(Chapter 14) If f has a local minimum at (a, b) and f is differentiable at (a, b), then â½f(a, b) = 0
Answers
Therefore, the statement is not necessarily true, and the value of ½f(a, b) depends on the specific function f and the nature of the local minimum at (a, b).
If f has a local minimum at (a, b) and f is differentiable at (a, b), then it is true that the partial derivatives of f at (a, b) must be zero (i.e., fx(a, b) = 0 and fy(a, b) = 0). This is because at a local minimum, the function is not increasing in any direction, so the directional derivatives in all directions must be zero, which implies that the partial derivatives are also zero.
However, this does not necessarily mean that ½f(a, b) = 0. For example, consider the function f(x, y) = (x - 1)² + (y - 1)². This function has a local minimum at (1, 1), and the partial derivatives are zero at that point. However, ½f(1, 1) = ½(0) = 0, so the statement is true in this case, but this is not necessarily true in general.
On the other hand, consider the function g(x, y) = x² + y². This function also has a local minimum at (0, 0), and the partial derivatives are zero at that point. However, ½g(0, 0) = ½(0) = 0, so the statement would suggest that g(0, 0) is a local minimum, which is not true (in fact, it is a global minimum).
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Related Questions
ms.graves gave her class 15 minutes to read. carrie read
Answers
The rate per hour of Carrie's reading is 27.5 pages per hour
How to determine the rate per hourFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as:
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.This means that the rate of reading is
Rate = 5 ½ pages per 12 minutes
Express as decimal
This gives
Rate = 5.5 pages per 12 minutes
Convert minute to hours
So, we have the following representation
Rate = 5.5 pages per 0.2 hour
Evaluate the quotient
Rate = 27.5 pages per hour
Hence, the rate is 27.5 pages per hour
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Complete question
Ms. Graves gave her class 12 minutes to read. Carrie read 5 ½ pages in that time.
At what rate, in pages per hour, did Carrie read?
what is the chart called when the paired data (the dependent and independent variables) are plotted?
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A scatter diagram is the chart called when the paired data (the dependent and independent variables) are plotted.
Explain the meaning of a scatter diagram.
In a scatter diagram, pairs of numerical data are graphed with one variable on each axis in an effort to find a correlation between them.
A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the better the association.
What three types of scatter diagrams are there?
The slope, or trend, of the data points can be used to classify the scatter plot, as was previously mentioned: With Strong Positive Correlation Scatter Diagram Spreadsheet with Weak Positive Correlation. Strongly Correlated Negative Scatter Diagram.
Learn more about A scatter diagram.
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a city has two water towers. one tower holds 4.37 x 106 6 gallons of water and the other holds 3.92 x 106 6 gallons of water. what is the combined water capacity of the two towers? responses
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If one-tower can hold 4.37×10⁶ gallons of water and other tower can hold 3.92×10⁶ gallons of water, then combined water capacity of two towers is 8.29×10⁶ gallons.
In order to find the combined water capacity of the two towers, we simply need to add their individual capacities.
The water capacity of one tower is = 4.37×10⁶ gallons of water, and the water capacity of other tower is = 3.92×10⁶ gallons of water,
So, their combined capacity is:
⇒ 4.37×10⁶ + 3.92×10⁶ = 8.29×10⁶ gallons
Therefore, the combined water capacity of the two towers is 8.29×10⁶ gallons.
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The given question is incomplete, the complete question is
A city has two water towers. one tower holds 4.37×10⁶ gallons of water and the other holds 3.92×10⁶ gallons of water. What is the combined water capacity of the two towers?
Is (5, 2) a solution to the equation y = 8x?
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Hey there! I'm happy to help!
To satisfy this equation, the y value has to be 8 times the x.
If you multiply 5 by 8, you get 40, not 2, so this is not a solution. The point (5,40) would be.
Have a wonderful day! :D
All we need to do is substitute and check.
5 = x
2 = y
y = 8x
2 = 8(5)
2 does not equal 40
Best of Luck!
is it A, B,C or D I wasen't here for the assigment in class
Answers
Answer:
C :minimum value of -4
Step-by-step explanation:
the curve is a u shape so its a minimum value
if its a n shape it wouldve been a maximum value
the curve goes on -4 so its -4
Can someone please do this for me?
Answers
Answer:
64°
Step-by-step explanation:
So supplement angles are equal to 180, so first our two angles added together will be 180:
x + x = 180
Now one of these angles is 6 greater than half:
x + (x/2 + 6) = 180
Then we will solve for x:
x + (x/2 + 6) = 180
x + x/2 + 6 = 180
x + x/2 = 174
\(\frac{3}{2}\)x = 174
x = 116
Plug it back in:
x + (x/2 + 6) = 180
/\
x/2 + 6
(116)/2 + 6
64
To check:
116 + 64 = 180 ✓
A 112.6 g mass of unknown material is submerged in 102 ml of water to yield a final volume of 126 ml. what is the apparent density of the unknown material?
Answers
Taking onto account the definition of density, the apparent density of the unknown material is 0.894 g/mL.
Definition of apparent densityThe apparent density of a material or a body is the ratio between the volume and the dry weight, including voids and pores that it contains.
In other words, apparent density is defined as the mass of many particles of the material divided by the total volume they occupy, which includes the volume of particles, the void volume between particles, and the internal pore volume.
Apparent density is not an intrinsic property of a material, that is, it can change depending on how the material is handled.
The expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
density= mass÷ volume
Apparent densityIn this case, a 112.6 g mass of unknown material is submerged in 102 mL of water to yield a final volume of 126 mL. This is, you know:
mass= 112.6 gfinal volume= 126 mLReplacing in the definition of apparent density:
density= 112.6 g÷ 126 mL
density= 0.894 g/mL
Finally, the apparent density of the unknown material is 0.894 g/mL.
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Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
Answers
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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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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It says use place value to round 314,609 to the nearest hundred thousand, to the nearest ten thousand, and to the nearest thousand. what's the answer?
Answers
The given number 314,609 is rounded to:
The nearest hundred thousand: 300,000
The nearest ten thousand: 310,000
The nearest thousand: 315,000
How to round the place values to the nearest values?To round the place values of a number to the nearest place values following rules are considered:
If the place value after the place value of the digit which is to be rounded is less than 5, then make all the digits after it as 0's.If the place value after the place value of the digit which is to be rounded is greater than 5, then add 1 to the rounding digit and make all the other digits as zero (The digits after it).Calculation:The given number is 314,609
The number name for 314,609 is " Three hundred and fourteen thousand, six hundred and nine "
The order of the places is Hth(Hundred thousand), Tth(Ten thousand), Th(Thousands), H(Hundreds), T(Tens), O(Ones)
Rounding to the nearest hundred thousand:
Hth Tth Th H T O
3 1 4 6 0 9
The digit in the hundreds of thousands place is "3". The digit next/after this place is "1" in ten thousand's place. Since 1 < 5, the digits after 3 are rounded as zeros. I.e., 300,000.
Thus, the nearest hundred thousand for the given number is 300,000.
Rounding to the nearest ten thousand:
Hth Tth Th H T O
3 1 4 6 0 9
The digit in the ten thousand places is "1". The digit after this place is "4" in the thousands place. Since 4 < 5, the digits after 1 are rounded as zeros. I.e., 310,000.
Thus, the nearest ten thousand for the given number is 310,000.
Rounding to the nearest thousand:
Hth Tth Th H T O
3 1 4 6 0 9
The digit in the thousand's place is "4". The digit after this place is "6" in the hundreds place. Since 6 > 5, the digit in the thousands place is added by 1, and the digits after it are made as zeros. I.e., 4 + 1 = 5 and the rounded number is 315,000.
Thus, the nearest thousand for the given number is 315,000.
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Write an equation in slope-intercept form for the line that passes through (0, 1) and (2, 5). socratic.org
Answers
Answer:
y = 2x + 1
Step-by-step explanation:
i used desmos
the following are amounts of total snow falls (in inches) in different midwestern cities in the united states in a certain year: 20 40 31 7 15 29 25 20 17 32 28 12 34 29 20 17 33 23 find the sample mean.
Answers
The sample mean of the given data is 24.
What do we mean by mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a measure of the central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values.To find the mean:
Mean = sum of terms/number of termsMean = 432/18Mean = 24Therefore, the sample mean of the given data is 24.
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Given r(x) =x' - 4x2 + 4x - 6, find the value of r(2). What does your answer tell you about x - 2 as a factor of r(x)? Explain.
Answers
We can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).
What is Factor?A function that accepts a real number as input, typically represented by the variable x and outputs another real number, typically the value of the function denoted by f is known as a real-valued function of a real variable (x).Any polynomial that is divisible by the polynomial P(x) is a factor of that polynomial (x).So, we know that the equation is:
r(x)=x^3-4x^2+4x-6:Now, calculate the equation when x = 2.
r(2)=2^3-4(2)^2+4(2)-6r(2)=8-16+8-6r(2)=-6Now, we can conclude that:
As we see that x=2 is not equal to zero.Implies x-2 does not divide r(x) evenly.Thus x-2 is not a factor of given r(x).Therefore, we can conclude that the value of r(2) which is -6 and x - 2 is not the factor for r(x).
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Write 0,37 in a fraction
Answers
Answer:
37/100
Step-by-step explanation:
Assuming you mean '0.37'
'0.37' is 37 hundredths.
37 would the the numerator and 100 would be the denominator.
\(\frac{37}{100}\)
Hope this helps.
Answer:
37/100
37%
Step-by-step explanation:
To convert 0.37 to fraction, follow these steps:
First write down the decimal number divided by 1 like this:
0.37
1
As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator
0.37 × 100
1 × 100
=
37
100
Hope this helps!
Simplifique a expressão: 5 √2^3
Answers
Answer:
10√2
Step-by-step explanation:
5√2³ = 5√8 = 5√(2 x 4) = (2 x 5)√2 = 10√2
1. The One Way Repeated Measures ANOVA is used when you have a quantitative DV and an IV with three or more levels that is within subjects in nature.
A. True
B. False
Answers
ANOVA is used when you have quantitative DV and IV with 3 or more levels, which means the correct answer is option A. True.
The One Way Repeated Measures ANOVA is a statistical test used to analyze the effects of an independent variable (IV) that has three or more levels on a dependent variable (DV) that is measured repeatedly on the same subjects over time. This test is appropriate when the IV is within-subjects in nature, meaning that each participant is exposed to all levels of the IV. Therefore, the statement is true as it accurately describes the use of this statistical test in relation to the IV and DV.
A. True
The One-Way Repeated Measures ANOVA is indeed used when you have a quantitative Dependent Variable (DV) and an Independent Variable (IV) with three or more levels that is within subjects in nature. In this case, the same subjects are exposed to different conditions or levels of the IV, allowing for the analysis of differences in the DV across those conditions.
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shelly sews a square blanket that has an area of 144 square feet. it has 36 square blocks, each the same size. what is the approximate length of each side of a block? (1 point)
Answers
The side of the square of each block = 2 feet
Given,
Shelly sews a square blanket that has an area of 144 square feet.
and, it has 36 square blocks, each the same size.
To find the approximate length of each side of a block
Now, According to the question:
36 square blocks of same size. We need to find the area of each square block. so we divide = area / square blocks
= 144/ 36
= 4
The area of each square = 4 square feet
We know that
Area of square = side ^2
Side ^2 = 4
side = \(\sqrt{4}\)
Side = 2
Hence, The side of the square of each block = 2 feet
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Whats 4x^3 times 2x^3
Answers
(4x^3)(2x^3)=8x^6
░░░░░░░░░
what is an equation of the parabola with vertex at the origin and focus (-5 0)
Answers
The parabola is symmetric with respect to the y-axis, and its shape and size are determined by the coefficient of x, which in this case is 20.
The equation of a parabola with its vertex at the origin can be expressed as y² = 4px, where p is the distance from the vertex to the focus. In this case, the focus is located at (-5, 0), which means the distance from the vertex to the focus is 5 units. Substituting the values into the equation, we get:
y² = 4(5)x
Simplifying further:
y² = 20x
Therefore, the equation of the parabola with vertex at the origin and focus (-5, 0) is y² = 20x.
This equation represents a parabola that opens to the right, with the vertex at the origin (0, 0). The focus is situated 5 units to the left of the vertex along the x-axis. The directrix of the parabola is a vertical line 5 units to the right of the vertex, given by the equation x = 5.
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A company owns two dealerships, both of which sells cars and motorcycles. The first dealer sells a total of 214 cars and motorcycles the second dealership sells twice as many cars in half as many motorcycles as first dealership and sells a total of 239 cars and motorcycles
Answers
Answer:
294 cars
Step-by-step explanation:
hope this helpt touch thanks it my birth day
Compare the two box plots. Which of the following statements is not true. Whoever gets right gets Brainly
Answers
BRAINLIEST
please help me! this is do very soon!
Answers
Answer: y=8x+7
Step-by-step explanation:
8 is the difference between the numbers (slope)
7 is the starting value (y-intercept).
Answer:
y = 8x + 7
Step-by-step explanation:
m = y2-y1 / x2-x1
m = 31-23 / 3-2
m = 8/1
m = 8
y=8x+b
(0,7)
7=8(0) + b
7=0+b
b = 7
y = 8x + 7
May I please have brainliest? Thank you! Hope it helps!
Fatima is taking a test that is 45 minutes long.
She finishes the test at 10:50 a.m.
What time did she start the test?
Answers
Answer:10:05
Step-by-step explanation:
subtract 45 from 50!
Answer:
She started the test at 10:05 am
Step-by-step explanation:
Take the end time and subtract the time of the test
10:50-45 = 10:05
She started the test at 10:05 am
PWEASE HELP MWEEEEE UwU
Answers
Answer: the second
one
Step-by-step explanation:
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
Answers
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.
the solution to be eliminated is -0.2s this is because time do not have negative values
What is a quadratic equation?ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.
Considering the given function, the answer is both real one is negative the other is positive.
The solution in this case represents time, and time of negative value do not apply in real life
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There are 9 chocolate bars in a bag of Halloween candy. The bag is dropped and 5 of the chocolate bars break. You take one random chocolate bar out, eat it and take another out. What is the probability that neither of these were broken?
Answers
Answer:
Below
Step-by-step explanation:
4 out of 9 are not broken first bar not broken chance is then 4/9
now there are 8 bars left and 3 are not broken so for the second bar thee is a 3/8 chance of not being broken
4/9 * 3/8 = 12/72 = 1/6
Answer:
it's below because
Step-by-step explanation:
1/6 !!!!!!!!!!!!!!
In a binomial situation, n=18 and π=0.60. Determine the expected
value
Answers
The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.
In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.
In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.
n = 18 (number of trials)
π = 0.60 (probability of success for each trial)
To find the expected value:
E(X) = np
Substitute the given values:
E(X) = 18 * 0.60
Calculate the expected value:
E(X) = 10.8
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find the lemgth of arc PQ
Answers
The arc length is D) 3.14 meters.
What is arc length?
In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.
It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.
The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.
\(A_L=\frac{\theta}{360\textdegree}2\pi r\)
Here the give circle Radius PR = 3m and θ=60°.
Now using arc length formula then,
=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)
=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)
=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)
=> \(A_L\) = 3.14 m.
Hence the arc length is D) 3.14 meters.
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I’ll give you brainliest!!!! What is the slope of the line containing (-4.3) and (2,-1)
Answers
Answer:
D
Step-by-step explanation:
The difference in the x is 6
The difference in the y is -4
-4/6 = -2/3
Answer:
-2/3
Step-by-step explanation:
The slope of a line when given two points is found by
m= (y2-y1)/(x2-x1)
= (-1 -3)/(2 - -4)
= (-4)/(2+4)
= -4/6
-2/3
50 POINTS (8th Grade Math)
Two basic math problems, answer correctly.
Trolling is not tolerated and will result to a report!
Correct answers only!
Answers
Answer: 1st; (-5, 1)
2nd;(-3, 1)
I’m pretty sure this is it, I’ve done questions like this for a while now, I think I got it right, sorry if I didn’t I tried my best.