Given the equation below, what is the equivalent expression of A(Bx + 8) + C, in standard form?

(x +8)(2x - 3) = Ax2 + Bx+C

A) -26x + 8
B) 26x +8
C) -26x - 8
D) 26x - 8

PLEASE HELP I HAVE A TEST RN

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:

(4a)^3

4^3 a^3

=12a

You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

for more such questions on equation

https://brainly.com/question/22688504

#SPJ8

Answer:2M+1

Step-by-step explanation: The 2 would be used to double Mark's age since the question says Joey is twice Marks age. The +1 is used to add one more year after multiplying Mark's age by 2 since the question says Joey is one year older. For example if Mark's age is 2 then plug it into the equation 2(2)+1 which would make Joey's age 5. Because the 2 would double the M in this case 2 and then add a 1 to his age after because of order of operations.

Step-by-step explanation:

1hr = 60

½ hr = 30

60 + 30 = 90

9514 1404 393

Answer:

  17

Step-by-step explanation:

Let s represent the smaller number. Then the larger is 3s-7 and their sum is ...

  s +(3s -7) = 61

  4s = 68 . . . . . . . add 7

  s = 17 . . . . . . . . . divide by 4

The smaller number is 17.

__

The larger number is 44.

Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

Just enter each value of x into the formula f(x) = x - 4. For example, f(x) = 2 - 4 = -2 when x = 2.

A general rule is that the algebraic expression should take any of the following forms: addition, subtraction, multiplication, and division. to ascertain x's value.

Finding the value of f(x) =... or y =... that corresponds to a given value of x is the definition of function evaluation. Simply swap out all instances of x with the value that has been allocated to x to do this. For instance, if f(4) is to be evaluated, then x has been given the value of 4.

Separate the variable. In this instance, you transfer the constant term across the equal sign by doing the reverse operation on both sides and adding 1 to isolate the variable term. Isolate the variable further, then simplify.

Given,

f(x)=x-4

⇒ when x = -2,

⇒ f(x) = -2 -4 = -6

When x = -1,

⇒ f(x) = -1 -4 = -5

When x = 0

⇒ f(x) = 0 -4 = - 4

When x = 1

⇒ f(x) = 1 -4 = -3

When x = 2

⇒ f(x) = 2 -4 = - 2

To learn more about formula f(x) refer to:

brainly.com/question/28871326

#SPJ1

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

The absolute value of the Rational number -474/513 is 474/513.

To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:

-8/9 = (-8/9) * (57/57) = -456/513

-2/57 = (-2/57) * (9/9) = -18/513

Now, you can add the fractions:

-456/513 + (-18/513) = (-456 - 18)/513 = -474/513

To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:

| -474/513 | = 474/513

Therefore, the absolute value of the rational number -474/513 is 474/513.

For more questions on Rational .

https://brainly.com/question/30339525

#SPJ8

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

For more questions on Velocity .

https://brainly.com/question/25749514

#SPJ8

Answer:

It would be C and E

Step-by-step explanation:

I know I'm extremely late but for anyone else who needs to know here you go :)

Answer:

y>= 2/3(x) - 2.5

Step-by-step explanation:

The sign should be "greater than or equal to" but my keyboard doesn't have that. Sorry.

The slope is "up two, over three" found by finding places where the line passes through the grid lines, and counting.

The y-intercept is -2.5. That tells you the "constant" to put in for "b" in the slope intercept form, y=mx+b

Answer:

5 tacos for 2 guests would mean more for each person, while 2 tacos for 5 guests would mean less for each person

Answer:

d. Line UR and Line VW are parallel

Step-by-step explanation:

If they were to continue going straight, they would not touch, making them parallel.

I hope this helps!

Answer:

\((x+4)^2+(y-4)^2=16\)

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

Since the circle is tangent to both axes, and the center of the circle is in the second quadrant, the center of the circle lies on the line y = -x.

As the circle is tangent to the x-axis, the distance between the center of the circle and the x-axis is equal to the radius of the circle.

Similarly, as the circle is tangent to the y-axis, the distance between the center of the circle and the y-axis is also equal to the radius of the circle.

Therefore, the center of the circle will be 4 units to the left of the y-axis and 4 units up from the x-axis. Therefore, the coordinates of the center are (-4, 4).

\(\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the center (-4, 4) and the radius, r = 4, into the standard equation of a circle:

\(\implies (x - (-4))^2+(y-4)^2=4^2\)

\(\implies (x+4)^2+(y-4)^2=16\)

Therefore, the equation of the circle that satisfies the given conditions is:

\(\boxed{(x+4)^2+(y-4)^2=16}\)

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

Real numbers are:

\(i^6\), 2 - 7i², -12, and √(-5)².

Complex numbers are:

7 - 5i, √-6, 0 + 9i, and -i² + i³.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A complex expression is in the form a + ib

Where i is the imaginary number.

a)

\(i^6\)

i² = -1

i³ = -i

So,

\(i^6\) = \(i^{2\times3\) = \((i^2)^{3\) = (-1)³ = -1

This is a real number.

b)

2 - 7i²

= 2 - 7 x (-1)

= 2 + 7

= 9

This is a real number.

c)

7 - 5i

This is a complex number.

d)

√-6

= √-1 x √6

= i√6

This is a complex number.

e)

0 + 9i

= 9i

This is a complex number.

f)

-12

This is a real number.

g)

√(-5)²

= √25

= 5

This is a real number.

h)

-i² + i³

= -(-1) + (-i)

= 1 - i

This is a complex number.

Thus,

Real numbers are \(i^6\),2 - 7i², -12, and √(-5)².

Complex numbers are 7 - 5i, √-6, 0 + 9i, and -i² + i³.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

(a)7.185

(b)0.000371

(c) 0.019

(d)Sample variance and Sample standard deviation

Step-by-step explanation:

We are given the following sample data.

7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.

(a) Calculate the sample mean. Round your answer to 3 decimal places.

The formula for sample mean =

Sum of terms/Number of terms

= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8

= 57.48/8

= 7.185

(b) Calculate the sample variance. Round your answer to 6 decimal places.

The formula for sample Variance =

(x - mean)²/n - 1

n = 8

Sample variance = (7.15 - 7.185)² + (7.20-

7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1

= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7

= 0.0026/7

= 0.000371428571

Approximately to 6 decimal places = 0.000371

(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.

The formula for Sample Standard Deviation = √Sample variance

= √0.000371428571

= 0.01927248223

To 3 decimal places = 0.019

(d) Which of the following are potential major sources of variability in the experiment

Sample variance

Sample standard deviation

Answer:

pogi mooooo loooodsssssssss

Answer:

15x - y = - 6.....15x + 6 = y...so we sub in 15x + 6 in for y on the other equation

5x - 3y = -13

5x - 3(15x + 6) = -13 <== the new equation

Step-by-step explanation:

Answer:

To solve this problem, we need to use the concept of distance, rate and time (D = R x T)

We know that the distance is 49 miles and the rate is 14 miles per hour.

We want to find the time T.

We can use the formula D = R x T, to find the time T:

T = D/R = 49 miles / 14 miles/hour = 3.5 hours

So it takes Nena 3.5 hours to ride from the city park to the nearby lake.

Now we know that she needs to arrive at the lake at 1:00 PM, so we have to work out what time she needs to leave the park. We can subtract the time T from the arrival time to find the departure time:

1:00 PM - 3.5 hours = 9:30 AM

Therefore, the latest Nena can leave the park in order to arrive at the lake at 1:00 PM is 9:30 AM

The precise equation that represents the situation is as follows:

His cell phone plan provides  300 free minutes each month for a flat rate of $19.

let

x = number of minutes used

Therefore,

$19, x ≤ 300

For any minutes over 300, Andrew is charged 0.39 per minute.

Therefore,

if x > 300

f(x) = 19 + 0.39(x - 300)

learn more on equation here: https://brainly.com/question/18127606

#SPJ1

Answer: 9.5 (D.)

Step-by-step explanation:

SOCAHTOA

the sin of an angle is equal to the opposite side over the hypotenuse.

angle: 32

opposite side: x

hypotenuse: 18 m

1. sin32 = x/18

2. 18(sin32) = x

3. 9.5 = x

if you are confused with how it went from 18(sin32) to 9.5, you can plug 18(sin32) into your calculator.

Explanation:

Total tickets = 500

Tickets number bought by David = 5, 6, 7 and 8

Number of tickets bought by David = 4

Remaining ticket = 500 - Number of tickets bought by David

Remaining ticket = 500 - 4

Remaining ticket = 496

Odds in favour of an event = success for the event/ failures for the event

success for winning the raffle = Number of tickets bought by David = 4

failures for winning the raffle = Remaining ticket = 496

Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)

Answer:

Explanation:

The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.

The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.

Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).

Hence, water boiling point in Denver is lower than 100°C.

The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.

In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.