is the statement true or false? if f(x, y) is a constant function, then df = 0.
Answers
The statement is true.
If the function f(x, y) is a constant function, then it does not change as x and y change. Therefore, the partial derivatives of f with respect to x and y are both zero everywhere, and the total differential df is also zero everywhere.
The derivative of a function gives the rate of change of that function with respect to its inputs. If a function is constant, it means that its value doesn't change, so its derivative must be zero.
To see why this is the case, let's look at the definition of the partial derivative of a function f(x,y) with respect to x:
∂f/∂x = \(\lim_{h \to \(0)} \frac{ [f(x+h,y)-f(x,y)]}{h}\)
If f(x, y) is a constant function, then f(x+h , y) = f(x, y) for all values of h. Therefore, the numerator in the limit above is always zero, and the partial derivative ∂f/∂x is also zero.
The statement is true.
If the function f(x, y) is a constant function, then it does not change as x and y change. Therefore, the partial derivatives of f with respect to x and y are both zero everywhere, and the total differential df is also zero everywhere.
Mathematically, we can express this as:
df = ∂f/∂x dx + ∂f/∂y dy = 0
since ∂f/∂x = 0 and ∂f/∂y = 0 for a constant function f(x, y).
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Related Questions
A traditional children’s riddle concerns a farmer who
is traveling with a sack of rye, a goose, and a mischievous dog.
The farmer comes to a river that he must cross from east to west. A
boat is ava
Answers
The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.
He comes to a river that he must cross from east to west, and there is a boat available to do so. Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."
The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.
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A project has an initial cost of $30 million.The project is expected to generate a cash flow of $2.85 million at the end of the first year.All the subsequent cash flows will grow at a constant growth rate of 3.85% forever in future.If the appropriate discount rate of the project is 11%,what is the profitability index of the project? a.1.917 b.1.328 c.1.387 d.1.114 ortcehov e. None of the above
Answers
Profitability index is 1.387. Thus, the correct option is (c) 1.387.
The formula for calculating the profitability index is:
P.I = PV of Future Cash Flows / Initial Investment
Where,
P.I is the profitability index
PV is the present value of future cash flows
The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.
The present value of cash flows can be calculated using the formula:
PV = CF / (1 + r)ⁿ
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
n is the number of periods
For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.
Substituting the values, we get:
PV = 2.85 / (1 + 0.11)¹ = $2.56 million
To calculate the present value of all future cash flows, we can use the formula:
PV = CF / (r - g)
Where,
PV is the present value of cash flows
CF is the cash flow in the given period
r is the discount rate
g is the constant growth rate
For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.
Substituting the values, we get:
PV = 2.85 / (0.11 - 0.0385) = $39.90 million
The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.
PV of future cash flows = $39.90 million + $2.56 million = $42.46 million
Profitability index (P.I) = PV of future cash flows / Initial investment
= 42.46 / 30
= 1.387
Therefore, the correct option is (c) 1.387.
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Multiply the MonomialsA) (4a^2) (-2a^5)
Answers
ANSWER
\(-8a^7\)EXPLANATION
We want to find the product of the monomials given:
\(4a^2\cdot-2a^5\)To do this, we will combine the terms that are alike and simplify them.
That is multiply the integers with the integers and the algebraic term with the algebraic term.
\(4\cdot\text{ -2 }\cdot a^2\cdot a^5\)Apply the addition law of indices:
\(\begin{gathered} -8\cdot a^{2\text{ + 5}} \\ =>-8a^7 \end{gathered}\)That is the answer.
A ∗
uses a heuristic function f(n) in its search for a solution. Explain the components of f(n). Why do you think f(n) is more effective than h(n), the heuristic function used by greedy best-first? Question 3 For A ∗
to return the minimum-cost solution, the heuristic function used should be admissible and consistent. Explain what these two terms mean.
Answers
A∗ is an algorithm that uses a heuristic function f(n) in its search for a solution. The heuristic function f(n) estimates the distance from node n to the goal.
The estimation should be consistent, meaning that the heuristic should never overestimate the distance, and should be admissible, meaning that it should not overestimate the minimum cost to the goal.
The A∗ heuristic function uses two types of estimates: heuristic function h(n) which estimates the cost of reaching the goal from node n, and the actual cost g(n) of reaching node n. The cost of a path is the sum of the costs of the nodes on that path. Therefore, f(n) = g(n) + h(n).
A∗ is more effective than greedy best-first because it uses a heuristic function that is both admissible and consistent. Greedy best-first, on the other hand, uses a heuristic function that is only admissible. This means that it may overestimate the cost to the goal, which can cause the algorithm to overlook better solutions.
A∗, on the other hand, uses a heuristic function that is both admissible and consistent. This means that it will never overestimate the cost to the goal, and will always find the optimal solution if one exists.Admissible and consistent are two properties that a heuristic function must have for A∗ to return the minimum-cost solution. Admissible means that the heuristic function never overestimates the actual cost of reaching the goal.
This means that h(n) must be less than or equal to the actual cost of reaching the goal from node n. Consistent means that the estimated cost of reaching the goal from node n is always less than or equal to the estimated cost of reaching any of its successors plus the cost of the transition.
Mathematically, this means that h(n) ≤ h(n') + c(n,n'), where c(n,n') is the cost of the transition from node n to its successor node n'.
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The slope of the line that passes through the point (2,4)and (3,8) is
Answers
Equation of the line:
y = 4x – 4
Slope: 4
Answer:
+4
Step-by-step explanation:
Slope is Rise over Run or the difference in the y values over the difference in the x values.
Rise = difference between 4 and 8 = 4
Run = difference between 2 and 3 = 1
So your slope is 4 and since the line slants upward from left to right, the slope is positive.
Please help I’m being timed!! A small dairy farm writes a business plan. It includes a graph showing the estimated amount of feed used each day in thousands of pounds, y, compared to the number of years since the farm began operating, x. What does the y-intercept represent? A) the estimated amount of years the farm can afford feed B) the maximum feed per day estimated for the life of the farm C) the estimated amount of feed per day for the start of the farm D) the maximum years the farm needs the originally estimated feed per day
Answers
Answer: The Answer is C
Step-by-step explanation: I just took the quiz on ed and this is the correct answer.
Answer: C: the estimated amount of feed per day for the start of the farm
Step-by-step explanation: 100% on quiz
mary has 42 peanuts frank has 22 peanuts how many fewer peanuts does frank have
Answers
Answer:
42 - 22 = 20
Mary has 20 more peanuts than Frank.
Answer:
20
Step-by-step explanation:
42-22=20
Which equation can be used to find the value of x?
Answers
Answer: D
Step-by-step explanation:
The perimeter is all the sides added up
2.5x + 2.5x + 10 + 2 + 10 =>
5x + 22
It is also given that the perimeter is 10.5x
meaning that both these values are equal
5x + 22 = 10.5x
The distances between some planets are given below. Planet Q is 3.5 x 10^6 km from planet P. Planet R is 1.2 x 10 km from planet P. Work out the shortest distance between planet Q and planet R. Give your answer in standard form.
Answers
Answer: male a right angle triage and solve for the shortest distance it's hould be bw 1.2 and 3.5
The average monthly cable TV rate from 1980 to 1997 can be modeled by R(t) = - 0.0036t ^ 3 + 0.13t ^ 2 + 7.7
where R(t) is the monthly rate (in dollars) and t is the number of years since 1980. Using this model, what would be the average monthly rate in 2012?
Answers
Answer:
Step-by-step explanation:
where
a
n
≠ 0, the exponents are allwhole numbers, and the coefficients are all realnumbers. For this polynomial function,
a
n
is the
a
0
is theand
n
is the A polynomial function is inif its terms are written in descending order of exponents from left to right.You are already familiar with some types of polynomial functions. For instance, thelinear function ƒ(
x
) = 3
x
+ 2 is a polynomial function of degree 1. The quadraticfunction ƒ(
x
) =
x
2
+ 3
x
+ 2 is a polynomial function of degree 2. Here is a summaryof common types of polynomial function
Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of prime rate plus 4%. The starting balance on October 1 was $9,300.
On October 4 they made a payment of $1,600. On October 13 the business borrowed $2,500, and on October 19 they borrowed $4,400. If the current prime rate is 8%, what is the new balance (in $)? (Round your answer to the nearest cent.)
Answers
Answer:
Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of prime rate Cook Security Systems has a $37,500 line of credit, which charges an annual percentage rate of prime rate plus 4%. The starting balance on October 1 was $9,100.plus 4%. The starting balance on Octobe The annual percentage rate is prime plus 4% so APR = 6% +4% =10 % · Periodic rate = APR/ 12 months = 10/12 = 0.8333333 % · Average daily balance = Sum of the
Step-by-step explanation:
if it's Not right Here ill give u more!!!!
P=-3(n-500)2 + 950 000
Answers
Answer:
n = - p - 950,000/6 + 500
Step-by-step explanation:
I have to find the area of this prism, could someone help me?
Answers
I think it is going to be base x height length
A ball, dropped vertically, falls d metres in t seconds.
d is directly proportional to the square of t.
The ball drops 45 metres in the first 3 seconds.
How far does the ball drop in the next 7 seconds?
Answers
Answer:
455m
Step-by-step explanation:
We know that acceleration is acceleration due to gravity, which is 10m/s, and initial speed u=0m/s
Use the motion equation to find distance when t=10:
d=ut+(1/2)at²
d=0t+(1/2)(10)(10²)
d=500m
The distance travelled in the seven seconds following the first three = 500-45=455m
assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. if 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125.
Answers
The probability that the mean blood pressure will be less than 125 is 0.9938
The mean of the pressure readings = 123
The standard deviation = 9.6
Total population = 144
The value is less than 125
The equation of the z-score is
z-score = (Observed value - Mean ) / (Standard deviation /\(\sqrt{N}\))
Substitute the values in the equation
z-score = (125 - 123) / (9.6/\(\sqrt{144}\))
= 2 / (9.6/12)
= 2 / 0.8
= 2.5
Using the statistical table
The probability of that their mean blood pressure less than 125
P(z < 2.5) = 0.9938
Therefore, the probability is 0.9938
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The vertical axis of the managerial grid measures ________, whereas the horizontal axis measures ________.
Answers
The vertical axis of the managerial grid measures concern for people, whereas the horizontal axis measures concern for production.
A managerial grid model is a self-assessment tool by which individuals and organizations can help identify a manager's or leader's style. The grid was originally developed by Robert R. Blake and Jane S. Mouton in the 1960s and has evolved in subsequent decades.
Based on the care for people and the concern for output, this model first identified five alternative leadership philosophies. Based on Theory Y, the ideal leadership stance in this approach. The grid hypothesis has always developed and changed.
Resilience was included as a new component and two more leadership philosophies were added to the theory. A new text, The Power to Change, was introduced to the grid management seminar in 1999.
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Freda waves a small flag pennant when her favorite player hits a grand slam. approximately how much fabric in square inches is used to make up the flag on her pennant
Answers
Answer: 15 inches
Step-by-step explanation:
Answer:
In a right triangle, the hypotenuse, 2x, is equal to twice the length of the shortest leg, x, and the longer leg is equal to the product of the length of the shortest leg, x, and the square root of 3.
Hypotenuse: 10 in.
Shortest Leg:2x=10 , so x=5 in,
Longer Leg: x sq rt 3 5 sq rt 3 in
area- 1/2 bh, 1/2 5*5 sq rt 3=
25t sq rt 3=21.65 sq inches
Two months ago, Marty’s dog weighed 3712 pounds. The dog was put on a diet and exercise plan and now weighs 2914 pounds. How much weight did the dog lose?
Answers
Answer:
Step-by-step explanation:
3712-2914= 798 pounds
Answer:
8 1/4
Step-by-step explanation:
you forgot to add the slash :) hopefully this helps anyone
A package of 3 pairs of insulated socks costs $23.07 . What is the unit price of the pairs of socks
Answers
The answer would be 23.07/3 = 23 is $7.69
send help my way please
Answers
Answer:
De acuerdo, el número es 911, ¿cuál es su ubicación para que pueda enviar ayuda?
Step-by-step explanation:
Answer:
D. 60°
Step-by-step explanation:
The interior angles of all triangles add up to 180 degrees.
There are two y's on the triangle
And one of the degree lengths is 60°, so we do:
2y + 60 = 180
Subtract 60 from both sides
2y + 60 - 60 = 180 - 60
2y = 120
Divide 2 from both sides
2y/2 = 120/2
y = 60°
Also, In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
All three sides are equal
All the three interior angles are equal to 60 degrees
The interior angles of all triangles add up to 180 degrees.
Heres a picture of an equilateral triangle
What is the area of a rectangle with a length of 5 inches and a with of 2 inches
Answers
Answer:
10 inches
Step-by-step explanation:
which point lies on the bisector of angle PQR ?
Answers
The point that lies on the bisector of angle PQR in the diagram given is: point Y.
What is an Angle Bisector?An angle bisector is a segment that cuts an angle into two equal parts.
From the image given, point Y lies directly opposite to vertex Q. Point Y divides angle PQR into equal parts.
Therefore, the bisector of angle PQR is: point Y.
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The sum of 2 times a number and 4 is 8. Translate the sentence into an equation. Use the variable x for the unknown number
Answers
Let:
x = Unknown number
The sum of 2 times a number and 4 can be expressed as:
\(2x+4\)Since the result is 8, the equation is given by:
\(2x+4=8\)Solve for x:
Subtract 4 from both sides:
\(\begin{gathered} 2x+4-4=8-4 \\ 2x=4 \end{gathered}\)Divide both sides by 2:
\(\begin{gathered} \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}\)Answer:
x = 2
i need help this is confusing!!!!!!!!!! helpppp
Answers
Expression: ( 2 1/2 x 2 ) divided by 1/4
Find the sum of the interior angles for a hexagon. 540° 720° 900° 1,080°
Answers
The sum of interior Angles of Hexagon is always 720°
Any hexagon's internal angles add up to 720° in all cases. By dividing 720° by 6, we may get the size of each interior angle of a regular hexagon. As a result, we have:
720°÷6 = 120°
In a regular hexagon, each inside angle is 120°.
An example of a regular hexagon with equal-length sides and angles is shown in the diagram below. By multiplying the six 120° angles together, we can demonstrate that the result is 720°.
Therefore, the interior angles of a hexagon are always added up to 720°.
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PLEASE HELP ive been stuck on this for a long time
Use the picture to fine c. Round to the nearest tenth, if necessary.
Answers
Answer:
Below
Step-by-step explanation:
You can use Pythagorean theorem to find the hypotenuse of a right triangle.
a2 + b2 = c2
The square root of 15 = 3.8729.... (a bunch of other numbers)
4^2 + 3.8729^2 = c2
16 + 15 = 31
Now that you have this, you need to find the square root
The square root of 31 = 5.56775436
Rounding this to the tenth it would be: 5.57
Final answer: C = 5.57
hope this helps! :)
The two triangles shown have the same perimeters. What is the perimeter of each triangle
Answers
Answer:
28 units
Step-by-step explanation:
Since the perimeter of both triangles is same,
the sum of all sides of first triangle = sum of all sides of second triangle
or, 6x + 3 + 2x + 4x = 5x + 5x + 3x + 2
or, 12x + 4 = 13x + 2
or, 4-2 = 13x - 12x
or, 2 = x
Now,
Putting the value of x in the perimeter of first triangle,
12x + 4= 12* 2+ 4
= 28 units
Two people are looking at a totem pole that is 65 feet tall. When the two people are looking at the top of the totem pole, they are exactly 200 feet apart the person closest to the totem pole has an angle elevation to the top of the totem pole of 32 degrees as shown. what is the value of x rounded to the nearest hundredth
Answers
The value of ‘x’ rounded to the nearest hundredth is 84.97 feet.
Let the height of the totem pole be ‘h’ and the distance between the two people be ‘d’.Given: Height of the totem pole, h = 65 feetDistance between the two people, d = 200 feetAngle of elevation of the top of the totem pole from the person closest to it,
θ = 32°We need to find the value of ‘x’. From the given diagram, we can see that the distance between the person closest to the totem pole and the base of the totem pole can be given by:
Distance = h / tanθ = 65 / tan 32°= 115.03 Feel Now,
we can calculate the distance between the two people by adding this distance to ‘x’.
Therefore, d = 115.03 + x Solving for ‘x’,
we get : x = d - 115.03x = 200 - 115.03x = 84.97 feet (rounded to the nearest hundredth)
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cooper 12.3.1 for each of the following functions, find the critical point(s) (if there is more than one critical point put the greater one first) and determine their type (max, min or inconclusive). (a) critical point -3 type a. local maximum b. local minimum c. 2nd derivative test inconclusive (b) critical point type a. local maximum b. local minimum c. 2nd derivative test inconclusive
Answers
The value of function x3 – 12x + 2 where x = 1/2 is a local minimum, x = -1/2 is a local maximum, and x = 0 is a point of inflection where the second derivative test is inconclusive.
For the function f(x) = x^3 - 12x + 2, we can find the critical points by setting the derivative equal to zero and solving for x:
f'(x) = 3x^2 - 12 = 0
x^2 - 4 = 0
x = ±2
So, the critical points are x = -2 and x = 2. For their type, we need to evaluate the second derivative of the function
f''(x) = 6x
At x = -2, we have f''(-2) = -12, which is less than zero.
x = -2 is a local maximum.
At x = 2, we have f''(2) = 12, which is greater than zero.
x = 2 is a local minimum.
For the function f(x) = (x + 1)^2, the critical point occurs when the derivative is equal to zero:
f'(x) = 2(x + 1) = 0
x = -1
The second derivative is f''(x) = 2, which is positive for all values of x. Therefore, x = -1 is a local minimum.
For the function f(x) = (x + 1)^4, the critical point occurs when the derivative is equal to zero:
f'(x) = 4(x + 1)^3 = 0
x = -1
The second derivative is f''(x) = 12(x + 1)^2, which is positive for all values of x. Therefore, x = -1 is a local minimum.
For the function f(x) = 2x - 27x^(-2), the critical point occurs when the derivative is equal to zero:
f'(x) = 2 + 54x^(-3) = 0
x = (-1/27)^(1/3)
The second derivative is f''(x) = -162x^(-4), which is negative for all values of x. Therefore, x = (-1/27)^(1/3) is a local maximum.
For the function f(x) = ln(x) - 2x^2, the critical points occur when the derivative is equal to zero:
f'(x) = 1/x - 4x = 0
x = 1/2 or x = -1/2
The second derivative is f''(x) = -1/x^2 - 4, which is negative for all values of x except x = 0. Therefore, x = 1/2 is a local minimum, x = -1/2 is a local maximum, and x = 0 is a point of inflection where the second derivative test is inconclusive.
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____The given question is incomplete, the complete question is given below:
For each of the following functions, find the critical point(s) (if there is more than one critical point put the greater one first) and determine their type (max, min or inconclusive). a. x3 – 12x + 2 Critical Point x = Type ? Critical Point x = Type ? a. (x + 1)2 Critical Point x = Type ? a. (x + 1)4 Critical Point x = Type ? a. 2x - 27x-2 Critical Point x = Type ? a. ln(x) – 2x2 Critical Point x = Type ? Critical Point x = Type no local maximum Critical local minimum
2nd derivative test inconclusive Critical Point x = type ?
Please help. I will give brainliest.
Answers
Answer:
e
Step-by-step explanation: