Answer:
-3.5x + 3y - 3
Step-by-step explanation:
1.2x + 3y - 3 - 4.7x
=> -3.5x + 3y - 3
Therefore, our simplified expression is -3.5x + 3y - 3
Hoped this helped.
An equation is not the same as a mathematical expression. The expression is -3.5x + 3y - 3.
Explain about the Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.
A mathematical expression can only result in one mathematical value. A character expression results in a single character value when evaluated. A logical or relational expression yields only one logical value upon evaluation.
= 1.2x + 3y - 3 - 4.7x
=> -3.5x + 3y - 3
Our abbreviated formula is -3.5x + 3y - 3.
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Edulastic
Full explanation please
*will give brainlist if able to :)
Answer:
50 degrees
Step-by-step explanation:
If AB is congruent to BC, then angles BAC and BCA are congruent.
Angle DCB+ angle BCA= 180 degrees
180 degrees- 115 degrees= 65 degrees
It means that angles BCA and BAC (which are congruent) are equal 65 degrees.
Sum of angles i side a triangle is 180 degrees so:
180 degrees- 2*65 degrees= 180 degrees- 130 degrees= 50 degrees
The angle ABC is equal to 50 degrees.
what is the diffrence between irregular and irrational numbers?
Answer:
Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.
Step-by-step explanation:
please make my answer as brainelist
Solve this system of linear equations without graphing: 3y + 7 = 5x 7x-3y = 1
Answer:
x = -3
Step-by-step explanation:
3y + 7 = 5x
3y = 5x - 7
y = 5x/3 - 7/3 (Isolate y.)
7x - 3y = 1
-3y = 1 - 7x
y = -1/3 + 7x/3 (Isolate y.)
5x/3 - 7/3 = -1/3 + 7x/3 (Set the equations equal to each other. Simplify.)
5x/3 - 2 = 7x/3
-2 = 2x/3
-6 = 2x
-3 = x
over which interval does h have a positive rate of change?
Answer:
I believe the answer is D
Step-by-step explanation:
Answer: 2,3
Step-by-step explanation:
Indicate below weather the equation in the box is true or false
Answer:
False
Step-by-step explanation:
4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10
chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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17. Write the first 4 terms of the
sequence defined by the explicit rule.
f(n) = 2n - 5
Answer:
The first four terms are: -3, -1, 1, and 3
Step-by-step explanation:
First 4 terms are:
f(1) = 2 (1) - 5 = -3
f(2) = 2 (2) - 5 = -1
f(3) = 2 (3) - 5 = 1
f(4) = 2 (4) - 5 = 3
Indicate the equation of the given line in standard form, writing the answer in the equation box below.
The line containing the longer diagonal of a quadrilateral whose vertices are A(2, 2), B(-2,-2), C(1, -1), and D16, 4).
9514 1404 393
Answer:
x -3y = 4
Step-by-step explanation:
A plot of the points reveals the longer diagonal to be BD. (Also, point C is on that line.)
We can write the standard form equation of the line through (x1, y1) and (x2, y2) as ...
(y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1
For points (-2, -2) and (16, 4), this equation is ...
(4 -(-2))x -(16 -(-2))y = (4 -(-2))(-2) -(16 -(-2))(-2)
6x -18y = -12 +36
Dividing by the greatest common factor (6), we have the standard-form equation ...
x -3y = 4
Adam reads 1/8 of a book in 1/6 of an hour. How much time does it take for him to read the whole book?
Let the time taken to read the whole be y
If he reads 1/8 of the whole book (x), it can be expressed as,
\(\frac{1}{8}\text{ of x =}\frac{1}{8}\times x=\frac{x}{8}\)If it takes Adam to read x/8 of a book in 1/6 hours,
To read the whole book, it will take Adam,
\(\begin{gathered} Adam\text{ read }\frac{x}{8}\text{ in }\frac{1}{6} \\ To\text{ read the whole book (x) in y time} \\ y\times\frac{x}{8}=x\times\frac{1}{6} \\ \frac{xy}{8}-\frac{x}{6} \\ \text{Crossmultiply} \\ 6\times xy=8x \\ \text{Divide both sides by }6x \\ \frac{6xy}{6x}=\frac{8x}{6x} \\ y=\frac{4}{3}=1\frac{1}{3}hours \end{gathered}\)Hence, it will take 1 1/3 hours for Adam to read the whole book.
Sarah is changing her refuse (garbage) service. “Junk Bunker” charges a one time start-up fee of $300 plus $20 per month. “Junk in the Trunk” charges no start-up fee but charges $35 per month. Write an equation to determine when the two companies would cost the same.
Answer:
300 + 20x = 35x
Step-by-step explanation:
if you need to know how many months it is when the prices are even the answer is 20
Answer:
esxcdrfvtgbhyjnkmlmjnhbgvtfcrdfvgbhnjmk
Step-by-step explanation:
A 12 ft ladder leans against the side of a house the top of a ladder is 11 Ft off the ground find x the angle of elevation of the ladder round your answer to the nearest tenth of a degree
PLZ HELP BEEN STUCK FOR A HOUR
Answer:
66.5 degrees
Step-by-step explanation:
use soh cah toa
sinx degrees= oppposite/hypotenuse
sinx degrees=11/12
sin x degrees= 0.916
sin 66.5 degrees = 0.916
if u need a full number do 66
n a survey of patients in a local hospital, 62.42% of the respondents indicated that the health care providers needed to spend more time with each patient. who makes up the population?
The survey is of the population of all the patients present in that particular hospital.
What is a survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population.
Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.
Surveys are used to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions.
Surveys might have narrow, focused objectives or they can have broad, more general objectives.
So, in the given situation the survey states that 62.42% of the respondents indicated that the health care providers needed to spend more time with each patient.
So, it is clear that the remaining respondents have the opposite view on this.
So, the respondents will be all the patients present in the local hospital.
Therefore, the survey is of the population of all the patients present in that particular hospital.
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giải tam giác ABC vuông tại A trong mỗi trường hợp sau:
a) b=4 cm; góc C = 62°
b) a=40 cm; góc B = 52°
c) c=42 cm; b=36 cm.
Answer:
the answer is C coz just 42 cm is abc
Each leaf of a certain double-leaf drawbridge is 130 feet long. If 130 ft an 80-foot wide ship needs to pass through the bridge, what is the minimum angle 0, to the nearest degree, which each leaf of the bridge should open so that the ship will fit
The minimum angle that each leaf of the bridge should open is 47 degrees.
How to calculate the angleWe can use the cosine function to solve this problem. The cosine function gives the ratio of the adjacent side to the hypotenuse of a right triangle. In this case, the adjacent side is the distance between the pivot point and the ship, which is 90 feet. The hypotenuse is the length of each leaf of the bridge, which is 130 feet.
The cosine function is defined as:
cos(theta) = adjacent / hypotenuse
cos(theta) = 90 / 130
theta = cos^-1(90 / 130)
theta = 46.2 degrees
The nearest degree to 46.2 degrees is 47 degrees.
Therefore, the minimum angle that each leaf of the bridge should open is 47 degrees.
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If ladders are difficult to use for high floors, what are some other options? What is the level of safety of each of your options? Explain using mathematical facts.
Answer:
Stairs, escalators, elevators, ramps...
Step-by-step explanation:
If ladders are difficult to use for high floors another very common options are stairs. you see them pretty much everywhere. Escalators and elevators are also used, elevators more often that escalators.
I don't know how to make it sound "mathy" but..
Ladders are super straight and so for high floors, the slope of the ladder will be too steep for anyone to climb without gravity interfering.
The level of safety with stairs is higher because instead of going straight up, The steps provide a flat surface for someone to stand on while climbing the stairs and there is a much more stable foundation. Stairs can have protection like a guard rail and even go in a spiral motion upwards because they are more stable and safe. It is still possible to fall if one is not careful because of pesky gravity.
Escalators are pretty much moving stairs and the level of safety is greater because of the strong foundation and flat surface to stand on. Of course falling can happen, lowering the safety, but this is not likely because of the slowly enough moving steps. There is a rail as well and as long as people are careful, there aren't usually any casualties.
Elevators take up way less space than stairs and escalators because they can go straight up and down. The level of safety is fairly high because an elevator is a pulley system and people don't involve all that much moving around. Just go in the mechanical box, the doors close for safety, click a button, and then go up or down.
I don't know how to incorporate mathematical facts into this question because this is literally logic not math in my opinion. Honestly, ladders aren't even used that much, I don't think, except for building and house work.
I hope this helps you with whatever you are doing!
<3
Please help anyone thank you.
By using proportionality, it can be calculated that-
a) Constant of proportionality that relates the length of paver in the model and the actual length is k = \(\frac{4}{3}\)
\(y = \frac{4}{3}x\) is the required equation which relates the length of paver in the model and the actual length of the paver
b) Area of the rectangle = \(\frac{1}{3}\) sq.feet
Constant of proportionality that relates the area of paver in the model and the actual area is k = \(\frac{9}{16}\)
What is proportionality?
Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio
Proportionality can be direct or inverse
Direct proportion
Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.
For example cost of a commodity and quantity of a commodity are in direct proportion
Inverse proportion
Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.
For example Number of men and number of days taken by those men to complete a job.
Length of paver in the model = \(\frac{2}{3}\) ft
Actual length of paver = \(\frac{1}{2}\) ft
Let the constant of proportionality be k
\(\frac{2}{3} = \frac{1}{2}k\)
k = \(\frac{2}{3} \div \frac{1}{2}\)
k = \(\frac{4}{3}\)
Let y be the length of paver in the model and x is the actual length
\(y = \frac{4}{3}x\) is the required equation which relates the length of paver in the model and the actual length of the paver
b) Area of the model = \(\frac{1}{2}\times \frac{3}{8} = \frac{3}{16}\) sq. feet
Actual area = \(\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}\) sq.feet
Let the constant of proportionality be l
\(\frac{3}{16} = \frac{1}{3}l\)
l = \(\frac{3 \times 3}{16}\\\)
l = \(\frac{9}{16}\)
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a sidewalk in the shape of two triangles, a rectangle, and a square was built around the edge of a building as shown. pls!!! I need it for tomorrow.
The requried area of the composite figure is given as 180 ft³.
What is surface area?Surface area is defined as the measure of a region or surface is called as surface area.
Here,
from the figure,
Surface area is given as,
Area = area of the lower rectangle + 2[area of the triangle] + area of the middle rectangle
Area = 6 × 6 + 2 × 1/2 ×(6×6) + 18 × 6
Area = 36 + 36 + 108
Area = 180 ft²
Thus, the requried area of the composite figure is given as 180 ft³.
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Which of the following notations correctly describe the end behavior of the polynomial graphed below
The notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
What is end behavior of polynomial?
The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.
From the graph we know that the vertex of this parabola is V(0, 8).
This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.
Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.
In a mathematical language this is:
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
Hence, the notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
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(L2) Given: P is the incenter of ΔMNO.PM¯,PN¯, and PO¯ are angle bisectors.PY=23 mm, PO=52 mm, m∠ZMP=30∘,m∠MON=40∘What is the length of PX¯ ?What is the measure of ∠PMX ?What is the measure of ∠POX ?What is the length of XO¯ ?
The measure of ∠POX = 160° The length of XOA = 16.95 mm ,We know that PM¯, PN¯, and PO¯ are angle bisectors of triangle MNO, so they divide the opposite sides in two equal parts. Let x = MY, y = NY, and z = OY. Then, we have:
MX / NO = MY / NY (by the angle bisector theorem)
MX / (MX + XO) = x / (x + y)
MX(x + y) = x(MX + XO)
MXy = XOx
NO / OX = NY / OY (by the angle bisector theorem)
(OX + XO) / OX = y / z
1 + XO/OX = y/z
XO/OX = (z - y)/y
Now, we can use these equations to solve the problem:
To find PX¯, we need to find MX. Using the angle sum property of triangles, we have:
m∠M = 180 - m∠MON = 140°
m∠PMX = m∠M/2 = 70°
m∠PMO = m∠MON/2 = 20°
m∠XMO = m∠PMX + m∠PMO = 70° + 20° = 90°
Therefore, PX¯ is the altitude from M to XO¯, so we have:
tan(30°) = PX / MX
MX = PX / tan(30°)
= 23 / √(3)
= 13.31 mm
To find m∠PMX, we can use the fact that PM¯ is an angle bisector:
m∠PMX = m∠M + m∠PMO
= 140° + 20°
= 160°
To find m∠POX, we can use the fact that PO¯ is an angle bisector:
m∠POX = m∠O + m∠PNO
= 180° - m∠MON + m∠PNO
= 180° - 40° + 20°
= 160°
To find XO¯, we need to find y and z. Using the fact that PX¯ is an angle bisector, we have:
PY / OY = PM / OM
23 / z = 52 / (x + y + z)
y + z = 52z / 23
z = 23y / (52 - 23)
Using the equation XO/OX = (z - y)/y, we have:
XOA / 52 = (23y / (52 - 23) - y) / x
XOA= 52 * 23y / ((52 - 23) * x - 23y)
Substituting MX = 23/√(3) - PX = 23/√(3) - 13.31, we get:
y = NO * PY / (PM + PN + PO) = 56.17 mm
z = OY + PY = 79.17 mm
XOA = 16.95 mm
Therefore, the answers are:
Length of PX¯: 13.31 mm
Measure of ∠PMX: 160°
Measure of ∠PO
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Use the shell method to find the volume of the solid generated by revolving the plane region about the line x
To find the volume of the solid generated by revolving the plane region about the line x using the shell method, we need more specific information about the given plane region and the boundaries of integration.
The shell method is a technique used to calculate volumes of solids of revolution. It involves integrating cylindrical shells along the axis of rotation. However, in order to apply the shell method, we require additional details regarding the given plane region and the boundaries of integration.
Typically, the plane region is defined by a function or an equation. For example, if the plane region is bounded by the curves y = f(x), y = g(x), and the line x = a, x = b (where f(x) > g(x) for all x in the interval [a,b]), we can proceed with the shell method.
To calculate the volume using the shell method, we integrate the circumference of each cylindrical shell multiplied by its height. The differential height is given by Δh = f(x) - g(x), and the differential circumference is 2πx.
The integral expression for calculating the volume using the shell method is:
V = ∫[a,b] 2πx * (f(x) - g(x)) dx
By evaluating this integral over the appropriate interval [a,b], we obtain the volume of the solid generated by revolving the given plane region about the line x.
However, without specific information about the plane region, the equations or functions defining it, and the boundaries of integration, it is not possible to provide a numerical value for the volume. If you can provide more details or specify the plane region, I would be happy to assist you further in using the shell method to determine the volume.
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Given: SP = PT=ST=2.6. Find: V Un S # 1 # O is centroid of ASPT, MOL(SPT). m/MPO = 70° M 0 T
Since O is the centroid of ASPT, it divides each median in the ratio 2:1. Therefore, OS = 2/3 * 2.6 = 1.7.
The area of triangle SPT is (1/2) * 2.6 * 2.6 = 3.36.
The area of triangle MPO is (1/2) * 1.7 * 2.6 = 2.22.
The area of triangle OSP is (1/2) * 1.7 * 1.7 = 1.54.
The area of triangle OPT is (3.36 - 2.22 - 1.54) = 0.58.
Therefore, V = 3.36 + 2.22 + 1.54 + 0.58 = 7.6.
The population of a city can be modeled by P(t) = 170.088 thousand persons, where t is the number of years after 2000. Approximately how rapidly was the city's population be changing between 2029 and 2037? The city's population was changing by ____ thousand persons/year.
The city's population was changing by approximately 170.088 thousand persons/year between 2029 and 2037.
The population of a city can be modeled by P(t) = 170.088 thousand persons, where t is the number of years after 2000. To find out how rapidly the city's population was changing between 2029 and 2037, we need to calculate the difference in population between these two years and divide it by the number of years.
First, we need to find the population in 2029 and 2037. We can do this by plugging in the values of t into the equation:
P(29) = 170.088 * 29 = 4932.552 thousand persons
P(37) = 170.088 * 37 = 6293.256 thousand persons
Next, we need to find the difference in population between these two years:
P(37) - P(29) = 6293.256 - 4932.552 = 1360.704 thousand persons
Finally, we need to divide this difference by the number of years to find the rate of change:
1360.704 / (37 - 29) = 170.088 thousand persons/year
Therefore, the city's population was changing by approximately 170.088 thousand persons/year between 2029 and 2037.
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solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
\(\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}\)The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
Graph: 3x-5y=15 an actual graph
See the attachment
Step-by-step explanation:Hi there !
x = 03(0) - 5y = 15
- 5y = 15 | (-)
5y = - 15
y = - 15 : 5
y = - 3
y intercept (0 ; - 3)
2. y = 0
3x - 5(0) = 15
3x = 15
x = 15 : 3
x = 5
x intercept ( 5 ; 0)Good luck !
What calculator is used for pre-calculus?
A scientific calculator is typically used for pre-calculus.
This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.
It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.
Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.
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The charity drive was held over two days. On the first day, the 20 artists worked for 6 hours. On the second day, 25 artists turned up and worked for 12 hours. Find the total number of art installations completed over the two days.
Answer:
The charity drive was held over two days. On the first day, the 20 artists worked for 6 hours. On the second day, 25 artists turned up and worked for 12 hours. Find the total number of art installations completed over the two days.
Step-by-step explanation:
Let's start by finding the total number of art installations completed on the first day by the 20 artists who worked for 6 hours. If each artist creates one art installation, then the total number of installations created by the 20 artists is:
20 artists x 6 hours/artist = 120 art installations
On the second day, 25 artists worked for 12 hours. Using the same assumption that each artist creates one art installation, the total number of installations created by the 25 artists is:
25 artists x 12 hours/artist = 300 art installations
Therefore, the total number of art installations completed over the two days is:
120 + 300 = 420
So, the charity drive produced 420 art installations over the two days.
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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2 2.1 Mathematical intro show that there is another form for spherical harmonics: 1 3 3 Y₁ x iy 1/√√2 (²-1) 2πT 2π 1 3 3 z YO 2 2π π r 1 3 x iy Y₁¹ 3 2π - - 12 √ √ 2² (²+²) 2 2π
Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:
Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)
Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:
Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)
Y1,0 = 1/2 √(3/π)cosθ
Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)
Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ
Y2,0 = 1/4 √(5/π)(3cos²θ-1)
Y0,0 = 1/√(4π)
The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.
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Express the recurring decimal 0.004 as a fraction.
Answer: 1/250
Step-by-step explanation: you could literally demos scientific calculator to get the Answer
in the citation 319 n.w. 2d 459, the number 459 represents the
The number 459 in the citation 319 N.W. 2d 459 represents the page number where the case or legal opinion can be found in the North Western Reporter, Second Series. The North Western Reporter is a series of case reporters that includes court decisions from various states in the northwestern region of the United States.
In legal citations, the number before the "N.W." indicates the volume number of the reporter. So in this case, "319" refers to the specific volume where the case is located. The abbreviation "N.W." stands for North Western Reporter, which is the name of the reporter series. The number "2d" after "N.W." indicates that this is the second series of the North Western Reporter.
To locate the case within the volume, the number "459" refers to the page number where the case begins. This allows readers, such as lawyers, judges, or researchers, to easily find and reference the specific case within the reporter.
In summary, the number "459" in the citation 319 N.W. 2d 459 represents the page number where the case can be found in the North Western Reporter, Second Series.
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