Determine C as a function of d1 , d2 , and A . Assume d1 d2 is much less than the dimensions of the plates.
Answers
The capacitance (C) of a parallel plate capacitor, with plate area A and distances d1 and d2 , is given by C = (ε₀ * A) / (d1 + d2), where ε₀ is the permittivity of free space.
To determine the capacitance (C) as a function of d1, d2, and A, we need to consider the geometry of the capacitor.
Assuming that d1 and d2 are much smaller than the dimensions of the plates, we can consider the capacitor as a parallel plate capacitor.
The capacitance of a parallel plate capacitor is given by the formula:
C = (ε₀ * A) / d,
where C is the capacitance, ε₀ is the permittivity of free space (a constant), A is the area of the plates, and d is the distance between the plates.
In this case, we have two distances, d1 and d2, which are assumed to be much smaller than the dimensions of the plates. We can assume that the effective distance between the plates is d = d1 + d2.
Therefore, the capacitance (C) as a function of d1, d2, and A can be expressed as:
C = (ε₀ * A) / (d1 + d2).
Note that this assumes that the plate dimensions are much larger than d1 and d2, and the electric field lines are approximately uniform between the plates.
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Related Questions
If C = x2 + 8x + 3 and B = x – 8, find an expression that equals 3C + B in
standard form.
Answers
Answer: 3x^2 + 25x + 1
Step-by-step explanation:
3C + B
=> 3(x^2 + 8x + 3) + (x - 8)
=> 3x^2 + 24x + 9 + x - 8
=> 3x^2 + 25x + 1
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
F(x) = 0 ; x < 0
x^2/25 ; 0 < x < 5
1 ; 5 < x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places)
a) P(x < 3) (lessthan/equal)
b) P(2.5 < x < 3) (All less than equal to)
c) P(x > 3.5)
d) The median checkout duration [solve 0.5 = F(u)]
e) F'(x) to obtain the density function f(x)
f(x0 = F'(x) =
f) E(X)
g) V(X) and standard deviation_x
Answers
(a) P(x ≤ 3) = 0.36
(b) P(2.5 ≤ x ≤ 3) = 0.11
(c) P(x > 3.5) = 0.51
(d) The median checkout duration of 50% is, u = 3.535 (approximately)
(e) The density function is given by, f(x) = 2x/25 when 0 < x < 5
(f) The expected value of X is given by, E(X) = 3.33 (approximately)
(g) The variance of X is, V(X) = 1.4
Standard Deviation of X = 1.18
Given the cdf of X is given by,
F(x) = 0 ; x < 0
= x²/25 ; 0 < x < 5
= 1 ; 5 < x
Evaluating the required probability we get,
(a) P(x ≤ 3) = (x²/25)|₃ - (x²/25)|₀ = 9/25 = 0.36
(b) P(2.5 ≤ x ≤ 3) = (x²/25)|₃ - (x²/25)\(|_{2.5}\) = 9/25 - 6.25/25 = 0.36 - 0.25 = 0.11
(c) P(x > 3.5) = 1 - P(x ≤ 3.5) = 1 - (3.5)²/25 - 0²/25 = 1 - 0.49 = 0.51
(d) The median checkout duration of 50% is,
P(x ≤ u) = 0.5
F(u) = 0.5
u²/25 = 0.5
u² = 12.5
u = 3.535 (approximately)
(e) The density function is given by,
f(x) = F'(x) = d(F(x))/dx = 2x/25 when 0 < x < 5
(f) The expected value of X is given by,
E(X) = \(\int_{-\infty}^{\infty}\) x f(x) dx = \(\int_0^5\) 2x²/25 dx = 2x³/75\(|_0^5\) = 10/3
(g) The variance of X is,
V(X) = E(X²) - (E(X))² = \(\int_{-\infty}^{\infty}\) x² f(x) dx - (10/3)² = = \(\int_0^5\) 2x³/25 - 100/9 = 5⁴/50 - 100/9 = 12.5 - 11.1 = 1.4
Standard Deviation of X = √1.4 = 1.18
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Use the graph of the parabola to fill in the table .
Answers
Using the given graph we can answer the questions:
a. The parabola opens upward.
b. The coordinates of the vertex, which is the point at the bottom of the parabola, are (2,1).
c. The equation of the axis of symmetry is x=2.
d. The y intercept is 5.
The graph has no x intercepts.
if each of seven persons in a group shakes hands with each of the other six persons, then a total of forty-two handshakes occurs.
A. True
B. False
Answers
Answer:
B. False
Step-by-step explanation:
You want to know if it is true that when each of seven persons in a group shakes hands with each of the other six persons, a total of forty-two handshakes occurs.
HandshakesThe count of 42 handshakes includes every one of 7 shaking hands with each of the remaining 6, without regard to whether they met before.
The count will include A shaking hands with B, and B shaking hands with A. That handshake will be counted twice, so the number 42 overstates the actual number of handshakes by a factor of 2.
It is false that there will be 42 handshakes. (There will be only 21.)
Need help pleaseeeeeeeee
Answers
Step-by-step explanation:
From the data given:
tan5 = 131 / d₁
d, is the distance for points A
d₂ = 131/tan21 = 341.26ft
d₂ is the distance for points B
Distance from A to B
1497.3368 - 341.26666 = 1,156.1 ft
Thus, the distance from point A to point B is 1,156.1 ft if A boat is heading towards a lighthouse, whose beacon light is 142 feet above the water.
Dan invests £13000 into his bank account. He receives 4.7% per year simple interest. How much will Dan have after 6 years? Give your answer to the nearest penny where appropriate.
Answers
Step-by-step explanation:
SI = PxTxR/100
SI= (13000)(6)(4.7)/100
SI = 366600/100
SI= 3666
Use distributive property:
3(x-4)+2(x+5)
Answers
Answer:
Step-by-step explanation:
3(x - 4) + 2(x + 5) = 3*x - 3*4 + 2*x + 2*5
= 3x - 12 + 2x + 10
= 3x + 2x - 12 + 10 {Combine like terms}
= 5x - 2
Please hurry and answer!
Answers
Answer:
B=-2
Step-by-step explanation:
82% of £134.18
Give your answer rounded to 2 DP
Answers
82 = 0.82 = multiplier
134.18 x 0.82 = 110.0276
= £110.03 (2.d.p)
Explain why: x2 + 4 >= 4x for all real x.
Answers
Answer:
x² + 4 > 4x
x² - 4x + 4 > 0
(x - 2)² > 0 (true for all real x)
Mount Hope Junior High has volunteered to pick up trash along a
stretch of road that measures 7 1/4 miles on Saturday morning. The
organizer believes that each student can clean 1/8 of a mile during the
time allotted. How many students need to volunteer to clean this
stretch of road?
give me the answer in the comments because I can't see anymore answers
Answers
The number of students that are needed to clean this stretch of road is given as follows:
58 students.
How to obtain the number of students?The number of students that are needed to clean this stretch of road is obtained applying the proportions in the context of the problem.
A proportion is applied as the number of students is given by the division of the the total length of the road by the length that can be cleaned by each student.
The parameters for this problem are given as follows:
The total length of the road is of 7 + 1/4 = 7.25 miles.The length that can be cleaned by each student is of 1/8 = 0.125 miles.Hence the number of students that are needed to clean this stretch of road is obtained as follows:
7.25/0.125 = 58 students.
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As long as N is significanly less than K, logistic growth is indistinguishable from exponential O True O False if dN/dt > 0, then N O equals to zero O decreases O remains stable O increases
Answers
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.
The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."
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this question
find the value of x y and z
Answers
Answer:
x = 6
y = 24
z = there is no z?
Step-by-step explanation:
All angles of a polygon add up to 360 degrees
The 2 parellel lines on top and bottom mean that there are 2 right angles on the left side
3y + 18 = 90
3y = 72
y = 24
15x + 30 + 10x = 180
25x = 150
x = 6
Simplify the expression and combine lime terms
. 2(x + 6) + 3x + 4
Answers
Answer:
5x+16
Step-by-step explanation:
2(x + 6) + 3x + 4
Distribute
2x+ 2*6 + 3x+4
2x+12 + 3x+4
Combine like terms
2x+3x +12 +4
5x+16
Answer:
5x+16
Step-by-step explanation:
The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. If the average number of shoppers in the original store at any time was 45, then the average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time?
A. 60
B. 70
C. 80
D. 50
Answers
To solve this problem, we need to first find the average number of shoppers in the new store at any time.
We know that during business hours, 90 shoppers per hour enter the store and each stays an average of 12 minutes.
To find the average number of shoppers at any time, we need to convert the time each shopper spends in the store to hours:
12 minutes = 0.2 hours
So, on average, each shopper takes up 0.2 hours in the store.
Therefore, the average number of shoppers in the new store at any time is:
90 shoppers/hour x 0.2 hours/shopper = 18 shoppers
Now we can find the percent less that the average number of shoppers in the new store is compared to the original store:
Percent less = (Original - New) / Original x 100%
Percent less = (45 - 18) / 45 x 100%
Percent less = 27 / 45 x 100%
Percent less = 60%
So the answer is A. 60.
To find the average number of shoppers in the new store at any time, we can use the formula:
Average number of shoppers at any time = (Number of shoppers per hour * Average time spent in store) / 60
For the new store:
Average number of shoppers at any time = (90 shoppers per hour * 12 minutes) / 60
Average number of shoppers at any time = 1080 / 60 = 18 shoppers
Now we will find the percentage difference between the average number of shoppers in the original store (45 shoppers) and the new store (18 shoppers):
Percentage difference = ((Original store shoppers - New store shoppers) / Original store shoppers) * 100
Percentage difference = ((45 - 18) / 45) * 100
Percentage difference = (27 / 45) * 100 = 60%
So the average number of shoppers in the new store at any time is 60% less than the average number of shoppers in the original store at any time. Your answer: A. 60
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A rectangle has a height of 7 and a width of 2x^2-. Expres the area of the entire rectangle.
Answers
Answer:
\(14x^2\)
Step-by-step explanation:
Height(Length)=7 units
Width = \(2x^2\)
As we know that Area of a rectangle= Length x Breadth
Area of the following rectangle= 7 x \(2x^2 = 14x^2\)
Hw02-dot-product: Problem 3 Problem Value: 1 point(s). Problem Score: 0%. Attempts Remaining: 2 attempts. Help Entering Answers (1 point) Consider a = i + 3k, b = i +3j - k, and c = i – k. Find the following scalar and vector projections. 1. proj, b = Σ 2. compab = M 3. projka = | M 4. compa = Σ 5. proji C = M 6. comPb C = м 7. comp.ca M
Answers
The scalar and vector projections are: 1. projb = (i + 3k) · (i + 3j - k) / |i + 3k|. 2. compab = (i + 3k) · (i + 3j - k) / |i + 3k| · (i + 3k)/|i + 3k|. 3. projka = (i + 3k) · i - k / |k|. 4. compa = (i + 3k) · i - k / |k| · i/|k|. 5. projc = (i - k) · i / |i|. 6. compbc = (i - k) · (i + 3j - k) / |i + 3j - k| · (i + 3j - k)/|i + 3j - k|. 7. compac = (i - k) · (i + 3k) / |i + 3k| · (i + 3k)/|i + 3k|.
1. projb = Σ
The scalar projection of vector b onto vector a is equal to the dot product of a and b, divided by the magnitude of a. Therefore, projb = (i + 3k) · (i + 3j - k) / |i + 3k|.
2. compab = M
The vector projection of vector b onto vector a is equal to the scalar projection of vector b onto vector a, multiplied by the unit vector of a. Therefore, compab = (i + 3k) · (i + 3j - k) / |i + 3k| · (i + 3k)/|i + 3k|.
3. projka = |M
The scalar projection of vector a onto vector k is equal to the dot product of a and k, divided by the magnitude of k. Therefore, projka = (i + 3k) · i - k / |k|.
4. compa = Σ
The vector projection of vector a onto vector k is equal to the scalar projection of vector a onto vector k, multiplied by the unit vector of k. Therefore, compa = (i + 3k) · i - k / |k| · i/|k|.
5. projc = M
The scalar projection of vector c onto vector i is equal to the dot product of c and i, divided by the magnitude of i. Therefore, projc = (i - k) · i / |i|.
6. compbc = M
The vector projection of vector c onto vector b is equal to the scalar projection of vector c onto vector b, multiplied by the unit vector of b. Therefore, compbc = (i - k) · (i + 3j - k) / |i + 3j - k| · (i + 3j - k)/|i + 3j - k|.
7. compac = M
The vector projection of vector c onto vector a is equal to the scalar projection of vector c onto vector a, multiplied by the unit vector of a. Therefore, compac = (i - k) · (i + 3k) / |i + 3k| · (i + 3k)/|i + 3k|.
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Please answer my question quickly.
Answers
Answer:
b=sqrt7
Step-by-step explanation:
16=9+b^2
Consider the linear expression.
32a - 1 - 4 1/3a + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Answers
Answer:
a. The phrases 3.2a, -413a, and -a, as well as -1 and 7, are similar.
b. The simplified linear expression is: -2.1a + 6.
a. 3.2a - 1 - 413a + 7 - an is a linear expression, and the following are like terms that also appear in the expression:
Due to the shared variable, 3.2a, -413a, and -a are similar phrases.
Given that they are constants, -1 and 7 are similar expressions.
b. Merge the terms that are similar to make the linear expression 3.2a - 1 - 413a + 7 - a simpler:
3.2a - 4⅓a - a - 1 + 7
3.2a - 4.3a - a - 1 + 7
-2.1a + 6
Step-by-step explanation:
I'm also in k12 hope this helps!
What is the solution given the expression 7x^-2 when X = 3 and y = 9
Answers
The expression with a variables is 7x²y when x is 3 and y is 9 is 567.
Given that,
The expression with a variables is 7x²y.
We have to find the value when x is 3 and y is 9.
Any thing that has multiple possible values is considered a variable. What does that mean, then? A variable is anything that could possibly change. Age, for example, might be considered a variable because it might signify different things to different people or to the same person at different periods. A person's nationality can function similarly by having a value assigned to it.
By substituting in the expression we get,
7(3)²(9)
7×9×9
567
Therefore, the expression of variables 7x²y when x is 3 and y is 9 is 567.
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The measure of each angle of an isosceles triangle is
Select one:
a. 15
b. none of these
c.5
d. 30
e. 90
Answers
i’m not 100% sure but that’s what i think
the covariance and the correlation coefficient between two variables should always have the same sign.True/False
Answers
The covariance and the correlation coefficient between two variables should always have the same sign is False.
The covariance and the correlation coefficient between two variables can have different signs. The covariance is a measure of the direction and strength of the linear relationship between two variables. It can be positive, indicating a positive relationship where both variables move in the same direction, or negative, indicating an inverse relationship where the variables move in opposite directions.
On the other hand, the correlation coefficient is a standardized measure of the linear relationship between two variables, ranging from -1 to 1. It can also be positive or negative, depending on the direction of the relationship, but its magnitude is always between 0 and 1, indicating the strength of the relationship.
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shawna saved $75 from each paycheck for until she had saved $1,500. Shawna is paid twice a month. How many months did it take Shawna to save the $1,500? Write and solve an equation for this situation
Answers
Answer:
10
Step-by-step explanation:
The equation to find how much money she did get(m = months) would be m x 75 x 2 = 1500. Well, we don't know the m variable. Let's work backwards to find it. First we must divide 1500 by 2. This is 750. Know we must divide 750 by 75. This is 10. There you go! Your answer is 10.
Candice leaves on a trip driving at 25 miles per hour.four hours later,her sister liz starts from the same location driving at 50 miles per hour.how long after liz leaves home will she catch up to candie
Answers
Answer:
Step-by-step explanation:
Candice = 25mph for 4 hours.
Candice has driven= 25 * 4= 100miles.
Liz =50mph
Liz time to catch up to candice= 50 * 2= 100miles.
Therefore, It would have taken Liz two hours to catch up with Candice
Find the sum 3/5+1/9
Answers
hope it helps you tell me in the comment box
(•‿•)
What is the answer I can't figure it out.
Answers
90 takeaway 70 equals 20
Alexander is in the business of manufacturing phones. He must pay a daily fixed cost
to rent the building and equipment, and also pays a cost per phone produced for
materials and labor. Let C represent the total cost, in dollars, of producing p phones
in a given day. A graph of C is shown below. Write an equation for C then state the y
-intercept of the graph and determine its interpretation in the context of the problem.
Answers
The linear function that gives the cost of producing p phones in a given day is of:
C(p) = 50p + 200.
The y-intercept of 200 means that the operating costs of the company are of $200 a day.
What is a linear function?The slope-intercept representation of a linear function is presented by the equation below:
y = mx + b
The coefficients of the a linear function are listed as follows:
m is the slope of the function, representing the rate of change of the linear relationship between x and y.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the function crosses the y-axis.In this problem, the function crosses the y-axis at y = 200, hence the y-intercept is:
b = 200.
Representing the costs that the company assumes even if there are no phones manufactured, hence they are called operating costs.
For each phone manufactured, the function increases by 50, hence the slope is given as follows:
m = 50.
Thus the equation is:
C(p) = 50p + 200.
Missing InformationThe graph is given by the image at the end of the answer.
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9 3/5 as a improper fraction
Answers
Answer:
48/5
Step-by-step explanation:
hope it helps!
......
2.000 pounds of sand is used to
fill sandboxes. 500 pounds can
fill the big sandbox, and the rest
can fill 5 equal-sized smaller
sandboxes. How much sand can
be put in each of the smaller
sandboxes?
K
Answers
Answer:
300 pounds
Step-by-step explanation:
2,000 - 500 = 1,500
1,500 / 5 = 300
300 pounds of sand can be put into each of the 5 smaller sandboxes
Hotel P offer two type of room for it cutomer: a Deluxe room and a Suite room. The price per night for the uite room for check-in on Sunday until Thurday i 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday i 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thurday. If the hotel management want to maintain the price difference between the two type of pace, and the price per night for a Suite room for check-in on Sunday until Thurday i $223, what hould be the price per night for a Suite room for check-in on Friday and Saturday?
Answers
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.
1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:
$223 / 1.70 = $131.18
2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:
$131.18 x 1.25 = $163.98
3. Calculate the price of a Suite room for check-in on Friday and Saturday:
$163.98 x 1.70 = $278.50
The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.
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