The partial derivatives (D₁f) (x, y) and (D₂f) (x, y) exist at every point of R², despite f not being continuous at (0,0).
The existence of partial derivatives (D₁f) (x, y) and (D₂f) (x, y) at a point (x, y) in R² is determined by the existence of the corresponding directional derivatives. The directional derivative in the direction of the x-axis, (D₁f) (x, y), measures the rate of change of f with respect to x, while the directional derivative in the direction of the y-axis, (D₂f) (x, y), measures the rate of change of f with respect to y.
In this case, f(0,0) is defined as 0, and the expression xy f(x, y) is given as x² + y². Since the given function evaluates to 0 at (0,0), we can conclude that the function is differentiable along the x and y axes, and therefore, the partial derivatives (D₁f) (x, y) and (D₂f) (x, y) exist at every point of R².
However, it is important to note that the existence of partial derivatives does not imply the continuity of the function. In this case, although the partial derivatives exist, the function f is not continuous at (0,0) because the limit of f as (x, y) approaches (0,0) does not exist. Thus, the existence of partial derivatives alone does not guarantee the continuity of the function.
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As part of a half-marathon route, Charlie ran 4.1 miles east then 9 miles south. How far is he from his starting point?
Write an equation for the following word problem.
Tyrone ate 16 hamburgers today, Tyrone's plate had a total of 24 hamburgers on it. How many hamburgers did Tyrone not eat?
Use h for hamburgers Tyrone did not eat.
1) 16 + h = 24
2) 16h = 24
3) h+ 24 = 16
4) h- 16 = 24
Answer:
Option 1 or 16 + h = 24
Step-by-step explanation:
Tyrone ate 16 hamburgers today.
Tyrone had 24 hamburgers.
Hamburger = h.
We want to find how much Tyrone had left so:
h = 24 - 16
OR (we can move 16 to the other side)
h + 16 = 24
Option 1 is the answer
How many grams does an 8-ounce portion of prime rib weigh?
Answer:
28.3495 gram
Step-by-step explanation:
hey can anyone pls answer dis!
Answer:
b
Step-by-step explanation:
Amaya is standing 30 ft from a volleyball net. The net is 8 ft high. Amaya serves the ball. The path of the ball is modeled by the equation y=-0.02(x-18)^2+12, where x is the ball's horizontal distance in feet from Amaya's position and y is the distance in feet from the ground to the ball. a. How far away is the ball from Amaya when it is at its maximum height? Explain. b. Describe how you would find the ball's height when it crosses the net at x=30. a. How far away is the ball from Amaya when it is at its maximum height? Explain. The ball is nothing ft away from Amaya when it is at its maximum height. Use the y-coordinate x-coordinate of the vertex.
Answer:
KINDLY CHECK EXPLANATION
Step-by-step explanation:
Given the equation : y=-0.02(x-18)^2+12 to model the horizontal distance of a ball from Amaya's position.
a. How far away is the ball from Amaya when it is at its maximum height?
The model takes the form of a parabolic equation. Maximum height is obtain at the Vertex :
Comparing the general model :
y = a(x - h)^2 + k
Maximum height is obtained at the Vertex :(h, k)
From the model given
Coordinate at the Vertex : (h, k) = (18, 12)
Hence, ball is 18 feets away from AMAYA
B.) Height of ball at x = 30
y=-0.02(x-18)^2+12
y=-0.02(30-18)^2+12
y=-0.02(12)^2+12
y = 9.12 feets.
Rewrite the following polynomial in standard form.
6.22 +1-
1-
1
-2
4
Answer:
Submit Answer
6.22 +1-1-1-2+4= 7.22
Answer:
6.22 +1-1-1-2+4= 7.22
Step-by-step explanation:
PLLLLLZZZ HEEELLLPPP FAST! multiply and simplify if possible -3 2/3 x (-2 1/4)
Answer:
8 1/4x
Step-by-step explanation:
I'm good at math.
find the slope of the line
Answer:
Step-by-step explanation:
When x=0 y=-3.75
When y=0 x=10
The following table lists the number of pizzas that each of four classes ate.
Class Amount of Pizza
Mr. Hernandez
Pizza
Ms. Green
Pizza
Mr. Adams
Pizza
Mrs. King
Pizza
What is the total number of pizzas the four classes ate together?
Answer:
11. 34
Step-by-step explanation:because you have to add all the whole numbers together and add the fractions expect the 1-2 because is a Improper fraction and have to simply it
PLease Help!! Brainliest answer! Thank you!
The answer is 135 your welcome
sorry I thought it was to find missing side
The measures of two complementary angles are represented by (x) and (x +20), what is the number of degrees in the measure of the smaller angle?
1. 35
2. 55
3. 80
4. 100
Angle measure of the smaller angle in two complement angles = x
Angle measure of the bigger angle = x + 20
Their sum = 90° ( the sum of two complementary angles is always equal to 90° )
This can be written in an equation as =
= x + x + 20 = 90
= 2x + 20 = 90
= 2x = 90 - 20 ( transposing +20 from LHS to RHS changes +20 to -20 )
= 2x = 70
= x = 70 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 )
= x = 35
Then the value of the smaller angle = x = 35°
The value of the bigger angle = x + 20 = 35 + 20 = 55°
Therefore , the measure of degrees in the the smaller angle is :
1. 35°Maria and Tom sold candy for a fundraiser. Maria sold seven less than twice the number of candy bars Tim sold maria and Tom sold 137 candy bars. How many did Maria sell?
Answer: 267
Step-by-step explanation: 137 x 2=274
274-7=267
2) −4 + n/3= −4 solve the equation
Answer: n=−6
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2-4+n/3-(-4)=0
simplify n/3
(-2+n/3)- -4=0
Rewrite the whole as a fraction using 3 as the denominator :
-2 • 3
-2 = -2/1 = -2X3/3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
-2 • 3 + n /3=n-6/3
n+6 = 0
Subtract 6 from both sides of the equation :
n = -6
Sorry I had to answer questions
Answer:
61
Step-by-step explanation:
Step 1: Define
8y² - y - 8
y = 3
Step 2: Substitute and Evaluate
8(3)² - 3 - 8
8(9) - 3 - 8
72 - 11
61
Answer:
61
Step-by-step explanation:
8*3²-3-8=61
Please solve (very simple)
5w – 7 = 2w + 1
What annual interest rate would you need to earn if you wanted a
$600 per month contribution to grow to $45,000 in six years? (Round
your answer to 2 decimal places.)
To calculate the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years, we can use the formula for future value of an annuity: FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuityPMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.
Using the given values, we have:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use trial and error or a financial calculator. Here, we will use a financial calculator.
To solve this problem, we will use the formula for future value of an annuity:FV = PMT x [((1 + r)n - 1) / r]where,FV = future value of an annuity PMT = the payment you will make in each periodr = the interest rate per periodn = the number of periods.
We are given:FV = $45,000PMT = $600n = 6 x 12 = 72 (since we are given in months, and there are 12 months in a year)r = ?To solve for r, we can use a financial calculator or trial and error. Here, we will use a financial calculator. We enter the values into the financial calculator and solve for r. We get
:r = 8.81% (rounded to two decimal places)Therefore, the annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.
The annual interest rate required to earn if you want a $600 per month contribution to grow to $45,000 in six years is approximately 8.81%.
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3*5^0.2w=720
What is the solution of the equation?
Round your answer, if necessary, to the nearest thousandth.
Answer: w = 1200
---------------------------------
What are some problems that equal 492009
Answer:
1 + 492008 = 492009
Step-by-step explanation:
OR
200009 + 292000 = 492009
W is less than or equal to 5 and greater than or equal to -2
Answer:
than it is any number between -2 and +5
y , add 4, then divide by 9.
whats the answer i need help
Roberto rode his bicycle for a local bike-a-thon. The bike-a-thon started at 9:00 A.M. and ended at 4:00 P.M. By 10:00 A.M., Roberto had ridden 16 miles. Except for a one-hour lunch break, Roberto rode at the same pace until 4:00 P.M.
How many miles did Roberto ride in the bike-a-thon?
Work out the percentage change when a price of £80 is increased to £100.
Answer:
125%
Step-by-step explanation:
80/100=8
80*x=100
100/80=1.25
1.25*100=125
x=125%
who knows the answer
Answer:
The answer to this question would be B.
help pls....................................
Answer:
Answer 1 is 3712000000
answer 2 is 8.624X10^10
answer 3 is 820
answer 4 is 380
answer 9 is 9200
answer 10 is 400
answer 11 is 8832000000
answer 12 is 1.3104X10^10
pls help thank you
168 = -84n
Answer:
n = -2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
usually, data collection in a functional analysis is based on a. duration b. frequency c. momentary time sampling
The correct answer is b. frequency.
Data collection in a functional analysis typically involves recording the frequency of a target behavior. In functional analysis, the focus is on understanding the function or purpose of a behavior, and frequency data helps to identify patterns and determine the relationship between the behavior and environmental events.
During a functional analysis, various conditions are manipulated to assess how they impact the occurrence of the behavior. The frequency of the behavior is typically recorded within each condition to determine if there are differences in its occurrence based on the specific environmental variables being manipulated.
While duration and momentary time sampling are also data collection methods used in behavioral analysis, they are not specifically associated with functional analysis. Duration refers to measuring the length of time a behavior occurs, while momentary time sampling involves recording whether a behavior is occurring or not at specific intervals of time.
In functional analysis, frequency data is typically the primary method for collecting and analyzing data to understand the relationship between behavior and environmental variables.
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Data collection in a functional analysis is usually based on three components: duration, frequency, and momentary time sampling. Duration observes the amount of time a behavior occurs. Frequency measures how often a behavior occurs. Momentary time sampling observes the existence of behavior at specified time intervals.
Explanation:In the context of a functional analysis, typically the data collection methods revolve around three primary types: duration, frequency, and momentary time sampling.
Duration refers to the total amount of time that a behavior happens. It generally is measured from the moment the behavior begins until it ends. It's important when the length of time that the behavior occurs can impact its functionality.
Frequency records how often a behavior occurs within a set observational period. It’s used when the number of times the behavior occurs is the important aspect to measure.
Momentary time sampling is a method of measuring behavior in which the existence or nonexistence of behaviors are recorded at precisely specified time intervals. This process involves observing whether the behavior occurs or does not occur at the moment the interval ends. This method is beneficial as it does not need continuous observation.
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hale's one-stop gas and auto service compete with Murray's gas and service mart. the local demand is given by P=2.5-0.01Q.
Hale's MC function is MCH: qH=0.35qH
Murray's MC function is MCM: qM=0.3qM
find hale's and Murray's reaction function; then find the Cournot solution. (price and quantities)
The Cournot solution for the price is approximately $2.425, and the quantities produced by Hale and Murray are approximately 3.47 and 4.03, respectively.
To find Hale's and Murray's reaction functions, we need to determine their profit-maximizing quantities given the local demand and their respective marginal cost functions.
Hale's profit function can be expressed as:
πH = (P - MCH) * qH
[tex]= (2.5 - 0.01Q - 0.35qH) * qH\\= 2.5qH - 0.01qH^2 - 0.35qH^2[/tex]
To maximize profits, we take the derivative of πH with respect to qH and set it equal to zero:
dπH/dqH = 2.5 - 0.02qH - 0.7qH
Setting the derivative equal to zero:
2.5 - 0.02qH - 0.7qH = 0
2.5 - 0.72qH = 0
0.72qH = 2.5
qH = 2.5 / 0.72
qH ≈ 3.47
Therefore, Hale's reaction function is qH = 3.47.
Similarly, Murray's profit function can be expressed as:
πM = (P - MCM) * qM
[tex]= (2.5 - 0.01Q - 0.3qM) * qM\\= 2.5qM - 0.01qM^2 - 0.3qM^2[/tex]
To maximize profits, we take the derivative of πM with respect to qM and set it equal to zero:
dπM/dqM = 2.5 - 0.02qM - 0.6qM
Setting the derivative equal to zero:
2.5 - 0.62qM = 0
0.62qM = 2.5
qM = 2.5 / 0.62
qM ≈ 4.03
Therefore, Murray's reaction function is qM = 4.03.
To find the Cournot solution, we substitute the reaction functions into the local demand equation:
Q = qH + qM
Q = 3.47 + 4.03
Q ≈ 7.5
Substituting Q back into the demand equation:
P = 2.5 - 0.01Q
P = 2.5 - 0.01(7.5)
P = 2.5 - 0.075
P ≈ 2.425
The Cournot solution for the price is approximately $2.425, and the quantities produced by Hale and Murray are approximately 3.47 and 4.03, respectively.
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The below is the dimensions if a running track are shown. the ends are circular.
a)Find the combined area of the (orange) track and the (green) grassed central area.
The calculated combined area of the track is 9166.625 square meters
Working out the combined area of the track and grassFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the individual shapes
So, we have
Area = 2 * Semicircle + Rectangle
Using the area formulas, we have
Area = 90 * 65 + 2 * 1/2 * 3.14 * (65/2) * (65/2)
Evaluate
Area = 9166.625
Hence, the total area of the figure is 9166.625 square meters
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properties of quadilateral
Opposite sides are equal and parallel.
Diagonals bisect each other.
Sum of any two adjacent angles is 180°
Opposite angles are equal
