Two cities whose longitudes are 10E and 20W on the equator are apart

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

Answer:

Step-by-step explanation:

y=-x+2 equation 1

y=3x-2 equation 2

sub equation 1 into 2

-x+2=3x-2

-x+2-3x+2 =0 (bring everything to one side and to equal 0)

-4x+4=0 (collect like terms and go with the sign given)

-4x=-4 (bring 4 over to the other side to isolate)

-4x/-4=-4/-4 (divide to isolate)

x=1

y=-3x+3 equation 1

2x+y=1 equation 2

y=-2x-1 Rearrage equation 2 (now equation 3)

sub equation 1 into 3

-3x+3=-2x-1

-3x+3+2x+1 =0 (bring everything to one side and to equal 0)

-x+4=0 (collect like terms and go with the sign given)

-x=-4 (bring 4 over to the other side to isolate)

Answer:

20 days

Step-by-step explanation:

40 feet - 35 feet is 5 feet needed to rise

5 x 12 (inches per foot) =60 inches

60 divided by 3 = 20 days

Answer:

if the scale used 1/4 inch = 3 feet, then what is the perimeter of the actual garden? AI Recommended Answer: The perimeter of the actual garden is 144 feet.

Step-by-step explanation:

Answer:

The proportion of hours will be the number of purchases at the online store exceed 1,400

P(z>1) = 0.1587

Step-by-step explanation:

Step (i):-

Given mean of the Population (μ) = 1200

Standard deviation of the population (σ) = 200

let   X be the random variable in normal distribution

Given x = 1400

Step(ii) :-

The proportion of hours will be the number of purchases at the online store exceed 1,400

\(Z = \frac{1400-1200}{200} = 1\)

P(z>1) = 0.5 - A(1)

           = 0.5 - 0.3413

           = 0.1587

The percentage of hours will be the number of purchases at the online store exceed 1,400  is  15.87%

Answer:

Answer C

Step-by-step explanation:

By the empirical rule, 68% of the number of purchases in an hour will be between 1,000 and 1,400, so 100%−68%=32% of the number of purchases in an hour will fall outside of the interval. Since the normal distribution is symmetric around the mean, half of 32%, which is 16%, of the number of purchases in an hour will exceed 1,400.

Answer:

13x - 2

Step-by-step explanation:

First Were going to do the distributive property:

So, 4(3x) + 4(-6) = 12x + -24

Now we have :

12x - 24 + x + 22

Now we have to add like terms together:

So, 12x + x = 13x

and 22-24 = -2

So in the end we have 13x -2

Answer:I think it Is the second

Step-by-step explanation:

The measure of angle labelled 4 as required to get determined in the task content is; 90°.

It follows from the task content in that the measure of the angle labelled 8 is to be determined

Recall, when a diameter of a circle intersects with the tangent of a circle at the point if tengency, a right angle is formed at the point .

Consequently, the measure of angle 4 is; 90°.

Read more on tangent and diameter;

https://brainly.com/question/28035740

#SPJ1

Answer: -19x +1

Step-by-step explanation: Do -10x -9x which is -19x and you have 1 which is unlike terms .So your final answer is -19x +1 .

Answer:

whats the question???

Step-by-step explanation:

Answer: theres no question????? um but uh hope ur having a good day

Step-by-step explanation:

:?

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

\(3x(x+6)=-10\)

\(3x^2+18x=-10\)

To create a quadratic equation, add 10 to both sides of the equation:

\(3x^2+18x+10=-10+10\)

\(3x^2+18x+10=0\)

The quadratic formula is defined as:

\(\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

\(\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}\)

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

\(\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}\)

Simplify the radicand:

\(\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}\)

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

\(\sqrt{4\times51}\)

Then, using the Product Property of Square Roots, break this into two radicands:

\(\sqrt{4} \times \sqrt{51}\)

Since 4 is a perfect square, it can be evaluated:

\(2 \times \sqrt{51}\)

To simplify further for easier reading, remove the multiplication symbol:

\(2\sqrt{51}\)

Then, substitute for the quadratic formula:

\(\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}\)

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

\(\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}\)

\(\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}\)

Then, simplify the numerator of the roots by factoring 2 out:

\(\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}\)

\(\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}\)

Then, simplify the fraction by reducing 2/6 to 1/3:

\(\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}\)

\(\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}\)

The final answer to this problem is:

\(\displaystyle x=\frac{-9 + \sqrt{51}}{3}\)

\(\displaystyle x=\frac{-9 - \sqrt{51}}{3}\)

-2(n + 1) = 6

Distribute the -2:

-2n -2 = 6

Add 2 to both sides:

-2n = 8

Divide both sides by-2

N = -4

Solution

The length of a rectangle is five times its width.

Let the length be represented by L

Let the width be represented by W

The length of the rectangle is five times the width i.e

To find the perimeter, P, of a rectangle, the formula is

Given that the perimeter, P, of the rectangle is 120ft,

Subsitute for length and width into the formula above

Recall that, the length of the rectangle is

To find the area, A, of a rectangle, the formula is

Substitute the values of the length amd width into the formula above

Hence, the area of the rectangle is 500ft²

Answer:

\(f(2\pi) = 32\pi^3 - 2\)

Step-by-step explanation:

Main steps:

Step 1: Use integration to find a general equation for f

Step 2: Find the value of the constant of integration

Step 3: Find the value of f for the given input

Step 1: Use integration to find a general equation for f

If \(f'(x) = g(x)\), then \(f(x) = \int g(x) ~dx\)

\(f(x) = \int [12x^2 - sin(x)] ~dx\)

Integration of a difference is the difference of the integrals

\(f(x) = \int 12x^2 ~dx - \int sin(x) ~dx\)

Scalar rule

\(f(x) = 12\int x^2 ~dx - \int sin(x) ~dx\)

Apply the Power rule & integral relationship between sine and cosine:

\(f(x) = 12*(\frac{1}{3}x^3+C_1) - (-cos(x) + C_2)\)

Simplifying

\(f(x) = 12*\frac{1}{3}x^3+12*C_1 +cos(x) + -C_2\)

\(f(x) = 4x^3+cos(x) +(12C_1 -C_2)\)

Ultimately, all of the constant of integration terms at the end can combine into one single unknown constant of integration:

\(f(x) = 4x^3 + cos(x) + C\)

Step 2: Find the value of the constant of integration

Now, according to the problem, \(f(0) = -2\), so we can substitute those x,y values into the equation and solve for the value of the constant of integration:

\(-2 = 4(0)^3 + cos(0) + C\)

\(-2 = 0 + 1 + C\)

\(-2 = 1 + C\)

\(-3 = C\)

Knowing the constant of integration, we now know the full equation for the function f:

\(f(x) = 4x^3 + cos(x) -3\)

Step 3: Find the value of f for the given input

So, to find \(f(2\pi)\), use 2 pi as the input, and simplify:

\(f(2\pi) = 4(2\pi)^3 + cos(2\pi) -3\)

\(f(2\pi) = 4*8\pi^3 + 1 -3\)

\(f(2\pi) = 32\pi^3 - 2\)

Answer:

\(f(2 \pi)=32\pi^3-2\)

Step-by-step explanation:

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given:

If g(x) is the first derivative of f(x), we can find f(x) by integrating g(x) and using f(0) = -2 to find the constant of integration.

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}\)     \(\boxed{\begin{minipage}{4 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\end{minipage}}\)

\(\begin{aligned} \displaystyle f(x)&=\int f'(x)\; \text{d}x\\\\&=\int g(x)\;\text{d}x\\\\&=\int (12x^2-\sin x)\;\text{d}x\\\\&=\int 12x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\int x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\cdot \dfrac{x^{(2+1)}}{2+1}-(-\cos x)+\text{C}\\\\&=4x^{3}+\cos x+\text{C}\end{aligned}\)

To find the constant of integration, substitute f(0) = -2 and solve for C:

\(\begin{aligned}f(0)=4(0)^3+\cos (0) + \text{C}&=-2\\0+1+\text{C}&=-2\\\text{C}&=-3\end{aligned}\)

Therefore, the equation of function f(x) is:

\(\boxed{f(x)=4x^3+ \cos x - 3}\)

To find the value of f(2π), substitute x = 2π into function f(x):

\(\begin{aligned}f(2 \pi)&=4(2 \pi)^3+ \cos (2 \pi) - 3\\&=4\cdot 2^3 \cdot \pi^3+1 - 3\\&=32\pi^3-2\\\end{aligned}\)

Therefore, the value of f(2π) is 32π³ - 2.

Answer:

If all you care about is whether you roll 2 or not, you get a Binomial distribution with an individual success probability 1/6. The probability of rolling 2 at least two times, is the same as the probability of not rolling 2 at zero or one time.

the answer is, 1 - bin(k=0, n=4, r=1/6) - bin(k=1, n=4, r=1/6). This evaluates to about 13%, just like your result (you just computed all three outcomes satisfying the proposition rather than the two that didn’t).

Step-by-step explanation:

The  probabilities of getting :

O Threes is 0.48

1 Three is  0.095

2 Threes is 0.019

3 Threes is 5/1296

4 Threes is 1/1296

the total out come = 6* 6* 6* 6 =1296

Find the probabilities of getting

O Threes =(5/6)^4 = 0.48

1 Three = 1/6*(5/6)^3 = 0.095

2 Threes = 1/6* 1/6* 5/6 *5/6 =0.019

3 Threes = 1/6* 1/6* 1/6 *5/6 = 5/1296

4 Threes =(1/6 )^4 =1/1296

To learn more probability about refer,

https://brainly.com/question/24756209

#SPJ2

Answer:

www.imsorryineedpoints.orgStep-by-step explanation:

Answer:

  C. RP = 4.5

Step-by-step explanation:

You want to know what condition is sufficient to show ∆ABC ~ ∆QPR, given  three sides and 2 angles in ∆ABC, and 2 sides in ∆QPR.

Similarity can be shown if all three sides are proportional, or if two angles are congruent.

The offered answer choices only list one angle, so none of those will work. The answer choice that makes the third side of ∆QPR be in the same proportion as the corresponding side of ∆ABC is the condition of interest.

  C. RP = 4.5

__

Additional comment

The side ratios in the two triangles are ...

  AB : BC : CA = 10 : 9 : 6

  QP : PR : RQ = 5 : PR : 3

For these ratios to be the same, PR must be half of BC, just as the other segments in ∆QPR are half their counterparts in ∆ABC.

Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.

The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.

For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.

Learn more about control variables here:

https://brainly.com/question/28077766

#SPJ1

Answer:

Step-by-step explanation:

B is the midpoint of AC. It means:

And we have a common side BD:

a) As per above we only have two sides congruent and this information is not sufficient to state the triangles ABD and CBD are congruent.

b) In addition to the two sides we also have:

With this additional information we have three sides congruent, so the triangles are congruent by SSS postulate.

Answer:

10769

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

rise over run. Find two places that land on a line I picked (0,0) and (3,1) then count up one from the first point and over 3 for the second.

Answer:

y = 1/3x

Step-by-step explanation:

Answer:

2  1/40  hours = 2.025  hours

Step-by-step explanation:

1300 + 655 + 285 x  3 = 2810 calories

2810 - 2000 = 810 calories

810 / 400 = 2 1/40 hours

The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

Learn more about substitution here:

brainly.com/question/22340165

#SPJ1

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

LEarn more about dilations at:

https://brainly.com/question/3457976

#SPJ1

Answer:

Step-by-step explanation:

okay so its 3•7

that's all u need put that

Answer:

\(3^{7}\)

Step-by-step explanation:

3×3×3×3×3×3×3= \(3^{1+1+1+1+1+1+1+1} =3^{7}\)

3+3+3+3+3+3+3= 3×7

Answer:

60 + 2 + 0.8 +0.03 +0.007

Step-by-step explanation:

Add these up and yo get the same number: 62.837.

Answer:20

Step-by-step explanation: