Suppose you observed the following sample:
6.2, 7.4, 9.6, 11.5, 13.5
Compute the 2nd sample moment. (please type in the exact number, do not round your answer)

Answer:

0.274714403

Step by step explanation:

Total stored energy = (1/625) ∞

Voltage, also known as electric potential difference, is the measure of the electric potential energy per unit of charge in an electric circuit. It is the force that drives the electric charge in a circuit, similar to how pressure drives water through a pipe. Voltage is measured in volts (V) and is usually represented by the symbol "V". Voltage can be either positive or negative, depending on the direction of current flow and the orientation of the voltage source.

A. The voltage across an inductor is proportional to the time derivative of the current through it, according to Faraday's law of electromagnetic induction. This can be expressed mathematically as:

v(t) = L di/dt

where v(t) is the voltage across the inductor, L is the inductance in henries, and di/dt is the time derivative of the current through the inductor.

In this case, we have \(v(t) = 8e^{(-4t)\) V and L = 250 H. Integrating both sides of the above equation with respect to time gives:

∫v(t) dt = L ∫di/dt dt

∫\(8e^{(-4t)} dt = 250\) ∫di/dt dt

\(-2e^{(-4t)\)= 250i(t) + C

where C is the constant of integration. We can assume that the initial current is zero, so at t = 0, i(0) = 0. This means that C = -2. Substituting this into the equation above, we get:

\(-2e^{(-4t)\)= 250i(t) - 2

Solving for i(t), we get:

i(t) = (2/250) \(- (2/250)e^{(4t)\)

B. The power absorbed by an inductor is given by:

P = i² R

where P is the power, i is the current, and R is the resistance of the circuit. In an ideal inductor, the resistance is zero, so the power absorbed is also zero.

However, the energy stored in an inductor can be calculated using the following formula:

E = 1/2 L i²

where E is the energy stored, L is the inductance, and i is the current.

In this case, we have L = 250 H and i(t) = (2/250) \(- (2/250)e^{(4t)\)Substituting these values into the above equation, we get:

E = 1/2 (250) [(2/250) \(- (2/250)e^{(4t)]^2\)

Simplifying this expression, we get:

E = (1/625) \(- (2/625)e^{(4t)\)+ (2/625)e^(8t)

To determine the total stored energy, we need to integrate this expression over the interval 0 to infinity, since the voltage and current are given for all values of t. This gives:

Total stored energy = ∫E dt from 0 to infinity

Total stored energy = (1/625) ∫1 dt from 0 to infinity\(- (2/625) ∫e^{(4t)\)dt from 0 to infinity + (2/625) ∫e^(8t) dt from 0 to infinity

Total stored energy = (1/625) ∞ \(- (2/625) [1/4 e^{(4t)]\)from 0 to infinity + (2/625) [1/8 e^(8t)] from 0 to infinity

Since the integrals involving exponential functions go to infinity as t goes to infinity, these terms become zero. Therefore, we are left with:

Total stored energy = (1/625) ∞

which is an infinite value. This is because the energy stored in an inductor is not finite, but rather is dependent on the magnetic field generated by the inductor, which can extend infinitely far.

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Answer:

OK, Here is your answer

Step-by-step explanation:

Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.

Answer:

18 Lieters.

Step-by-step explanation:

found the answer in his answer. ↑↑↑↑

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

f(x) approaches positive infinity as x approaches negative infinity; f(x) approaches positive infinity as x approaches positive infinity

Step-by-step explanation:

We have q(x)=3x^4+8x^3-13x^2-22x+24

The leading term of this polynomial is 3x^4 (it has the highest degree) where the degree is 4 [it is even] and the leading coefficient is 3 [it is positive]

Therefore the end  behavior of the polynomial is f(x) --> ∞ as x ----> - ∞ and f(x) ----->  ∞ as x --->  ∞

Answer:

B and D

Step-by-step explanation:

This is because for B you do 8x9x1 which is basically 8x9 which is 72. Then, for D you do 12x3x2. Do 3x2 first and you get 6. Then, do 6x12 which is also 72. So the correct answers that will give you the volume of 72 units cube is B and D. Hope this helps!

Check the picture below.

Answer: B  :)

Step-by-step explanation:

you need to find the number of containers for all the juice so add all of them together and then divide by 1.4 or the volume of the containers to get to amount you need

The three points which are a solution to the equation are:

(-4,1) , (-6,5) and (-3,-1)

Given:

2x+y=-8

Solving (a): The possible coordinates.

we have:

(x,y) = (-7,-3)

⇒ 2x+y=-7

⇒ 2(-7)+(-3) = -7

⇒ -14-3 = -7

⇒-18=-7

hence (-7,-3) is not a point on the grid.

(b) (-4,1)

we have:

(x,y) = (-4,1)

⇒ 2x+y=-7

⇒ 2(-4)+(1) = -7

⇒ -8+1 = -7

⇒ -7 = -7

hence (-4,1) is a point on the grid.

(c) (-6,5)

we have:

(x,y) = (-6,5)

⇒ 2x+y=-8

⇒ 2(-6)+(5) = 8

⇒ -12+5 = -7

⇒ -7= -7

hence (-6,5) is a point on the grid.

(d) (0,3)

we have:

(x,y) = (0,3)

⇒ 2x+y=-8

⇒ 2(0)+(3) = 8

⇒ 0+3 = -7

⇒ 3= -7

hence (0,3) is not a point on the grid.

(e) (-4,6)

we have:

(x,y) = (-4,6)

⇒ 2x+y=-8

⇒ 2(-4)+(6) = 8

⇒ -8+6 = -7

⇒ -2= -7

hence (-4,6) is not a point on the grid.

(f) (-3,-1)

we have:

(x,y) = (-6,5)

⇒ 2x+y=-8

⇒ 2(-3)+(-1) = -7

⇒ -6-1= -7

⇒ -7= -7

hence (-3,-1) is a point on the grid.

The three points on the grid are:

(-4,1) , (-6,5) and (-3,-1) are the points on the grid.

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Answer:

Takis

.................

Answer:

Step-by-step explanation:

The given equation is a trigonometric expression with complex operations involving tangent, sine, cosine, and inverse cosine functions, and its value is 37.3.

This equation involves multiple applications of trigonometric functions and inverse trigonometric functions to a complex expression. To solve for x, one must simplify the equation by applying the properties of these functions and simplifying the expression.

The expression involves finding the value of inverse cosine, which can be done by using the identity cos^-1(x) = theta, where theta is the angle that satisfies cos(theta) = x. The resulting expression will be a complex equation involving x, which can be solved by various methods, such as numerical or graphical methods.

Here's a general approach to simplifying the equation:

This simplified equation can then be solved for x using numerical or graphical methods, or other mathematical techniques.

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1.243 is the measure of the value of x from the given expression

Rational equations are those that contain rational expressions. A rational expression is a fraction with polynomial numerator and denominator. A rational expression, in other terms, is a ratio between two polynomials.

Given the following rational equation

√11 x = √17

We need to determine the measure of the value of x.

Taking the square of both sides we will have:

(√11 x)² = (√17)²

11x² = 17

x² = 17/11

x² = 1.545

Take the square root of both sides

√x² = √1.545
x = 1.243

Hence the measure of the value of x from the given equation is 1.243.

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The given limit is 0.

To solve the given limit, we can recognize the sum as a Riemann sum and convert it into an integral.

The given sum can be rewritten as:

\(\lim_{n \to \infty} \sum_{i=1}^{n} \frac{3}{n} \sqrt{1+\frac{3i}{n}}\)

Let's rewrite it in terms of integration:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}}\)

Since we are taking the limit as n approaches infinity, we can approximate the sum as an integral.

The integral that corresponds to the given sum is:

\(\lim_{n \to \infty} \frac{3}{n} \sum_{i=1}^{n} \sqrt{1+\frac{3i}{n}} \approx \lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx\)

To solve this integral, we can use a change of variables.

Let u = 1 + 3x, then du = 3dx.

The integral becomes:

\(\lim_{n \to \infty} \frac{3}{n} \int_{0}^{1} \sqrt{1+3x} ,dx = \lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du\)

Integrating \(\sqrt{u}\), we get,

\(\lim_{n \to \infty} \frac{1}{n} \int_{1}^{4} \sqrt{u} ,du = \lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} u^{3/2}\right]_{1}^{4}\)

Substituting the limits, we have:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (4)^{3/2} - \frac{2}{3} (1)^{3/2}\right]\)

Simplifying further:

\(\lim_{n \to \infty} \frac{1}{n} \left[\frac{2}{3} (8 - 2)\right] = \lim_{n \to \infty} \frac{1}{n} \left[\frac{12}{3}\right] = \lim_{n \to \infty} \frac{4}{n} = 0\)

Therefore, the given limit is 0.

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Answer:

125 ft²

Step-by-step explanation:

Hello!

Let the length be called \(l\) and the width be called \(w\).

If the length is 5 times the width, that means \(l = 5w\).

We also know that the perimeter is 60ft, or \(2(l + w) = 60\)

Substitute \(5w\) for \(l\) and solve for the dimensions:

That means \(l\) is 5(5) or 25.

The area is 125 ft².

Answer:

its A because the Y intercept is at 3

Answer:

-152

Step-by-step explanation:

-152 < 12

-152 is negative, which means it is less than 1.

12 is positive, which means it is greater than 1.

Therefore, -152 is the lesser of the two given numbers.

Have a great rest of your day! :)

Hi!

-152 is less than 12, because:

\(\mathbb{NUMBER \ LINE}\)

\(_ < \!\!\!\rule{300}{1}\!\!\!_ >\)

     \(-152\)                                                                         \(12\)

Cheers!

Have a nice day!

I hope this helps!

Answer:

x = 2

Step-by-step explanation:

Direct variation is in the form

y = kx

Using the first coordinates (4,6) we can determine k

6 = k*4

Divide each side by 4

6/4 =k

3/2 = k

y = 3/2 x

We want to determine x

3 = 3/2 x

Multiply each side by 2/3

3 * 2/3 = 3/2 * 2/3 x

2 =x

The linear expression for 2h - 1 and 3h + 4 is 5h + 3. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

According to mathematicians, the four fundamental operations, also referred to as "arithmetic operations," can be used to describe all real numbers. Division, multiplication, addition, and subtraction are the four mathematical operations that result in the terms quotient, product, sum, and difference, respectively.

We are given two expressions as 2h - 1 and 3h + 4.

On adding both, we get

2h - 1 + 3h + 4 = 5h + 3

Hence, the linear expression for 2h - 1 and 3h + 4 is 5h + 3.

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Answer:

Step-by-step explanation:

Function values and the extent of the graph can be determined by reading the graph.

The domain of the function is the set of values for which the function is defined. It is the horizontal extent of the graph. The graph shows the function is defined for all real numbers.

  The domain is -∞ < x < ∞.

The range of the function is the set of output values the function may have. It is the vertical extent of the graph. The graph shows the function can have any value no greater than -1.

  The range is -∞ < y ≤ -1.

Function values can be read from the graph by locating the x-value on the x-axis, and following the vertical line to its intersection with the function graph. The y-value of that point is the function value.

  f(-5) = -2

  f(-1) = -4

Or, we can write the function definition based on the graph, and use that definition to find the values at specific points. The graph is of the absolute value function reflected over x and translated <-4, -1>.

  f(x) = -|x+4| -1

  f(-5) = -|-5 +4| -1 = -1 -1 = -2

  f(-1) = -|-1 +4| -1 = -3 -1 = -4

Answer:

Step-by-step explanation:

Its is

6CM wide. as to find the area we have to times the length x height :)

Answer:

wide = 6 cm

Step-by-step explanation:

\(t=tall=10\)

\(w=wide=?\)

\(P=perimeter=32\)

The equation:

\(P=2t+2w\)

\(32=2(10)+2w\\32=20+2w\)

\(32-20=2w\\12=2w\)

\(\frac{12}{2} =w\)

\(6=w\)

Hope this helps.

don't give up you got it always stay positive

Answer:

A. 3/2

Step-by-step explanation:

I like to think of it as shift left or right by the numerator and shift up or down by the denominator. So I go over three and up two from (-3, -1) to reach (0, 1)

Answer:

3divided by 2 I think...

Answer:

42

dnndndndndndnd

dndndndndj

The shape that we obtained will be a triangle. Then the correct option is E.

In terms of geometry, a pyramid is a polygon that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. It has a polygonal basis and is a conic solid. There are n + 1 points, n + 1 sides, and 2n edges in a pyramid with an n-sided base. Every pyramid is dual in itself.

If the base of the pyramid is a rectangle then the pyramid is known as a rectangular pyramid.

If the pyramid is separated by slicing a rectangular pyramid perpendicular to its base. Then the shape that we obtained will be a triangle.

Then the correct option is E.

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Answer:

yes

Step-by-step explanation:

By placing the given value in equation , we get u + v - 4u = (-20, 13)

A physical quantity that has both directions and magnitude is referred to as a vector quantity.

A lowercase letter with a "hat" circumflex, such as "û," is used to denote a vector with a magnitude equal to one. This type of vector is known as a unit vector.

To evaluate u + v - 4u, we first need to find the vector 4u, which is obtained by multiplying the vector u by the scalar 4:

4u = 4(5,-2) = (20,-8)

Now, we can add u and v, and subtract 4u from the result:

u + v - 4u = (5,-2) + (-5,7) - (20,-8)

= (5 - 5 - 20, -2 + 7 + 8)

= (-20, 13)

Therefore, u + v - 4u = (-20, 13).

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"To figure out how long an airplane will take to reach Beijing, divide the distance to Beijing by the airplane's speed."

The statement makes sense.

Reason: Because time is equal to distance divided speed.

The meaning of the word rational is according to thoughts and logical considerations. In line with this definition, the Oxford Dictionary explains that rational has a meaning based on or in accordance with reason or logic, being able to think wisely or logically, and having the ability to reason.

Experts reveal that rational thinking is a person's ability to draw conclusions that are based and can be justified or supported by data, rules, and logic.

From the above understanding, it can be concluded that rational is an adjective related to a person's ability to think relevantly and logically, supported by reliable data, and justified by applicable regulations.

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