A scalar potential function f(x,y), the vector field f(x,y) = x^2 i + y j is conservative.
To show that the vector field f(x,y) = x^2 i + y j is conservative, we need to find a scalar potential function f(x,y) such that grad f(x,y) = f(x,y).
So, let's first calculate the gradient of a potential function f(x,y):
grad f(x,y) = (∂f/∂x) i + (∂f/∂y) j
Assuming that f(x,y) exists, then f(x,y) = ∫∫ f(x,y) dA, where dA = dx dy, the double integral is taken over some region in the xy-plane, and the order of integration does not matter.
Now, we need to find f(x,y) such that the partial derivatives of f(x,y) with respect to x and y match the components of the vector field:
∂f/∂x = x^2
∂f/∂y = y
Integrating the first equation with respect to x gives:
f(x,y) = (1/3)x^3 + g(y)
where g(y) is a constant of integration that depends only on y.
Taking the partial derivative of f(x,y) with respect to y and comparing it to the y-component of the vector field, we get:
∂f/∂y = g'(y) = y
Integrating this equation with respect to y gives:
g(y) = (1/2)y^2 + C
where C is a constant of integration.
Therefore, the scalar potential function is:
f(x,y) = (1/3)x^3 + (1/2)y^2 + C
where C is an arbitrary constant.
Since we have found a scalar potential function f(x,y), the vector field
f(x,y) = x^2 i + y j is conservative.
Learn more about potential function here
https://brainly.com/question/28156550
#SPJ11
A UFO is coming in to pick up some test subjects. Their elevation above the ground is 60,000 feet. Their laser sights tell them that a direct (diagonal) path to the nearest landing area is 90,000 feet away. What is the angle of depression as they come in to land?
Answer:
41.83°
Step-by-step explanation:
It is given that :
The vertical distance of the UFO from the ground = 60,000 feet
The diagonal distance of the landing area to the UFO = 90,000 feet
In order to find the angle of depression, we have to use the trigonometric ratios, i.e.,
[tex]$\sin \ \theta = \frac{\text{perpendicular distance}}{\text{hypotenus}}$[/tex]
[tex]$\sin \ \theta = \frac{60,000}{90,000}$[/tex]
[tex]$\sin \ \theta = \frac{2}{3}$[/tex]
[tex]$\sin \ \theta = 0.667$[/tex]
∴ [tex]$\theta = \sin^{-1 }(0.667)$[/tex]
= 41.83°
Shaun climbed Mount Rushmore at a unit rate of
1,250 meters per minute. How long did it take him to
climb 75,000 meters?
Answer:
60
Step-by-step explanation:
75,000/1,250= 60 mins or an hour
Use the graph to answer the following question.
For which interval is the function increasing and changing by a constant
rate of change?
A. between 2 and 4
B. -2 and 0
C. between -4 and -2
D. between 0 and 2
We can conclude that in the interval -4 and 2, the function increasing and changing by a constant rate of change.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is the graph of a function as shown in the image.
Between the interval -4 and 2, the function increasing and changing by a constant rate of change.
Therefore, we can conclude that in the interval -4 and 2, the function increasing and changing by a constant rate of change.
To solve more questions on functions, visit the link-
https://brainly.com/question/29014197
#SPJ5
How many solutions does this equation have?
-7p - 16 = -17p + 8 + 12p
•no solution
•one solution
•infinitely many solutions
Answer:
One solution
Step-by-step explanation:
-7p - 16 = -17p + 8 + 12p
-7p-16=-5p+8
-7p+5p=8+16
-2p=24
p=-12
If f(x)=3x-2 and g(x)=2x+1 find (f-g)(x)
9514 1404 393
Answer:
(f-g)(x) = x -3
Step-by-step explanation:
(f-g)(x) = f(x) -g(x)
= (3x -2) -(2x +1)
= 3x -2 -2x -1 = (3x -2x) +(-2 -1)
(f-g)(x) = x -3
Two rectangular rugs are ordered at Cardi’s furniture: small rugs and large rugs.
Small rugs are 36 inches long and 18 inches wide.
Large rugs are 90 inches long and 45 inches wide.
a. Are the rugs similar shapes? Explain your reasoning.
b. Find the ratio of the two perimeters and the ratio of the two areas. Is there anything you notice about these ratios? What can you deduce?
c. It takes 180 feet of yarn to create a square foot of either rug. How many inches of yarn are needed to make the small rug? How many feet or yarn is needed to make the large rug?
d. If a “skein” of yarn costs $4.50 and one skein is exactly 180 feet of yarn, how many skeins of yarn are needed to make the large rug? Given this answer what is the lowest Cardi’s must sell the large rug in order to make a profit
PLEASE HELP EVEN IF U CAN ANSWER JUST 1
Answer:
a.) yes they are similar shapes, the width for both rugs is 1/2 of the length. This means that they are both similar in shape.
b.) 2:5 (perimeter rug 1 and 2 compared), 4:25 ( area for 1 and 2). The numers in the perimeter ratio are the square root of the numbers in the area ratio.
c.) You will need 648 sq in for the small rug and 4050 sq in for the large rug.
d.) 2: she has to sell the large rugs x>$9 and the small rugs for s>$1.50
Step-by-step explanation:
total perimeter for rug 1 = 108 For rug 2 = 270
area for run 1 = 648 For rug 2 = 4050
180 ft = 2150 in
The large rug needs two skeins of yarn which cost 9 dollars, if she wants to make a profit she will have to sell them over that price.
You can make 3 small rugs with one skein meaning if she wants to make a profit from the small rugs she has to sell them over 1/3 of the price of the skein (which is sold for $4.50). She will have to sell the small rug for over $1.50
find the slope of (-20, -9), (-6,0)
Step-by-step explanation:
use the formula to calculate slope
Someone please help!
Answer:
10=1x+25
slope=1
y-int-25
Thats all i know so far i will keep working on it
Step-by-step explanation:
PLEASE HELP ME WITH THIS
Answer:
help with what?
Step-by-step explanation:
Jane was running for 2 hours and 25 minutes and reached her journey at 2:05pm. Calculate the time she started.
Answer:
11:40 am
Step-by-step explanation:
First, I started by subtracting 5 minutes from the additional 25 minutes of running that couldn’t fit into another hour. That would bring the running time to 2 hours and 20 minutes and the end time to 2:00 pm. Take away another 2 hours and you would be left with 20 minutes, with a start time of 12:00 pm. Get rid of the last 20 minutes and you get the start time as 11:40 am.
Check:
11:40 + 2 hours = 1:40 pm
1:40 + 20 minutes = 2:00 pm
2:00 + 5 minutes = 2:05
This is correct
Answer:
11:40 am
First, I started by subtracting 5 minutes from the additional 25 minutes of running that couldn’t fit into another hour. That would bring the running time to 2 hours and 20 minutes and the end time to 2:00 pm. Take away another 2 hours and you would be left with 20 minutes, with a start time of 12:00 pm. Get rid of the last 20 minutes and you get the start time as 11:40 am.
el resultado de 17.96 × 32.22
Answer:
El resultado: 5.786.712
Answer:
578.6712
Step-by-step explanation:
Find the unit rate for this situation: ride a bike 64 miles in 4 hours
Evaluate the algebraic expression at the given value of the variables.
Answer:
17
Step-by-step explanation:
Three times the differnece of fredicos age and 4, increased by 7, is greater than 37. What are possible values of fredicos age?
Answer:
Possible values of fredicos age satisfy [tex]x>14[/tex] where [tex]x[/tex] denotes fredicos age.
Step-by-step explanation:
Let [tex]x[/tex] denotes fredicos age.
Three times the difference of fredicos age and 4, increased by 7 = [tex]3(x-4)+7[/tex]
According to the question,
[tex]3(x-4)+7>37\\3(x-4)>37-7\\3(x-4)>30\\x-4>10\\x>10+4\\x>14[/tex]
So, possible values of fredicos age satisfy [tex]x>14[/tex]
Here, [tex]x[/tex] denotes fredicos age.
The area of a rectangle is 44m2. Work out the missing length x.
Answer:
Your answer is
How to determine length without width or other things.
11*4,,,
22*2
Want more answer then follow me, like and MARK MY ANSWER AS BRAINLIST ANSWER.
I need that urgently.
Answer:
44=(L)ength x (W)idth
if x=length, x=44/W
if x=width, x=44/L
2 x (c2 - 5) for c = 4 sos!!
Answer:
6
Step-by-step explanation:
2(4·2-5)
2(8-5)
2·3
6
Answer:
6
Step-by-step explanation:
2 x (c2 - 5) = 2 x (4 x 2 - 5)
= 2 x (8 - 5)
= 2 x (3)
= 6
HELP!!
A.x=6
B.x=24
C.x=12
D.x=12 sqr root 3
E.x=36
1 Which of the following could be the sides of a right triangle? Check all that apply. A. 10, 24, 26 B. 4, 5, 9 C. 18, 24, 30
Answer:
A and C
Step-by-step explanation:
Let Triangle ABC is a right angle traingle.
From Option A
AB= 24, BC= 26 and AC=10
By Pythagorean Triplet
(AB)^2 + (AC)^2 = (24)^2 + (10)^2
= 576+100
(AB)^2 + (AC)^2 = 676 ---------------- (I)
(BC)^2 = 26^2 = 676 -------------------(ii)
From (I) and (ii)
(BC)^2 = (AB)^2 + (AC)^2
Therefore, the sides 10,24 and 26 are the sides of the right angle triangle.
From Option C
AB= 18, BC= 30 and AC=24
By Pythagorean Triplet
(AB)^2 + (AC)^2 = (18)^2 + (24)^2
= 324+576
(AB)^2 + (AC)^2 = 900---------------- (I)
(BC)^2 = 30^2 = 900 -------------------(ii)
From (I) and (ii)
(BC)^2 = (AB)^2 + (AC)^2
Therefore, the sides 18, 24 and 30 are the sides of the right angle triangle.
b) ¿Cuál es la relación entre el diametro y el radio?
Answer:
La circunferencia es una línea curva, y su longitud depende del radio o del diámetro. La relación matemática entre el radio (o diámetro) y la circunferencia se da por la siguiente fórmula: C = 2πr = πD. Donde C es la circunferencia y π=3.14.
Step-by-step explanation:
Answer:
Él radio mide la mitad de lo que mide él diámetro
Step-by-step explanation:
Espero te ayude la respuesta :)
Axel owns stock in a company. He purchased the stock In January at a price of $250 a share. From January to February, the stock price decreased by 38% a share. From February to March, the stock price increased by 20% a share. By what percentage did the price of the stock decrease per share from January to March?
Answer:
25.6%
Step-by-step explanation:
Purchase price = $250 / share
Jan - feb : 38% decrease
(100 - 38)% * 250 = $155
February - March : 20% increase
(100 + 20)% * $155
120% * $155 = $186
Percentage decrease from January to March :
[(250 - 186) / 250] * 100%
(64 / 250) * 100%
0.256 * 100%
25.6%
In ΔGHI, g = 790 inches, h = 200 inches and i=820 inches. Find the measure of ∠I to the nearest degree
urgenttttt !!!!
Answer:
92
Step-by-step explanation:
Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area of the cover? Use = 3.14 and round the answer to the nearest square foot. ft2
Answer:
38 ft
Step-by-step explanation:
Give the person underneath me brainless now.
What is the ratio of the length of the rectangle to its width 24 and 20
A dog walking service offer daily services in weekly service in the winter the ratio decor Shmurda weekly customer was 125 however in Springmore Cozumel motivate the daily service because of all the nice weather out of the chair while change the ratio was 4 to 2 if there was a 125 weekly? In the winter how many dell customer would it be in the spring
Answer:
100 customers
Step-by-step explanation:
The computation of the number of dell customers would be in the spring is shown below:
Given that
In winter season
The ratio of daily customers to weekly customers = 1:5.
In Spring season :
The ratio of daily customers to weekly customers = 4:2.
And, the Number of the weekly customer in the winter is 125
So if we can see that the weekly customers would be 5 times of daily customers
So, the daily customers in winter is
= 125 ÷ 5
= 25 customers
Now in the spring it would be
= 25 × 4
= 100 customers
Jeffrey rented a car for spring break. It costs $100 to rent the car plus $8 per mile he was charged $1,316. How many miles did he drive.
Answer:
152 miles
Step-by-step explanation:
Answer:
he drived around 300 mile
35 points!!! Help!! Make sure u answer all!!!
Answer:
Expression for Perimeter: 6x + 6
x = 12 cm
Verify A = 360:
2(12) x (12+3) = 360
24 x 15 = 360
360 = 360
Step-by-step explanation:
Please help me answer all three
Step-by-step explanation:
You have to give us more information, who is the character. Is it you? Someone else?
the answers are the back of the book. I know because I have the same one
What is additive inverse of the check?
7x -3
-7x + 3
-7x - 3
7x - 3
Answer:
Make sure that all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
Search Results
Page Navigation
Footer links
I need help on this question as soon as possible
Answer:
choice 2) rotation 90 CW
Step-by-step explanation:
Answer:
Rotation 90 CW
Step-by-step explanation:
Can I have Brainliest?
WILL MARK AS BRAINLIEST Write a complete Spanish sentence to indicate what the following people
eat/drink each day. Make sure to capitalize the first word of the sentence, end
with a period and include the correct article (el, la, los, las)! If there is more
than one of an item, you need to make that food/beverage plural. Follow the
model.