449.86
To compute the moment of the second sample, we need to compute the sum of the squares of the sample values.
This formula is:
Sum = ∑(x_i^2)
After inserting the example values:
Sum = 6.2^2 + 7.4^2 + 9.6^2 + 11.5^2 + 13.5^2
Simplifying this formula to:
Total = 38.44 + 54.76 + 92.16 + 132.25 + 181.25
Adding these terms gives us the following final result:
Total = 449.86
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Find the exact value of tan 5 π .
Answer:
0.274714403
Step by step explanation:
An inductor of l = 250 is subjected to a voltage v(t) = 8 e-4t V:
A. Knowing that, integrate both sides to determine the current i(t). You may assume that the initial current is zero.
B. Given that the absorbed power is, determine the total stored energy.
Total stored energy = (1/625) ∞
What understand by voltage?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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A drum of water is 3/4 full. When 9 litres are drawn from it, it is half full. How much water does the drum hold what is the capacity of the drum
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. ↑↑↑↑
A plane flying with a constant speed of 360 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30°. At what rate (in km/h) is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
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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Describe the end behavior of polynomial q(x)=3x^4+8x^3-13x^2-22x+24
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 ---> ∞
I BEG FOR MY LIFE EZ PLS
{{{{{{{PICTURE PROVIDED}}}}}}}}}
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!
The graph of a function g is shown below. Find g(1).
Check the picture below.
Which equation shows how to solve the problem? (2.79 – 1.4) + (3.06 – 1.4) + (2.44 – 1.4) + (3.82 – 1.4) = 6.51 2.79 + 3.06 + 2.44 + 3.82 = 12.11; 12.11 × 1.4 = 16.954 2.79 + 3.06 + 2.44 + 3.82 = 12.11; 12.11 ÷ 1.4 = 8.65 (2.79 × 1.4) + (3.06 × 1.4) + (2.44 × 1.4) + (3.82 × 1.4) = 16.954; 16.954 ÷ 1.4 = 12.11
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
Determine which three out of the six points shown below are a solution to the
equation 2x + y = -7. Plot the three points that are in the solution set, draw a line
through the three points and then answer the questions below.
(-7,-3), (-4,1), (-6,5), (0, 3), (-4, 6),
(-3,-1) come up with two additional solutions with fractions and decimals please help
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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Which of the shows the correct sums that would be found when clustering is used to find the answer to the problem 41 x 22?
820 + 82 = 912
800 + 2 = 802
820 + 82 = 902
820 + 80 = 900
Takis or Hot cheetos?
Answer:
Takis
.................
2 tan (0.06 Sin x - 0. 4 sin(cos^-1 (0.0592 +0.0432cos x) /0.144))/ (0.06cosx-0.18-0.4 COS (Cos^-1 ( 0.0592+0.0432cosx) / 0.144)) =37.3
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:
Simplify the argument of the first sine function:This simplified equation can then be solved for x using numerical or graphical methods, or other mathematical techniques.
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Find x. √11 X = √17 VIRI X
1.243 is the measure of the value of x from the given expression
Solving rational equationsRational 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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need help please. any body
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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The length of a rectangle is five times it’s width. If the perimeter of the rectangle is 60ft, find it’s area
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:
\(2(l + w) = 60\)\(2(5w + w) = 60\)\(2(6w) = 60\)\(6w = 30\)\(w = 5\)That means \(l\) is 5(5) or 25.
Solve for the area:\(A = lw\)\(A = (25)(5)\)\(A = 125\)The area is 125 ft².
I need some help! i will try to give brainliest!!!
Answer:
its A because the Y intercept is at 3
Select the lesser of The two given numbers -152, 12
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:
It's negative, and 12 is positive!It's to the left of 12 on the number line!\(\mathbb{NUMBER \ LINE}\)
\(_ < \!\!\!\rule{300}{1}\!\!\!_ >\)
\(-152\) \(12\)
Cheers!
Have a nice day!
I hope this helps!
SOMEONE HELP ME PLEASE
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
whats the liner expression for 2h - 1 and 3h + 4
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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what is the functions domain ?
what is the functions range ?
find the values of the function f(-5)= and f(-1)=
Answer:
domain: -∞ < x < ∞range: -∞ < y ≤ -1f(-5) = -2f(-1) = -4Step-by-step explanation:
Function values and the extent of the graph can be determined by reading the graph.
DomainThe 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 < ∞.
RangeThe 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 valuesFunction 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
The perimeter of a playing card is 32 centimeters. It is 10 centimeters tall. How wide is it?
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.
Hi Folks, please any hand with this equation of a straight line / gradients coordinates excercise please. thanks
don't give up you got it always stay positive
3. What is the length of AB?
pls help, dont put link pls
I’ll mark u plz help
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...
HELP ASAP PLS SHOW WORK
Answer:
42
dnndndndndndnd
dndndndndj
Click on all the shapes that can be created by cutting a rectangular pyramid perpendicular to its base.
A. pentagon
B. rectangle
C. square
D. trapezoid
E. triangle
The shape that we obtained will be a triangle. Then the correct option is E.
What is the pyramid?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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At an arcade, a book of 20 tickets costs $5, a book of 30 tickets costs $7, and a book of 50 tickets costs $10. Would a graph of the relationship between price and number of tickets in a book be a straight line? Explain.
Answer:
yes
Step-by-step explanation:
Find u+v-4u.
u=(5,-2) and v= (-5,7)
By placing the given value in equation , we get u + v - 4u = (-20, 13)
How to evaluate vector?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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4. Find the value of 8 + 12 + 4 + 6 x 1 + 2. Guys I am doing a test and I need help!!
Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. Be sure to consider whether the units are appropriate to the statement, as well as whether the stated amount makes any sense. For example, a statement that someone is 15 feet tall uses the units (feet) appropriately, but does not make sense because no one is that tall. I know a professional bicyclist who weighs 290 kilograms.
"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.
About RationalThe 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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