In the electric field [tex]{\vec{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex], find the potential difference between the points A(1,3,5) and B(3,2,7)​

Answers

Answer 1

Let's recall that, the potential difference between any two points X(x,y,z) and Y(a,b,c) is given by ;

[tex]{\boxed{\bf{V_{Y}-V_{X}=\displaystyle \bf -\int_{X}^{Y}\overrightarrow{E}\cdot \overrightarrow{dr}}}}[/tex]

So, here ;

[tex]{:\implies \quad \sf \overrightarrow{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex]

So, now our second component of the Integrand will just be ;

[tex]{:\implies \quad \sf \overrightarrow{dr}=dx\hat{i}+dy\hat{j}+dz\hat{k}}[/tex]

So, now the whole integrand will just be ;

[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=(3x\hat{i}-2y\hat{j}+5z\hat{k})(dx\hat{i}+dy\hat{j}+dz\hat{k})}[/tex]

[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=3xdx-2ydy+5zdz}[/tex]

Now, Let's move to the final answer ;

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\int_{X}^{Y}3xdx-2ydy+5zdz}[/tex]

As,X is the point (1,3,5) and Y being (3,2,7) , so seperate the integral into three integrals with limits as follows respectively;

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(\int_{1}^{3}3xdx-\int_{3}^{2}ydy+\int_{5}^{7}zdz\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(3\int_{1}^{3}xdx-2\int_{3}^{2}ydy+5\int_{5}^{7}zdz\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{3\bigg(\dfrac{x^2}{2}\bigg)\bigg|_{1}^{3}-2\bigg(\dfrac{y^2}{2}\bigg)\bigg|_{3}^{2}+5\bigg(\dfrac{z^2}{2}\bigg)\bigg|_{5}^{7}\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{2\bigg(\dfrac{9}{2}-\dfrac12\bigg)-2\bigg(\dfrac{4}{2}-\dfrac92\bigg)+5\bigg(\dfrac{49}{2}-\dfrac{25}{2}\bigg)\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{3(4)-(-5)+5(12)\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{12+5+60\}}[/tex]

[tex]{:\implies \quad \displaystyle \boxed{\bf{V_{Y}-V_{X}=-77\:\: Volt}}}[/tex]

Hence, this is the required answer


Related Questions

Answer quickly please !!

Answers

Answer: 65 degrees

            Using the property of vertical angles, the measurement of angle x is going to be 65 degrees.

            Single angle x is directly opposite of the 65° angle given, we can figure out what angle x will be as they will be congruent.

By using the Vertical Angle Theorem, we can say

   --> x = 65

Definition of Vertical Angle Theorem: states that the opposite (vertical) angles of two intersecting lines are congruent.

PLEASE HELP I WILL GIVE BRAINLIEST

Answers

Answer:

65 degrees

Step-by-step explanation:

The angles will sum up to 360, just do 360 - all known angles

360 - 90 - 128 - 77 = 65

Answer:

Step-by-step explanation:

Sum of all angles is 360 degrees

Let the measure of angle M equal x.

x+90+77+128=360

x=65

Measure of angle M is 65 degrees

Six times a number increased by 4 is no less than 50.
Which inequality represents this statement?
1: 6x+4≤50
2: 6x+4<50
3: 6x+4≥50
4: 6x+4>50

Answers

Answer:

3.

Step-by-step explanation:

For this question, you just have to pick apart what "no less than" means. If I say I can have no less than 2 apples to eat, that's me saying that that's the minimum number I can have, but 2 apples is also still fine. In this case, that minimum is 50 but we can still have over 50. So, 6x+4 can be greater than or equal to 50.

Help picture below problem 14

Answers

Answer:

c is the answer

DO MARK BRAINLIEST

find the equation (in the terms of x) of the line through the points (-2,-5) and (5,0)

Answers

Answer:

-5x+7y+25=0

Step-by-step explanation:

vecto AB= (7;5)

vecto n = (-5;7)

line through the points (-2;5) and (5;0) :

-5*(x+2)+7*(y+5)=0

-5x+7y+25=0

What is the slope-intercept equation for this line?
y = [?]x +[?]

Answers

Answer:

y = -3x + 1

Step-by-step explanation:

as we can see the y intercept is 1 because on the y- axis (0,1)

for slope it is 3 because rise over run. We rise 3 and run 1 = 3/1 = 3

the slope is negative because of the line

Hope this helps!!

Answer:

y=-3x+1

Step-by-step explanation:

what is 1/4 - 41 1/4 + 3

Answers

Answer:

-38

Step-by-step explanation:

i hope this helps you

good luck on your quiz or lesson!

Answer:

-38

Step-by-step explanation:

[tex]\frac{1}{4} = 0.25[/tex]

[tex]\frac{1}{4} -41\frac{1}{4} +3[/tex]

[tex]0.25-41.25+3[/tex]

[tex]-41+3[/tex]

[tex]-38[/tex]

the ratio between two no is 2:3 . if the consequent is 24 the antecendent is​

Answers

antecedent : 16

ratio: 2 : 3

=========

antecedent : 2

consequent : 3

=============

[tex]\rightarrow \sf \dfrac{2}{3}=\dfrac{x}{24}[/tex]           [ x is antecedent ]

[tex]\rightarrow \sf 2(24)=3(x)[/tex]

[tex]\rightarrow \sf 48=3(x)[/tex]

[tex]\rightarrow \sf x= 16[/tex]

Additional information:

In the ratio, a : b  Here the "antecedent is a" and "consequent is b"

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Mt. Everest, the tallest mountain in the world, is 29,029 ft tall. K2, the world’s second tallest mountain is 28,251 ft tall. How much taller is Mt. Everest than K2?

Answers

Answer:

778ft

Step-by-step explanation:

Factor completely 4a^2-b^2-2a+b GUYS HELP THERE ARENT ANY CORRECT ANSWERS ON BRAINLY URGENT

Answers

Answer:

(2a-b)(2a+b-1)

Step-by-step explanation:


Create the equation of a circle that has a center at (1,3) and a radius of 4 units.

Answers

The equation of the circle centered at (1, 3) with a radius of 4 units is:

(x - 1)^2 + (y - 3)^2 = 16

How to write the equation of a circle?

For a circle with the center on the point (a, b) and radius R, the equation is:

(x- a)^2 + (y - b)^2 = R^2

In this case, the center is (1, 3) and the radius is R = 4, so the equation will be, so we just replace these in the general equation that we have above.

(x - 1)^2 + (y - 3)^2 = 4^2

(x - 1)^2 + (y - 3)^2 = 16

If you want to learn more about circles, you can read:

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No Calculator Let gbe a twice-differentiable function. The function g and its derivatives have the properties indicated in the table above. 0 0​

Answers

Hi there!

Part D:

We can use the Taylor Polynomial expansion for a second-degree polynomial:

[tex]P_3(x) = g(c) + \frac{g'(c)}{1!}(x - c) + \frac{g''(c)}{2!}(x - c)^2[/tex]
Where c is the value that the polynomial is centered about.

We are given that:
[tex]g(c) = 1\\\\g'(c) = 0\\\\g''(x) = 2[/tex]

Therefore:
[tex]P_3(x) = 1 + \frac{0}{1}(x - 2) + \frac{2}{2!}(x - 2)^2\\\\\boxed{P_3(x) = 1 + (x - 2)^2}[/tex]

The cost of 3 scarves is $71.25. What is the unit price?
The unit price is $
per scarf.

Answers

Answer:

unit price= $23.75

Step-by-step explanation:

$71.25/ 3

unit price means the price of 1

In a simple economy (assume there are no taxes, thus, Y is disposable income), the consumption function is:
C = 200+ 0.80Y
00
The current level of real GDP is $4000.
At this level of real GDP, consumption will be $, and savings will be $1. If GDP were to increase by $1000, consumption would increase by $(Round your
responses to the nearest dollar.)

Answers

Using linear function concepts, it is found that consumption would increase by $800.

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.

In this problem, the function is given by:

C = 200 + 0.8Y.

Which means that the slope is of m = 0.8 per unit of Y.

For 1000 units:

0.8 x 1000 = 800.

Consumption would increase by $800.

More can be learned about linear function concepts at https://brainly.com/question/24808124

the process of splitting a numbers into equal parts or groups

Answers

Answer:

Division

Step-by-step explanation:

Dictionary Definition:

the action of separating something into parts or the process of being separated.

Hope that helps

The figure is made up of a cylinder and a half sphere. What is the volume of the composite figure? Use 3.14 for Pi. Round to the nearest hundredth.


A cylinder and half sphere. Both have a radius of 4 millimeters. The cylinder has a height of 7 millimeters.

Recall the formulas V = B h and V = four-thirds pi r cubed

Answers

Answer:

351.68 millimeters for the cylinder and 8 23/75 millimeters for the half circle.

Step-by-step explanation:

Volume Cylinder = 3.14(16)(7) = 351.68

Volume Half sphere = 2/3(3.14)(4) = 8 23/75

If you want both of them together just add up the two numbers.

Answer:

351.68 millimeters cylinder

8 23/75 millimeters half circle

Step-by-step explanation:

Find the measure of x

Answers

Answer:

x=23

Step-by-step explanation:

An inscribed angle is half of the intercepted arc.

What is the slope-intercept equation for this line?

y = [?]x+ [ ]

Answers

Answer:

y = -2x - 2

Step-by-step explanation:

Find the length of AB.

Answers

Answer:

6.286

Step-by-step explanation:

♢C=⊙/360x 22/7x D

=45/360x22/7x16

=6.286

At his son's birth, a man invested $2,000 in savings at 6% for his son's college education.

Approximately how much, to the nearest dollar, will be available in 19 years? (Do not use comma placeholder in response.)

Rounded to the nearest year, approximately how long will it take for the man’s investment to double?

Answers

now, this is assuming the 6% is at simple interest rate.

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &19 \end{cases} \\\\\\ A=2000[1+(0.06)(19)]\implies A=2000(1.54)\implies A=3080 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$4000\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years \end{cases} \\\\\\ 4000=2000[1+(0.06)(t)]\implies \cfrac{4000}{2000}=1.06t \\\\\\ 2=1.06t\implies \cfrac{2}{1.06}=t\implies 1.89\approx t\implies \stackrel{\textit{rounded up}}{2\approx t}[/tex]

Answer:

value in 19 years: $6051

years to double: 12

Use the drop-down menus to label the points on the number line.

Point A is at
.
Point B is at
.
Point C is at
.
Point D is at
.

Answers

Can u put a photo? It’s hard when their isn’t any reference

Answer: B,D,C,A

Step-by-step explanation:

I hope that helps

Please mark me the brainiest !

Simplify expression:
2(4x + 3) - 3(x + 1)

Answers

Answer:

5x+3

Step-by-step explanation:

[tex]\left[Thank\;you\;for\;Joining\;Brainly!][/tex]

Answer:

5x + 3

Step-by-step explanation:

[tex]2\left(4x+3\right)-3\left(x+1\right)[/tex]

[tex]\mathrm{Expand\;2(4x+3)}:8x+6[/tex]

[tex]=8x+6-3\left(x+1\right)[/tex]

[tex]\mathrm{Expand\;-3(x+1)}:-3x-3[/tex]

[tex]=8x+6-3x-3[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=8x-3x+6-3[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:6-3=3[/tex]

[tex]=8x-3x+3[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:8x-3x=5x[/tex]

[tex]=5x+3[/tex]

Hence, your answer is 5x + 3

[RevyBreeze]

Please answer this relatively quickly, I'm not in very much of a rush but would like to get this done.

Answers

The answers is X = 23

Answer:

x=23

Step-by-step explanation:

2x-6/4 = 10

2x-6 = 10(4)

2x-6 = 40

2x = 40+6

2x = 46

x = 46/2

x = 23

Luka and Gabby rent a tandem bike for $25/hr.Which value is the dependent variable? Which is the independent variable? Write an equation to represent the relationship between the number of hours, h, and the total cost of c.

Answers

c = 25(h)

dependent variable : They must give $25 per hour.

independent variable: time is independent as no specific time given.

total cost = $25 * hours taken

c = 25 * h

c = 25(h)

Answer:

See below ↓

Step-by-step explanation:

Given

rate of renting a tandem bike = $25/hh = number of hoursc = total cost

Solving

Clearly, as the number of hours does not depend on another variable, h is the independent variableTherefore, c is the dependent variableThe equation is :⇒ c = 25h

Help help help help help

Answers

Answer:

x = 12

Step-by-step explanation:

Becuase 6/12 = 2 and 9 + 2 = 11

12

what is is the volume of a box with 3 inches long 1 inch wide and 5/3 inch tall

Answers

Answer:

5 inches cubed

Step-by-step explanation:

Use the formula for volume: V = length * width * height, and plug in the values. V = 1 * 3 * 5/3, which equals 5.

Hopefully this helps - let me know if you have any questions!

100 divided by 35,513.22

Answers

Answer:

0.002816 or 0.003

Step-by-step explanation:

Be sure to use a calculator to double check the answer

Hope this helps!

Evaluate the expression (3-2i)(3-2i) and write the result in the form a+bi ,where a is the real part of your answer and bis the coefficient in front of the imaginary part

Answers

Answer:

a = 5, b = -12

Step-by-step explanation:

By basic factoring, you get 9 - 12i + [tex]4i^2[/tex]. Since [tex]i^2[/tex] is simply -1, the expression evaluates to 9 - 12i - 4, which is 5 - 12i.

A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.5 yards.

What is the surface area of the actual ramp, including the underside?

Enter your answer as a decimal in the box.

yd²
Right triangular prism. Each base is a triangle whose legs are 13 in, 13 in, and 24 in. The height of the triangles is 5 in. The prism is oriented so that the side labeled 24 in is on the bottom. The distance between the bases is labeled 12 in.

Answers

Answer:

The answer is 7.2

The surface area of the actual ramp, including the underside is 16.8 ft²

H1 = 1.2 feet (height of the actual ramp)

and, H2 = 6 cm (height of the model)

The scale factor (k) is:

k = 1.2 feet / 6 cm

k = 0.2 ft/cm

The actual measurements would be:

16cm = 16 cm x 0.2 ft/cm = 3.2 ft

and, 9 cm = 9 cm x 0.2 ft/cm = 1.8 ft,

and, 10 cm = 10 cm x 0.2 ft/cm = 2 ft,

So, the surface area is

Area = 2(0.5 x 3.2 ft x 1.2 ft) + 2(2 ft x 1.8 ft) + (1.8 ft x 3.2 ft)

Area = 16.8 ft²

Hence, the surface area of the actual ramp is 16.8 ft²

Learn more about surface areas here:

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Type the correct answer in each box, Spell all the words correctly, and use numerals instead of words for numbers. If necessary, use / for the
fraction bar(s).
y +10
А
18
6
B
X
+
- 10
-8
-6
-4
-2
2
4
6
8
10
-2
B
-4
C
-8
-10
units)
and a
across the
-axis
We can show that ABC is congruent to AABC by a translation of

Answers

Step-by-step explanation:

We can Show that ∆ABC is congruent to∆A'B'C' by a translation of 1 units(s) to the left and a reflection across the X -axis.

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.

What is a reflection?

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given that the two triangles ABC and A'B'C'.

The points are A(8, 8), B(10, 4) and C(2, 6).

And A'(6, -8), B'(8, -4), and C'(0, -6).

The translation rule 2 units to the left and reflection across the x-axis.

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.

Therefore, the required translation rule is given above.

To learn more about the reflection;

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