The sample should be milled to a radius that is approximately 7.19 times its original radius in order to increase its work function by 2%.
The work function of a material is related to its surface area, and milling a sample into smaller nano-spheres increases its surface area. The increase in work function can be approximated by the following equation:
ΔW = kTln(A/A₀)
where ΔW is the change in work function, k is Boltzmann's constant, T is the temperature in Kelvin, A is the new surface area of the milled sample, and A₀ is the original surface area of the sample.
To find the size to which the sample should be milled to increase its work function by 2%, we need to rearrange the equation to isolate the new surface area:
A/A₀ = e^(ΔW/kT)
Plugging in the known values, we get:
A/A₀ = e^(0.02 * 5.1 eV / (8.62 * 10⁻⁵ eV/K * 300 K))
= 51.64
The new surface area is 5064% larger than the original surface area.
Since the sample is being milled into nano-spheres, the new surface area is proportional to the square of the radius. Let's call the original radius of the sample "r₀". Then the new radius is:
r = √(A/A₀) * r₀ = √(51.64) * r₀ = 7.19 * r₀
--The question is incomplete, answering to the question below--
"g a gold (au) macro scale sample has a work function of 5.1 ev. to what size should the sample be milled to increase its work function by 2 %? assume that the sample is milled into nano-spheres and give the size in terms of radius. What is the relation between the new radium and original radius?"
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Find a increased by 25% pls help ASAP.
Answer:
1.25a
Step-by-step explanation:
Original value = a
An increase of 25% can be found by a x 25/100 = 0.25a
The resulting increased value = Original value + Increase in value
= a + 0.25a
= 1.25a
Sometimes it is a more direct approach to use the final value as original value(1 + increase%/100) in which case it would be a(1+25/100) = a(1 + 0.25) = a(1.25) = 1.25a
25 points
Matthew is planning a party and found pizzas for $5 each and drinks for $1 each.
Write an expression that represents how much he will spend. (p = pizza, d = drinks)
The expression that represents how much he will spend would be = y ( 5p + 1d)
How to derive the expression that shows how much he will spend?The amount of money that each pizza(p) is sold = $5 each.
The amount of money that each drink(d) is sold = $1.
The total money that Matthew may spend on the party is represented by = y.
Therefore the expression that will show how much he will spend would be = y ( 5p + 1d).
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what the solution to practice arithmetic sequences as linear functions?
The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.
Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.
Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.
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Solve for h.
Z =
M
g (h-f)
h = 0
X
믐
Ś
PLEASEEEEE WILL MARK!
On solving the provided question, we can say that value of the equation , h = [tex]\frac{M}{Zg} + f[/tex]
Which equation is this?Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.
here,
the equation
[tex]Z=\frac{M}{g(h-f)}[/tex]
[tex]for, h , \\h - f = \frac{M}{(Zg)}\\h = \frac{M}{Zg} + f[/tex]
value of the h will be [tex]\frac{M}{Zg} + f[/tex]
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Finish the patterns
12, _ , _ , _ , 60
1, 3, 5 , 7, _
9, _, _ ,_, 81
_,_,15,_.20
Answer:
Step-by-step explanation:
12, 28, 44, 60
1, 3, 5, 7, 11
9, 25, 49, 81
4, 8, 15, 16, 20
Answer:
1. 12 , 24 , 36 , 48 , 60
2. 1, 3, 5, 7, 9
3. 9, 27, 45, 63, 81
4. 1, 2, 15, 16, 20
Step-by-step explanation:
1. The rule is +12, or add 12.
2. The rule is +2, or add 2.
3. The rule is +18, or add 18.
4. The rule is +1, +13, +1, +4, or add 1, add 13, add 1, add 4.
Carina hiked at Yosemite National Park for 1.75 hours. Her average
speed was 3.5 mi/h. How many miles did she hike?
O 20 mi
O 6.125 mi
O 2 mi
O 61.25 mi
1/9 multiplied by 1.5
Answer:
1/6
Step-by-step explanation:
You can change 1.5 into a fraction.
1.5 = 3/2
Now you can multiply the two fractions easily: the two numerator values multiply and the two denominator values multiply.
1/9 * 3/2 = 3/18.
You can further simply this fraction by noting that 3 divides into 18.
So the answer is 1/6.
I need to prove that AC bisects BD. Can anyone help?
Answer:
let the position vector of A,B,C,D and E be OA,OB,OC,OD andOE respectively.
IN triangle OBD , OE = OD+OB/2
OE=OA+AB+OD/2. (in triangle,OB=OA+AB)
OE=OA+OD+DC/2
OE=OA+OC/2. (in triangle ODC,OD+DC=OC)
proved....
in this article fogel only looks at data from one year (1890). how does he justify drawing conclusions about a much longer time period (1850-1890) from data from just one year?
Robert W. Fogel, in his famous article, used data from one year, 1890, to make inferences about a longer time period, 1850-1890. He did so through the use of statistical methods, including regression analysis and comparative economic growth analysis.
The basic idea behind this approach is to use the data from 1890 as a snapshot of the state of the economy at that time and to use this information to make inferences about the longer time period. The assumption behind this approach is that the data from 1890 is representative of the economy over the entire period 1850-1890, and that the underlying trends and patterns that existed in 1890 were also present in the earlier period.
Fogel used a combination of economic theory, demographic data, and historical information to validate his assumptions and to support his conclusions. He also conducted extensive sensitivity analysis to ensure that his results were robust to different assumptions and data sources.
In conclusion, while using data from one year to draw conclusions about a much longer time period might seem unconventional, it was a valid approach used by Robert W. Fogel in his research and allowed him to make important contributions to our understanding of the economic history of the United States.
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Kim used sticks to make a pattern of squares. Number of squares: 1, 3, 6, 10, 15. Number of sticks: 4, 10, 18, 28, 40. When a shape consists of 28 squares, how many sticks will the shape have?
Answer:
70
Step-by-step explanation:
Find the number pattern (check image)
The shape consisting of 28 squares will have 812 sticks.
Determining the number of sticks the shape will haveFrom the given data, we can see that the number of squares is increasing by consecutive odd numbers, starting from 1:
1, 3, 6, 10, 15, ...
Also, the number of sticks is increasing by consecutive even numbers, starting from 4:
4, 10, 18, 28, 40, ...
This suggests that the number of sticks required to make a pattern of n squares can be found using the formula:
sticks = 2n + (n-2) + (n-4) + ... + 4
This formula represents the sum of the first n even numbers, which can be simplified to:
sticks = n(n+1)
Using this formula, find the number of sticks required to make a pattern of 28 squares:
sticks = 28(28+1) = 28(29) = 812
Therefore, a shape consisting of 28 squares will have 812 sticks.
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how to find 20.5% of 1850
Answer:
379.25
Step-by-step explanation:
20.5% of 1850 means 20.5/100 × 1850
0.205×1850
= 379.25
therefore 20.5% of 1850 is 379.25
Asking for help: does anyone have the answer?
Answer:
D
Step-by-step explanation:
AD≅AB because they are tangent segments from the same point, A
x² + 2 = 11
x² = 9
x = √9 = 3, -3 (two solutions of [tex]\sqrt{9}[/tex])
a floor plan is given for the first floor of a new house. one inch represents 10 feet. if the walk-in closet is 2/5. in. by 2/3 in. on the floor plan, what are the actual dimensions? (round to the nearest hundredth).
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
Finding actual dimensions:To find actual dimensions multiply the given measurement with the measurement given in scale.
In the given problem, given that 1 in = 10 feet which is the scale given, we need to multiply the given measurements that are in the plan with the scale measurement 10 feet.
Here we have
A floor plan is given for the first floor of a new house.
One inch represents 10 feet.
The walk-in closet is 2/5 in. × 2/3 in. on the floor plan
As we know 1 inch = 10 feet
=> 2/5 in = (2/5) × 10 feet = 4 feet
=> 2/3 in = (2/3) × 10 feet = 6.67 feet
Therefore,
The actual dimensions of the walk-in closet are 4 feet × 6.67 feet.
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Suppose that you are given the following expression: -(-20). Which of the following is NOT equivalent to ?-(-20)
A. 20
B.-20
C.[20}
D.{-20}
E.-(-(-(-20)))
The expression that will be not equal to -{-20} are -20,{-20}. The correct options are B and D.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is -(-20). The not equivalent expressions are written below,
-(-20) ≠ 20
-(-20) ≠ {-20}
Therefore, expressions like -20, and -20 will not be equal to —20. B and D are the appropriate choices.
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Two triangles are considered the same if they have the same three side lengths. Find all possible values of P such that there is only 1 possible triangle with integer side lengths and perimeter P.
Answer:
P ∈ {3, 5, 6, 8}
Step-by-step explanation:
You want the possible perimeter values such that there can only be one triangle with that perimeter and integer side lengths.
ConditionsThe requirement that the triangle satisfies the triangle inequality means the longest side must be shorter than P/2.
TrialsThe smallest triangle with integer side lengths is the {1, 1, 1} equilateral triangle.
P=3, {1, 1, 1}
For P=4, the longest side can be neither 1 nor 2, so P=4 is not an option.
For P=5, the longest side can be 2, requiring the other sides to be 2 and 1:
P = 5, {2, 2, 1}
For P=6, the longest side must be less than 3, so all sides must be 2.
P = 6, {2, 2, 2}
For P=7, two triangles are possible: {3, 3, 1} and {3, 2, 2}.
For P = 8, the longest side must be less than 4, so will be 3. The other two sides must be 3 and 2.
P = 8, {3, 3, 2}
For all values of P above 8, there are at least two possible triangles.
Possible values of P are 3, 5, 6, 8.
what is the difference between precession and nutation?
Precession and nutation are two distinct motions of a spinning top or gyroscope. Precession is a slow, uniform motion that results from the gravitational force acting on a spinning top or gyroscope.
It is a slow, uniform motion in which the spinning object's axis of rotation moves in a cone-like motion.
Nutation is a fast, non-uniform motion that is caused by the torque of a nearby force. It is a rapid, irregular motion that causes the spinning object's axis of rotation to wobble back and forth.
Precession is a regular, predictable motion, whereas nutation is an unpredictable, irregular motion. Precession is typically used to describe the motion of a satellite or planet in its orbit, while nutation is used to describe the motion of a spinning top or gyroscope.
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Precession and nutation are two different types of rotational movements in astronomy.
Precession refers to the slow, conical movement of an object's rotational axis, which changes the orientation of the object over time. In the case of Earth, precession causes the direction of the North Pole to change over time.
Nutation, on the other hand, is a rapid, irregular movement of an object's rotational axis. It is caused by the combined gravitational forces of the Sun, Moon, and other celestial bodies on the Earth. Unlike precession, nutation occurs in small, cyclical changes in the orientation of the rotational axis, causing the axis to move slightly back and forth.
In summary, precession is a slow, systematic change in the orientation of an object's rotational axis, while nutation is a rapid, irregular movement of the axis caused by external forces.
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Ethan starts an IRA (Individual Retirement Account) at the age of 34 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65, his retirement savings is $709,165.25. Determine the amount of money Ethan deposited over the length of the investment and how much he made in interest upon retirement.
Ethan deposited 400 each month into his IRA for 31 years.
This totals 148,800 (400 x 31 years = 12,400 x 12 months = 148,800). Upon retirement, Ethan's total savings was 709,165.25. To determine the amount of interest he made, we subtract the total deposits from the total savings: 709,165.25 - 148,800 = 560,365.25. This shows that Ethan made 560,365.25 in interest on his retirement savings over the 31 years. The formula used to calculate the amount of interest Ethan made is: Interest = Total Savings - Total Deposits.Ethan deposited $400 each month into his IRA for 31 years.
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A ball is dropped from 10 feet above the ground. The function h (t) = -16 t² + 10, where t represents the time
in seconds, h gives the height, in feet, of the ball above the ground. When will the ball be 4 feet above the ground? Use
the given quadratic function model to answer questions about the situation it models.
Answer: The equation to find the time when the ball is 4 feet above the ground is:
-16t^2 + 10 = 4
We can solve for t by subtracting 4 from both sides:
-16t^2 + 6 = 0
And then dividing both sides by -16:
t^2 = -6 / -16
t^2 = 3/8
Taking the square root of both sides:
t = ±√(3/8)
Since time cannot be negative, we choose the positive solution:
t = √(3/8)
So the ball will be 4 feet above the ground after √(3/8) seconds.
Step-by-step explanation:
when looking to invest money in a company by purchasing stock why is it important to look at many companies to invest
It is important to look at many companies to invest and compare their advantages to one another before investing money in a company by purchasing stock.
It's crucial to research a variety of businesses before investing your money in them because you can compare their advantages to one another and determine which one will provide you with a higher return on your investment in addition to a guaranteed return.
It's crucial to take into account a company's financial fundamentals when choosing stocks, such as earnings, operating margins, and cash flow. When considered collectively, these elements can provide a fair picture of the company's current financial situation as well as its prospects for short- and long-term profitability.
Diversification is a portfolio's greatest asset. With diversity, you can more easily manage risk, weather market downturns, and generate better long-term returns. Due to these factors, you'll need a variety of stocks in various industries that can counteract one another.
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Which soup has more sodium per cup
Answer:
Soup B
Step-by-step explanation:
Soup A = 5 grams sodium = 12 cups
Soup B = 8 grams of sodium = 13 cups
Find the unit rate, so, soup B has more sodium.
I hope this helps.
Also, next time can you write the question entirely?
Find the value of x that makes this a true statement (1/3)^x=27
Answer:
x= -3
Hope this helped
8 chicken will lay 20 eggs in 3 days
how many days will it take 12 chickens to lay 100 eggs?
Answer:
it will take approximately 3 and 1/3 days for 12 chickens to lay 100 eggs.
a cylindrical can with an open top is to be constructed so that its volume is 167 cubic inches. what height will minimize the amount of tin that will be required to construct the can?
The minimum height of the cone is 17.87 in (approx)
What is the Cylinder:In geometry, the cylinder is a fundamental 3 dimension shape that has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center.
Total surface area, A = 2πr²+ 2πrh square units
The volume of the Cylinder, V = πr²h cubic units
Here we have
A cylindrical can with an open top is to be constructed so that
The volume of the cone is 167 in³
As we know volume of cone = (1/3) πr²h
=> (1/3) πr²h = 167
=> h = 501/πr²
As we know Surface Area of the cone = 2πrh + 2πr²
Substitute h = 501/πr² in Surface Area of cone
=> SA = 2πr(501)/πr² + 2πr²
=> SA = 1002r⁻¹+ 2πr²
Differentiate SA with respect to r
=> SA' = (-1) 1002r⁻²+ 4πr
=> SA' = - 1002r⁻² + 4πr
Here - 1002r⁻² + 4πr = 0
=> - 501r⁻² + 2πr = 0
=> - 501/r² + 2πr = 0
=> [-501 + 2πr³ ]/r² = 0
=> [-501 + 2πr³ ] = 0
=> 2πr³ = 501
=> πr³ = 250.5
=> r³ = 79.70
=> r = 8.92 (approx)
Hence the height of the cone, h = 501/πr²
= 501/π(8.92)
= 17.87 (approx)
Therefore,
The minimum height of the cone is 17.87 in (approx)
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find end behavior of f(x)=2^x-5
The end behavior of the function f(x) = 2ˣ - 5 will be increasing only.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The function is given below.
f(x) = 2ˣ - 5
We know that the function is an exponential function. And the exponential function is always inceasing.
Thus, the end behavior of the function f(x) = 2ˣ - 5 will be increasing only.
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Determine whether VY//ZW. Justify your answer. ZX = 18, ZV = 6, WX = 24, and YX = 16
Answer:
Step-by-step explanation:
To determine whether VY is parallel to ZW, we need to see if the ratio of their corresponding sides is equal.
The ratio of corresponding sides of two parallel lines is constant, so we can set up an equation to compare the ratios:
ZV/ZX = WX/YX
6/18 = 24/16
Simplifying the fractions, we get:
1/3 = 3/2
Since the two sides of the equation are not equal, VY is not parallel to ZW.
Help!!!!!!!!!!!!!!!!!!!!!!
Answer:
the second option
Step-by-step explanation:
the limit coming to x = 4 from the left (the '-' side) is -4.
the limit coming to x = 4 from the right (the '+' side) is 2.
it does not matter that the point itself is excluded. but the tendency of the function coming from the right is clear and defined.
the one-sided limit would not exist, if the function violently oscillates at the limit point.
or if the limit is infinite. then officially it does not exist, but we can write ±infinite.
for the case of the violent oscillation there is nothing else we can write but DNE.
44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8 mean and MAD answer
For the values 44. 4, 43. 8, 45. 6, 45. 9, 44. 1, 45. 6, 44. 0, 44. 9, 45. 8, the mean of the data set is 49.52. The Mean Absolute Deviation (MAD) of the data set is 4.83.
To find the mean of the given data set, we add up all the values and divide by the number of values:
Mean = (44.4 + 43.8 + 45.6 + 45.9 + 44.1 + 45.6 + 44.0 + 44.9 + 45.8) / 9 = 445.7 / 9 = 49.52
So, the mean of the data set is 49.52.
To find the Mean Absolute Deviation (MAD), we first find the absolute difference between each value and the mean, and then find the mean of these absolute differences:
Absolute Difference = |44.4 - 49.52|, |43.8 - 49.52|, ..., |45.8 - 49.52|
MAD = (Absolute Difference1 + Absolute Difference2 + ... + Absolute Difference9) / 9
Calculating the MAD gives:
MAD = (5.12 + 5.72 + 3.92 + 3.62 + 5.42 + 3.92 + 5.52 + 4.62 + 5.32) / 9 = 43.5 / 9 = 4.83
So, the Mean Absolute Deviation (MAD) of the data set is 4.83.
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Help, Find the expression of the nth term of the sequence.
WILL MARK BRANLIEST!
The expression of the nth term of the sequence is 1/n
How to determine the expression of the nth term of the sequence.From the question, we have the following parameters that can be used in our computation:
The sequence definition
From the sequence, we can see that only the denominator increaes by 1
The numerator is constant at 1
Using the above as a guide, we have the following:
Tn = 1/n
Hence, the expression is 1/n
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Find the sum of the squares of the solutions of $x^2-13x+4=0$.
The equation [tex]$x^2-13x+4=0$[/tex] is a quadratic equation and can be solved using the quadratic formula.
The sum of the squares of the solutions of the equation [tex]$x^2-13x+4=0$[/tex]can be found in the following steps:
Solve for the solutions: The equation can be solved using the quadratic formula. The solutions are given by
[tex]$x = \frac{13 \pm \sqrt{13^2 - 4 \cdot 4}}{2 \cdot 1} = \frac{13 \pm \sqrt{169 - 16}}{2} = \frac{13 \pm \sqrt{153}}{2} = \frac{13 \pm 9}{2} = 11$ or $-6$.[/tex]
Square the solutions: Find the square of each solution by raising it to the power of 2.
[tex]$11^2 = 121$ and $(-6)^2 = 36$.[/tex]
Sum the squares: Add the squares of the solutions together to get the final answer: 121 + 36 = 157.
Therefore, the sum of the squares of the solutions of
[tex]$x^2-13x+4=0$[/tex] is 157.
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An employee receives a 2% raise once per year. If the employee's initial salary is $ 77,000.00, what will the employee's salary be after 8 years?
Answer:
90,217.77
Step-by-step explanation:
We can use the equation S+RS=M to figure this out where S is the initial salary before the raise, R being the rate at which the salary is increased, and M being the Salary after the raise.
By plugging it in for the first year we get
77,000+2%*77,000=M
Solving it, we get 78,540 and since there is a new salary increase 78,540 is the new starting salary
78,540+78,540*2%=80,110.8
80,110.8+80,110.8*2%=81,713.016
83,347.27632
85,014.2218464
86,714.506283328
88,448.796408995
90,217.772337175
Or rounded up
90,217.77