The process to show the vector field V(x,y,z) as conservative is show below and the scalar potential f is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .
The Gradient is vector that is made from partial derivatives of potential function .
The Vector function is given as , V(x,y,z) = [tex](yz^{2} )i + (xz^{2} )j + (2xyz)k[/tex] ,
So , we can write the partial derivatives function of potential function as :
[tex]\frac{\partial f}{\partial x} = yz^{2}[/tex] ; [tex]\frac{\partial f}{\partial y} = xz^{2}[/tex] ; [tex]\frac{\partial f}{\partial z} = 2xyz[/tex],
On Antidifferentiating any of the above three partial derivatives ,
we get ; [tex]f=xyz^{2} + C[/tex] , here the constant C can take any value ,
so , we take C as [tex]e^{\pi }[/tex] .
Therefore , the potential Function is [tex]f(x,y,z) =xyz^{2} + e^{\pi }[/tex] .
The given question is incomplete , the complete question is
Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .
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Find the volume of a right circular cone that has a height of 3.9 in and a base with a radius of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
Step-by-step explanation:
radius r = 3.9 in
height h = 14.3 in
slant height s = 14.822280526289 in
volume V = 227.76860897791 in3
lateral surface area L = 181.60571368226 in2
base surface area B = 47.783624261101 in2
total surface area A = 229.38933794336 in2
In Terms of Pi π
volume V = 72.501 π in3
lateral surface area L = 57.806894052526 π in2
base surface area B = 15.21 π in2
total surface area A = 73.016894052526 π in2
Which expression could be used to find the volume of the prism shown below?
A rectangular prism with length of 12, height of 10, and width of 4.
(4 times 12) times 10
(4 + 12) times 10
(10 + 4) times 12
(10 + 12) times 4
write the equation of the line passing through the point (4, -6) with a slope of 1/2?
Answer:
Step-by-step explanation:
We know that , the equation of line when the slope and the coordinates are given is:
y - y1 = m(x - x1)
where x1 = 4 , y1 = -6 and m = 1/2
therefore, y -(-6) = 1/2(x - 4)
y + 6 = x/2 - 2
6+2 = x/2 - y
8 = x - 2y/2
16 = x - 2y
required equation : x-2y-16=0
What is the slope of a line that pass through the points (3,-2) and (5,-2)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{-2 +2}{2} \implies \cfrac{ 0 }{ 2 } \implies \text{\LARGE 0}[/tex]
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, - 2 ) and (x₂, y₂ ) = (5, - 2 )
m = [tex]\frac{-2-(-2)}{5-3}[/tex] = [tex]\frac{-2+2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0
Simplify the expression: 9a + 6b - 4a + 3b
Answer:
5a + 9b
Step-by-step explanation:
Combine like terms
9a + 6b - 4a + 3b
- 4a + 9a = 5a
6b+3b=9b
so 5a+9b
Answer:
= 5a+9b
Step-by-step explanation:
hope this helps :)
What is the degree of polynomial 2 y² Y³ 2y8?
The degree of the polynomial [tex]2yA^2yA^32y^8[/tex] is 15
A polynomial's degree is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer.
The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).
Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]
The polynomial has a degree of 6.
This is because the exponent values of x and y in the second term of the algebraic formula, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the multivariable polynomial expression has a degree of 6.
As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]
The total sum of power is: 1+2+1+3+8=15
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Please Help!!
In desperate need!
Find the distance between the two points.
Usa test prep
PLEASE HELP ANSWER GETS BRAINIEST!
Simplify by using order of operations:
4+(9 x 2) divided by (4 - 1) -4
given that y=15-2x,copy and complete the table below giving the values of y for x=-4,0,4,8,12
Please help as soon as possible!
22. x=?
23. y=?
The unknown angles in the parallel lines are as follows;
x = 28
y = 23
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as linear angles, vertically opposite angles, interior angles, corresponding angles, alternate interior angles, alternate exterior angles etc.
using vertical angles and same side interior angles,
5y - 4 + 3y = 180 (same side interior angles are supplementary)
8y - 4 = 180
8y = 180 + 4
8y = 184
divide both sides by 8
y = 184 / 8
y = 23
Hence,
3y = 2x + 13(corresponding angles)
corresponding angles are congruent.
Hence,
3(23) = 2x + 13
69 - 13 = 2x
2x = 56
x = 56 / 2
x = 28
Therefore,
x = 28
y = 23
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Hi I need help on this I've tried about 55 times already and I want to smash my computer into bits so if anyone can help please I need it
Answer:
150.35 units²
Step-by-step explanation:
area of full circle = πr² = (3.14)(13²) = 530.66 units²
area of 102° segment = (102/360)(530.66) = 150.35 units²
A semi-circular protractor has a diameter of 15 cm.
Calculate the perimeter of the protractor.
Give your answer to a suitable degree of accuracy
A semi-circular protractor with a diameter of 15 cm has the perimeter of 38.5 cm.
What is the perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The formula for perimeter of a semi-circle is -
πr+2r
Where r is the radius of the semi-circle.
The diameter d of semi-circle is 15 cm.
The radius of the semi-circle is -
r=d/2
r=15/2
r=7.5 cm
Plugging the values in the equation -
=πr+2r
=(3.14)(7.5)+2(7.5)
=23.5+15
=38.5 cm
Therefore, the value for perimeter is obtained as 38.5 cm.
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Select the correct answer.
The class sizes of the Introductory Psychology courses at a college are shown below.
121, 134, 106, 93, 149, 130, 119, 128
The college adds a new Honors Introductory Psychology course with 45 students. What effect does the new class size have on the center and spread of the class sizes of the Introductory Psychology courses at the college?
A. The value of the center increases and the distribution has a larger spread.
B. The value of the center decreases and the distribution has a smaller spread.
C. The value of the center decreases and the distribution has a larger spread.
D. The value of the center increases and the distribution has a smaller spread.
Center : Mean Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5 After the introduction of the new course, center = average(121,134,106,93,149,130,119,128,45) = 113.9 The center has moved to the left (if plotted in a graph) because of the low intake for the new course. Spread before introduction of the new course : Arrange the numbers in ascending order: (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132 Spread = Interquartile range = Q3-Q1 = 19.5 After addition of the new course,
(45,93, 106,119,) 121, (128, 130,134, 149)
Q1=median(45,93,106,119)=99.5
Q3=median (128, 130,134, 149)= 132
Spread = Interquartile range = 132-99.5 =32.5
We see that the spread has increased after the addition of the new course.
A grocer can buy strawberries for $1.38 per pound. What is the constant of proportionality?
It means that the grocer has to pay $1.38 for each pound of strawberries. So the constant of proportionality for this scenario is $1.38
What is proportionality?Proportionality is a mathematical relationship between two variables, where the ratio of one variable to the other is always the same, regardless of the values of the variables. The variables are said to be in proportion if there is a constant of proportionality "k" such that one variable is equal to "k" times the other variable. In other words, if y is proportional to x, the relationship is represented by an equation of the form y = kx, where "k" is the constant of proportionality.
What is constant?A constant is a value that does not change. In mathematical terms, it refers to a value in an equation that remains the same and does not depend on the variables. For example, in the equation y = kx, "k" is a constant. It is a fixed numerical value that relates two variables in a proportionality relationship. Constants can be represented by a number, a letter or a symbol.
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In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm find the radiu of the circumcircle
In triangle abc, i the circumcenter bc i equal to 72cm d i equal to 15cm then the radiu of the circumcircle is 39
A chord is the line segment joining two points of the circumference of a circle as shown in the image attached.
If the chord is passing through the center of the circle then it will become diameter which means the diameter is the longest possible chord inside a circle.
A chord is always within the circumference because it is inside the circle.
Whats the definition of a circumference?
a line that goes around or encloses a circle. : the outer boundary of a figure or area. 3. : the distance around something. the circumference of the earth at the equator.
since ABC is an equilateral triangle
therefore SD bisects BC
BD= BC/2
BD= 36
IN Triangle ABC
since angle BDS = 90 degree
Therefore
BS = 39
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A restaurant meal for a group of people cost $85 total. This amount included a 6% tax and an 18% tip, both based on the price of food. Which equation could be used to find f, the cost of the food?
What is the volume of a sphere with a radius of 4 dm
Answer:
267.95 dm³
Step-by-step explanation:
Volume of a sphere of radius r is V = (4/3)πr³
In this case, V = (4/3)(3.14)(4 dm)³ = 267.95 dm³
6x + 11= 21 tape diagram
Answer:
x = 5/3
Step-by-step explanation:
6x + 11 = 21
6x = 10
x = 10/6
x = 5/3
Let's check
6(5/3) + 11 = 21
30/3 + 11 = 21
10 + 11 = 21
21 = 21
So, x = 5/3 is correct!
What is the relationship between the line of reflection and the segments connecting the corresponding points?
The relationship between the line of reflection and the segments connecting the corresponding points is perpendicular bisector.
Here we have to find the relationship between the line of reflection and the segments connecting the corresponding points
In order to find the relationship we must know what is meant by line of reflection.
The term line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.
As per the definition of the term we have identified that the relationship between these two element is perpendicular to the segment and bisects it. Because the line of reflection is the perpendicular bisector of the segment joining corresponding points of the preimage and image.
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What does P(vowel and even) mean?
Probability of getting a vowel or an even number
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
D
Step-by-step explanation:
This part two of the problem
Answer:
d seems like the only one that would be correct
Step-by-step explanation:
lmk if this is wrong
help me please . I don't know which method to use. maybe the time=
[tex] \frac{distance}{speed} [/tex]
or....
I dont know what this person meant, help :)
they said "what period are you in 7th?" exactly like this is how they said it
Answer:
as in what class period are you so for example
period 1:math etc
Answer:
im guessing they meant classes, they probably asked what time are your classes in 7th grade... ( I.D.K. i tried my best lol)
Step-by-step explanation:
4 Siobhan and Ralph shared £700 in the
ratio 2:3.
Siobhan gave a quarter of her share to Karen.
Ralph gave a fifth of his share to Karen.
What fraction of the £700 did Karen receive?
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
What is a proportion?The rule of three is used to link the measures because a proportion is a fraction of a total amount. It is possible to construct equation or relations between variables that are either direct (when both rise or decrease) or inverse proportional (when one increases and the other declines, or vice versa) in order to determine the necessary measures in the situation.
Here,
Given :
Siobhan and Ralph shared £700 in the
ratio 2:3.
Thus,
280 / 420 = 2/3
Thus,
Siobhan and Ralph has £280 and £420 respectively.
and Siobhan gave a share of quarter to karen :
So,
280/4 =70
Therefore ,the solution to the given problem of proportion comes out to be karen got £70.
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Select the least common multiple of 6 and 8. OA 2 OB: 14 O C. 24 OD. 48
Answer:
C. 24
Step-by-step explanation:
The LCM is the least common multiple between two or more numbers.
6: 6, 12, 18, 24, 30, 36, 48, 54
8: 8, 16, 24, 32, 40, 48, 54, 64
24 is the smallest number both numbers have in common.
Therefore, 24 is the least common multiple.
On average, what value is expected for the F-ratio if the null hypothesis is true? a. 1 b. k-1 c. N-k on average, what value is expected for the F-ratio if the null hypothesis is false? a.1 b. 0
c. Between 0 and 1.00 d. Much greater than 1.00
The F-ratio is a measure used in statistical tests, specifically in ANOVA (Analysis of Variance) to test for differences between means of multiple groups.
a) On average, what value is expected for the F-ratio if the null hypothesis is true?
The answer is a. 1. If the null hypothesis is true, it means that there is no significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value close to 1, as the variance between the groups is not significantly different from the variance within the groups.
b) On average, what value is expected for the F-ratio if the null hypothesis is false?
The answer is d. Much greater than 1.00. If the null hypothesis is false, it means that there is a significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value much greater than 1, as the variance between the groups is significantly larger than the variance within the groups.
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what is the measurement of angle 6
Answer: 59
Step-by-step explanation: angle 3 is equal to angle 6 and to find angel 3 do 180-121
What is the first step to prove that 9n - 4n is divisible by 5?
Answer:
Collect like terms, ie do 9n-4n = 5n ...
5n will then be exactly divisible by 5 as 5n / 5 = n