = 5\)
i.e. $70 will buy 5 pint bottles
Use this explanation to find solution to your question
Solve for x. Assume that lines which appear tangent are tangent.
Answers
The figure is an illustration of intersecting chords.
The value of x is 16 units
How to determine the value of x?From the figure, we can see that the two lines are intersecting chords.
To calculate the value of x, we make use of the intersecting chord theorem.
So, we have:
x * 21 = 24 * 14
Divide both sides by 7
x * 3 = 24 * 2
Divide both sides by 3
x = 8 * 2
Evaluate the products
x = 16
Hence, the value of x is 16 units
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Which table of values satisfies the linear equation y=−34x −6?
Answers
The table of values satisfies the linear equation y = −3x/4 − 6 is: C. table C.
How to determine the solution?In order to determine which ordered pairs are valid and true solutions based on the given linear equation, we would have to test the given ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (-4, -9), we have:
y = −3x/4 − 6
-9 = −3(-4)/4 − 6
-9 = 3 − 6
-9 = -3 (False).
For ordered pair (-8, -12), we have:
y = −3x/4 − 6
-12 = −3(-8)/4 − 6
-12 = 8 − 6
-12 = 2 (False).
For ordered pair (-4, -3), we have:
y = −3x/4 − 6
-3 = −3(-4)/4 − 6
-3 = 3 − 6
-3 = -3 (True).
For ordered pair (0, -6), we have:
y = −3x/4 − 6
-6 = −3(0)/4 − 6
-6 = 0 − 6
-6 = -6 (True).
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Complete Question:
Which table of values satisfies the linear equation y = −3x/4 − 6?
How would you "say" the image on the right?
A.) Prime A, B, C, and D
B.) A prime, B prime, C prime, D prime
Answers
Answer:
a
Step-by-step explanation:
prime abc and d
hope this helps
Annual snowfall in Anchorage, Alaska, is normally distributed with a mean height of 76 inches and a standard deviation of 4.7 inches. What is the probability this year that it will snow between 71.4 and 80.7 inches in Anchorage?
Answers
Using the Empirical Rule, it is found that there is a 68% probability this year that it will snow between 71.4 and 80.7 inches in Anchorage.
What is the Empirical Rule?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, the mean height of 76 inches and a standard deviation of 4.7 inches, hence 71.4 and 80.7 inches is within 1 standard deviation of the mean, that is, there is a 68% probability this year that it will snow between 71.4 and 80.7 inches in Anchorage.
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11(5+6i)-7i(8i-4) simplify
Answers
Answer:
55 - 56i² + 94i
Step-by-step explanation:
11(5 + 6i) - 7i(8i - 4)
=> 55 + 66i - 56i² + 28i
=> 55 - 56i² + 94i
Therefore, 55 - 56i² + 94i is our simplified form.
Answer:
11(5+6i)−7(−4+8i)
11(5+6)−7(−4+8)
11(5+6)−(−28−56)
11(5+6)−(−56−28)
11(5+6)+56+28
55+66+56+28
(55+56)+(66+28)
111+94
Step-by-step explanation:
Erin gets her exercise by running. The graph shows the distances she covers in a given amount of time. How many hours does it take for Erin to run 25 miles?
Answers
The correct answer is c. 2 \(\frac{1}{2}\) hours
Explanation:
The graphic shows the relationship between the distance Erin covers by running and the time this requires. Additionally, to know the specific time that takes for Erin to run a specific distance or vice versa it is necessary to observe at which point the two variables intersect in the line of the graph.
According to this, Erin runs 25 miles (y-axis) in 2.5 hours (x-axis), which you can know because in the line shown by the graph the distance 25 miles that is in the middle of 20 and 30 miles intersects with 2.5 hours or the middle between 2 and 3. Additionally, this number can be expressed as 2 and a half hours, 2.5 or even 2 \(\frac{1}{2}\) hours because the fraction represents half. This makes option C the answer.
Question 7
2 pts
In a integer optimization problem with 5 binary variables, the maximum number of potential solutions is:
32
125
25
10
Question 8
Answers
The correct answer is 32.
In an integer optimization problem with binary variables, each variable can take one of two possible values: 0 or 1. Therefore, for 5 binary variables, each variable can be assigned either 0 or 1, resulting in 2 possible choices for each variable. The maximum number of potential solutions in an integer optimization problem with 5 binary variables is 32 because each binary variable can take on 2 possible values (0 or 1)
In this case, we have 5 binary variables, so the maximum number of potential solutions is given by 2 * 2 * 2 * 2 * 2, which simplifies to 2^5. Calculating 2^5, we find that the maximum number of potential solutions is 32.
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The population of a town increases 10% every 3 years if the present population is 72600 calculate its population after 6 years and 6 years ago
Answers
Answer:
After 6 years = 87120 people.
Before 6 years = 5808 people.
Step-by-step explanation:
To calculate how many populations that are added in every 10% in 3 years:
72600 × 10/100 = 7260
After 6 years = 72600 + 7260 × 2 = 87120 people.
Before 6 years = 72600 - 7260 × 2 = 5808 people.
If someone would help Me that would be great! will give BRAINLLIEST!
Answers
Answer:
where are the pictures???
Step-by-step explanation:
Answer:
Where are the answers?
Step-by-step explanation:
5) Triangle ERT is congruent to triangle CVB.
• The measure of ZE is 32°.
• The measure of LC is (7x + 4)°.
• The measure of LB is (15x + 7)º.
What is the measure of ZV?
A. m2V = 4°
B. m2V= 32°
C. m2V = 67°
D. m2V= 81°
(SHOW WORK AND ILL MARK YOU AS BRAINLIST)
Answers
The calculated value of the measure of the angle V is 81 degrees
Calculating the measure of the angle V?From the question, we have the following parameters that can be used in our computation:
The measure of E is 32°.The measure of C is (7x + 4)°.The measure of B is (15x + 7)º.Because the triangle ERT is congruent to triangle CVB, then we have
E = C
So, we have
7x + 4 = 32
Evaluate the like terms
7x = 28
Divide by 7
x = 4
Also, we have
V = R
This means that
V = 180 - C - B
Substitute the known values in the above equation, so, we have the following representation
V = 180 - 7x - 4 - 15x - 7
So, we have
V = 180 - 7(4) - 4 - 15(4) - 7
Evaluate
V = 81
Hence, the measure of the angle is 81 degrees
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In a factory, eggs are packaged in groups of 12 per box.How many full boxes of eggs can the factory make with 2321 eggs?
Answers
So 193 full boxes of eggs
Find a polynomial function f(x) of least possible degree having the graph shown
Answers
first off let's notice a few things on that function.
the graph "passes" -5, that's a root, the graph "touches" 3 and goes back up, that's another root, but that's a root with an "even multiplicity", the heck does that mean? well, it means there are at least two roots, could be 4 or 6 or 18, so long is even, but we're shooting for the least degree, so we'll settle for 2.
now hmm, let's reword that
what's the equation of a function with roots at -5 and 3 twice, that it passes through (0 , 9)?
\(\begin{cases} x = -5 &\implies x +5=0\\ x = 3 &\implies x -3=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +5 )( x -3 )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=9 \end{cases} \\\\\\ a ( 0 +5 )( 0 -3 )( 0 -3 ) = 9\implies 45a=9\implies a=\cfrac{9}{45}\implies a=\cfrac{1}{5} \\\\[-0.35em] ~\dotfill\)
\(\cfrac{1}{5}(x+5)(x-3)^2=y\implies \cfrac{1}{5}(x+5)(x^2-6x+9)=y \\\\\\ \cfrac{1}{5}(x^3-x^2-21x+45)=y\implies {\Large \begin{array}{llll} \cfrac{x^3}{5}-\cfrac{x^2}{5}-\cfrac{21x}{5}+9=y \end{array}}\)
Check the picture below.
A number time 5 less that number has a product of -4. What are the two numbers?
Answers
Let the first number be x.
The second number is 5 times less than x => x - 5
Therefore, we can write the statement as
\(\begin{gathered} x\times(x-5)=-4 \\ x^2-5x=-4 \\ \therefore \\ x^2-5x+4=0 \end{gathered}\)Solving the quadratic equation:
Let us replace -5x in the equation with -4x and -x to be able to factorize.
Hence,
\(\begin{gathered} x^2-4x-x+4=0 \\ x(x-4)-1(x-4)=0 \\ (x-4)(x-1)=0 \\ \text{Therefore} \\ x-4=0\text{ } \\ or \\ x-1=0 \end{gathered}\)Hence,
\(\begin{gathered} x=1 \\ or \\ x=4 \end{gathered}\)Therefore, the number can be 1 or 4.
The second number can be
\(\begin{gathered} 1-5=-4 \\ or \\ 4-5=-1 \end{gathered}\)Therefore, the pair of numbers can be
\((1,-4)\text{ or (4, -1)}\)A bag contains 200 pennies & 400 nickels. What is the probability of drawing a penny on the 1st try?
Answers
Given that the bag contains 200 pennies and 400 nickels. We are asked to find the probability of drawing a penny on the 1st try.
Explanation
The probability of an event is given as;
\(Pr(E)=\frac{numbe\text{r of favourable outcomes}}{number\text{ of total possible outcomes}}\)In this case, the number of favorable outcomes is the number of pennies while the total possible outcomes
is the sum of the coins in the bag.
Therefore, we will have
\(\begin{gathered} Pr(\text{Pennies) = }\frac{200}{200+400} \\ =\frac{200}{600} \\ =\frac{1}{3} \end{gathered}\)Answer:
\(\frac{1}{3}\)For each expression, write an equivalent expression that uses only addition. Do not include any spaces in your answers. Keep the terms in the same order. 20−9+8−7 and 4x−7y−5z+6
Answers
Answer:
(a)\(20+(-9)+8+(-7)\)
(b)\(4x+(-7y)+(-5z)+6\)
Step-by-step explanation:
We are required to write an equivalent expression that uses only addition for each of the given term.
Note that the product of + and - is always -.
Therefore:
(a)20−9+8−7
\(20-9+8-7 \\=20+(-9)+8+(-7)\)
(b)4x−7y−5z+6
\(4x-7y-5z+6\\=4x+(-7y)+(-5z)+6\)
You want to have $25,000 in your account after five years. Assuming you do not deposit or withdraw from the account, how much money should you deposit now if the savings account has a 6. 0% annual interest rate, compounded monthly?
Answers
The amount of money to be deposited now to have $25,000 in the account after five years is $18,580.65.
To find the amount of money to be deposited now to have $25,000 in the account after five years if the savings account has a 6.0% annual interest rate, compounded monthly, assuming that there is no deposit or withdrawal, we can use the formula for compound interest which is given by:
A=P(1+r/n)^nt
Where:
A is the future value, P is the present value, r is the annual interest rate, n is the number of times compounded in a year, and t is the number of years.
To solve the problem, we are to find P.
Thus, we can rewrite the formula above as:
P = A / (1+r/n)^nt
Here A = $25,000,
r = 6.0%,
n = 12 (compounded monthly),
t = 5 years.
Plugging in the values:
P = $25,000 / (1 + 0.06/12)^(12*5)P
P = $18,580.65
Therefore, To have $25,000 in your account after five years with the assumption to not deposit or withdraw from the account then the amount of money to be deposited now to have $25,000 in the account after five years is $18,580.65.
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A number z is fewer than 3/4
Answers
Answer:
z < ¾
Step-by-step explanation:
Or z < 0.75
...........
PLEASE HELP! BRAINLIEST IF CORRECT!
Over a 20-year period, a certain city recorded a total rainfall of 621 inches. The rainfall during this past year was 28 inches. If the variable "r" stands for the total amount of rain for the other 19 years, which of the following units could apply to that variable?
A. months
B. inches
C. years
Answers
Answer: B inches
Step-by-step explanation:
I took the quiz
Answer:
its B
Step-by-step explanation:
When she subtracts 4 from both sides, 1/2x=-1.2x result.What is the value of x
Answers
Explanation :
1/2x = -1/2x
1/2x + 1/2x = 0 ( pull the one with smaller value to the bigger ones )
2/2x = 0
x= 0
in the schedule of cost of goods sold, which of the following is true? cost of goods available for sale
Answers
In the schedule of cost of goods sold, the cost of goods available for sale represents the total cost of all goods that were available for sale during a particular period.
The schedule of cost of goods sold is an important financial statement that shows the cost of goods that a company has sold during a particular period. The cost of goods available for sale is a key component of this statement and represents the total cost of all goods that were available for sale during the period.
The cost of goods available for sale is calculated by adding the beginning inventory to the cost of goods purchased during the period. This calculation gives the total cost of all goods that a company had available for sale during the period.
Once the cost of goods available for sale is determined, the cost of goods sold can be calculated by subtracting the ending inventory from the cost of goods available for sale. This calculation gives the cost of all goods that were sold during the period.
Overall, the schedule of cost of goods sold is an important financial statement that helps companies track their inventory and understand their cost of goods sold. The cost of goods available for sale is a critical component of this statement and represents the total cost of all goods that a company had available for sale during a particular period.
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(Find the value of): (125)-2/3