The probability density function of Y = exp(U) is given by:
f(y) = { 1/y, 2 ≤ y ≤ e³ ; 0, elsewhere }.
Given that: U follows the Uniform distribution U ~ U[2, 3]. We have to find the probability density function of Y = exp(U).
The formula used: The probability density function of a random variable X, is denoted by f(x), is the derivative of the cumulative distribution function (cdf), denoted by F(x). We have F(x) = P(X ≤ x).
The probability density function of the uniform distribution U(a,b), is given by
f(x)=1/(b-a), where a ≤ x ≤ b.
Here, U[2,3]So, a = 2, b = 3
Let's find the probability density function of Y = exp(U).
So, for finding the probability density function of Y = exp(U), first, we need to find the cumulative distribution function F(y) of Y. Let's do that.
So, F(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln y)
We have, Y = exp(U), which is a one-to-one function of U and increasing in U. Hence, we can use the one-to-one transformation formula. Hence, the probability density function of Y, f(y) = f(u) / |dy/du|.f(u) = 1/ (3-2) = 1
Here, dy/du = d/dy [exp(u)] = exp(u) = Y
Therefore, f(y) = 1/Y, for 2 ≤ u ≤ 3.
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Suppose that U follows the Uniform distribution U ~ U[2, 3].
Find the probability density function of Y = exp(U).
Let fU(u) be the pdf of U.Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:
fU(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.
Now we need to find the pdf of Y = exp(U).
Let FY(y) be the cdf of Y.
Then we can write:
FY(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.
Since U is continuous and its pdf is given by fU(u), we have:
[tex]FY(y) = ∫_{2}^{ln(y)} fU(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]
We can differentiate FY(y) to find the pdf of Y:
fy(y) = d/dy FY(y) = (1 / y) fY(ln(y)) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.
Therefore, the probability density function (pdf) of Y = exp(U) is given by:
fy(y) = (1 / y), 2 ≤ y ≤ e3, and 0 elsewhere.
In general, if U is a continuous random variable with pdf fU(u) and Y = g(U) is a monotonic transformation of U, then the pdf of Y can be found using the formula:
[tex]fy(y) = fU(g^{-1}(y)) / |dg^{-1}(y) / dy|,[/tex]
where g^{-1}(y) is the inverse function of g(y) and |dg^{-1}(y) / dy|
is the absolute value of the derivative of g^{-1}(y) with respect to y.
The probability density function (pdf) of the random variable
Y = exp(U)
where U is distributed uniformly over the interval [2, 3] can be found as follows:
Let f_U(u) be the pdf of U.
Since U has a Uniform distribution over the interval [2, 3], its pdf is given by:
f_U(u) = {1 / (3 - 2)} = 1, 2 ≤ u ≤ 3, and 0 elsewhere.
Now we need to find the pdf of Y = exp(U).
Let F_Y(y) be the cdf of Y.
Then we can write:
[tex]F_Y(y) = P(Y ≤ y) = P(exp(U) ≤ y) = P(U ≤ ln(y)), for y > 0.[/tex]
Since U is continuous and its pdf is given by f_U(u), we have:
[tex]F_Y(y) = ∫_{2}^{ln(y)} f_U(u)du = ∫_{2}^{ln(y)} 1du = ln(y) - 2, 2 ≤ ln(y) ≤ 3, and 0 elsewhere.[/tex]
We can differentiate F_Y(y) to find the pdf of Y:
[tex]fy(y) = d/dy F_Y(y) = (1 / y) f_Y(ln(y)) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.[/tex]
Therefore, the probability density function (pdf) of Y = exp(U) is given by:
fy(y) = (1 / y), 2 ≤ y ≤ e^3, and 0 elsewhere.
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Lavonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28. Is her estimate reasonable?
a. Yes, her estimate is reasonable.
b. No, her estimate is too high.
c. No, her estimate is too low.
d. It is impossible to determine without more information.
No, her estimate is too high.
Given,
Lavonne estimated 38% of 63 by rounding 38% up to 40%, rounding 63 up to 70, and then multiplying 70 by 0.4 to get 28 .
Now
Firstly calculate the actual answer:
38% of 63
= 38/100 * 63
= 23.94
Now
The approximated portion :
40% of 70
= 0.4 *70
= 28
Hence the answer should be around 24 but after approximation it is coming 28 .
Thus the estimate made by Lavonne is high .
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Function B has a greater rate of change and a smaller y-intercept than function A. Which equation could represent function B?
Answer:
function A : y = 50 + 0.5x ; y = 40 + 0.6x
Step-by-step explanation:
Function is a relationship between values in set x & set y.
In case functional relationship equation is y = c + sx . c is the y intercept ie constant value of y when x = 0, & s is slope rate of change ie = change in y / change in x.
If function A is y = 50 + 0.5x. Intercept (c) = 50 , change rate (slope) = 0.5
If function B is y = 40 + 0.6x. Intercept (c) = 40 ie lesser, change rate (slope) = 0.6 ie greater
I really need help please!!!!!
Step-by-step explanation:
area of a quadrilateral is b x h
if the base is 7 the height is x and the area is 63 then:
7x=63
divide both sides by 7
7/7x=63/7
x=9
Hope that helps :)
what is this please? i'll give u brainliest
Answer:
i dont know i just want points
Step-by-step explanation:
>;)
convert 53 m = cm
help pls
Suppose x’s represent solutions and y’s represent problems. S(x, y) means "x is a solution for problem y". Explain, in English, what each of these statements is saying. They do not mean the same thing.
1. ∃x∀yS(x, y)
2. ∀y∃xS(x, y)
The first statement focuses on the existence of a single solution that works for all problems, while the second statement emphasizes that for each problem, there is at least one solution available, without specifying whether it is the same solution for all problems.
1) ∃x∀yS(x, y):
This statement means "There exists at least one solution that works for all problems." In other words, there is a specific value of x that can be applied to every problem y, resulting in a solution.
2) ∀y∃xS(x, y):
This statement means "For every problem, there exists at least one solution." In other words, for any given problem y, there is at least one value of x that can be applied to it to find a solution.
The main distinction between these two statements lies in the order of quantifiers (∃ and ∀). In the first statement, the existential quantifier (∃x) appears before the universal quantifier (∀y), indicating that there is a single solution that can be applied to all problems.
In the second statement, the universal quantifier (∀y) appears before the existential quantifier (∃x), indicating that for each problem, there is at least one solution that exists.
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What is the area of the base?
You measure 47 watermelons' weights, and find they have a mean weight of 33 ounces. Assume the population standard deviation is 7.7 ounces. Based on this, construct a 90% confidence interval for the true population mean watermelon weight. Give your answer as m (round to 2 decimal places) + ounces You measure 21 turtles' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 2.9 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Enter your answer as #Im.Give your answers as decimals, to two places + ounces You measure 34 textbooks' weights, and find they have a mean weight of 62 ounces. Assume the population standard deviation is 9.4 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places Out of 200 people sampled, 104 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Enter your answer as p m Give your answers as decimals, to three places. + Out of 300 people sampled, 189 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places
a. The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.
b. The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.
c. The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.
d. The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.
e. The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.
a. For the watermelon weights:
Sample mean (m) = 33 ounces
Population standard deviation (σ) = 7.7 ounces
Sample size (n) = 47
Confidence level = 90%
To construct the confidence interval, we can use the formula:
Confidence Interval = m ± Z * (σ/√n)
Where Z is the z-score corresponding to the desired confidence level. For a 90% confidence level, Z = 1.645 (obtained from the standard normal distribution table).
Confidence Interval = 33 ± 1.645 * (7.7/√47)
Confidence Interval ≈ 33 ± 2.586
Confidence Interval ≈ (30.41, 35.59) ounces
The 90% confidence interval for the true population mean watermelon weight is 30.41 to 35.59 ounces.
b. For the turtle weights:
Sample mean (m) = 56 ounces
Population standard deviation (σ) = 2.9 ounces
Sample size (n) = 21
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 56 ± 2.576 * (2.9/√21)
Confidence Interval ≈ 56 ± 1.438
Confidence Interval ≈ (54.56, 57.44) ounces
The 99% confidence interval for the true population mean turtle weight is 54.56 to 57.44 ounces.
c. For the textbook weights:
Sample mean (m) = 62 ounces
Population standard deviation (σ) = 9.4 ounces
Sample size (n) = 34
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 62 ± 2.576 * (9.4/√34)
Confidence Interval ≈ 62 ± 5.116
Confidence Interval ≈ (56.884, 67.116) ounces
The 99% confidence interval for the true population mean textbook weight is 56.884 to 67.116 ounces.
d. For the proportion of people with kids:
Number of people with kids (p) = 104
Sample size (n) = 200
Confidence level = 99%
To construct the confidence interval for a proportion, we can use the formula:
Confidence Interval = p ± Z * √[(p(1-p))/n]
Using the z-score corresponding to a 99% confidence level (Z = 2.576), we can calculate the confidence interval.
Confidence Interval = 104/200 ± 2.576 * √[(104/200)(1 - 104/200)/200]
Confidence Interval ≈ 0.52 ± 0.056
Confidence Interval ≈ (0.464, 0.576)
The 99% confidence interval for the true population proportion of people with kids is 0.464 to 0.576.
e. For the proportion of people with kids:
Number of people with kids (p) = 189
Sample size (n) = 300
Confidence level = 99%
Using the same formula as above and considering a 99% confidence level, the z-score is Z = 2.576.
Confidence Interval = 189/300 ± 2.576 * √[(189/300)(1 - 189/300)/300]
Confidence Interval ≈ 0.63 ± 0.045
Confidence Interval ≈ (0.585, 0.675)
The 99% confidence interval for the true population proportion of people with kids is 0.585 to 0.675.
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question number 7 and 8 only.
There are 20,502 seats in the stadium. If there are 19,624 people in attendance, what percent of the seats are filled?
Approximately 4.28% of the seats are filled in the stadium when there are 19,624 people in attendance. To determine the percentage of seats filled in the stadium, we need to calculate the ratio of the number of people in attendance to the total number of seats and then convert it to a percentage.
The number of seats filled can be found by subtracting the number of empty seats from the total number of seats. Using the given information:
Number of seats filled = Total number of seats - Number of empty seats
Number of seats filled = 20,502 - 19,624
Number of seats filled = 878
Now, we can calculate the percentage of seats filled by dividing the number of seats filled by the total number of seats and multiplying by 100:
Percentage of seats filled = (Number of seats filled / Total number of seats) * 100
Percentage of seats filled = (878 / 20,502) * 100
Percentage of seats filled ≈ 4.28%
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4. Mark says to do the problem 12 % + 3 %, you just find 12 +3 =4 and % +3/4=1/3 to get 4- How do you respond?
Mark's approach to solving the problem is incorrect.
We have,
To find the sum of percentages, you cannot simply add the numbers together as you would with regular numbers.
Percentages represent proportions or ratios, so they must be converted to their corresponding decimal or fraction forms before adding them.
To solve 12% + 3%, you need to convert each percentage to its decimal form and then add the decimals together.
Here's the correct approach:
12% = 12/100 = 0.12
3% = 3/100 = 0.03
Now, add the decimals:
0.12 + 0.03 = 0.15
Therefore,
The value of 12% + 3% is 0.15 or 15%.
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To find the area, multiply the area of the entire circle by __?
What number goes in the box.
Answer:
3.142 × 6 = 18.852, thats : 19cm, then multiply 19 by 6 , so 19 would go in the square.
because area of a circle is p × r sq. u multiply one of the 6 by 3.142, you get 19, then multiply that 19 by the other 6. the answer is approximately 113.112.
For the following estimated multiple linear regression equation,
Y = 8 + 45X_1 + 16X_2
a. what is the interpretation of the estimated coefficient of X_2
b. if R^2? (Goodness of Fit Coefficient) is 0.98 in this estimated regression equation, what does that tell you?
(a) The estimated coefficient of X₂ captures the average impact of X₂ on the response variable Y, given the specified regression model. (b) a higher R² value indicates a better fit of the model to the data and a higher degree of explained variability.
(a.) The estimated coefficient of X₂ in the multiple linear regression equation (Y = 8 + 45X₁ + 16X₂) represents the expected change in the dependent variable (Y) for a one-unit increase in the independent variable X₂, while holding all other independent variables constant.
In this case, the estimated coefficient of X₂ is 16, so for every one-unit increase in X₂, the expected change in Y is an increase of 16 units, assuming X₁ and other variables remain constant.
(b.) The coefficient of determination (R²) is a measure of the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variables (X₁ and X₂) in the regression model. In this case, if the R² value is 0.98, it means that approximately 98% of the total variation in Y can be explained by the linear relationship between X₁, X₂, and the constant term.
A high R² value of 0.98 indicates a very strong fit of the regression model to the data. It suggests that 98% of the variability in the dependent variable Y is accounted for by the independent variables X₁ and X₂, while the remaining 2% may be attributed to other factors or random variation.
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A population of 60 foxes in a wildfire preserve doubles in size every 12 years. The function y = 60*2^x, where x is the number of 12-year periods, models the population growth. How many foxes will there be after 24 years?
Bob a builder has come to you to build a program for his construction business. He needs to determine the square footage of a room in order to buy materials and calculate costs. Bob charges $425 per square metre. The program is going to ask the user to enter the name of a room. It will then ask for the width and length of the room (in meters) to be built. The program will calculate the room area and use this information to generate an approximate cost. Your program will display the room, the total area and the approximate cost to the screen. Using Pseudocode, develop an algorithm for this problem.
Answer : The below pseudocode will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.
Explanation:
Given:Bob charges $425 per square metre.To develop an algorithm to calculate the area of the room and the approximate cost.
Pseudocode:
Step 1: Start Step 2: Declare variables : room Name of string type,Width of float type,Length of float type,Cost of float type
Step 3: Display "Enter the name of the room:" Step 4: Read the room Name Step 5: Display "Enter the width of the room (in meters):" Step 6: Read the Width Step 7: Display "Enter the length of the room (in meters):" Step 8: Read the Length Step 9: Calculate the area of the room as Area = Width * Length Step 10: Calculate the cost of the room as Cost = Area * 425 Step 11: Display "Room Name:", roomName Step 12: Display "Area of the Room (in square metres):", Area Step 13: Display "Approximate Cost of Construction:", Cost Step 14: Stop
The program will take the input as the name of the room, width, and length of the room, and then it will calculate the area of the room by multiplying width and length. Then it will calculate the cost by multiplying the area with 425. The output will be the room name, area of the room, and approximate cost to construct the room in dollars.
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Please answer this I will give brainliest!!!
Perpendicular means that two lines intersect at a right angle.
D and E have perpendicular sides
(blue rectangle at the bottom left and green trapezoid all the way at the bottom right)
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
-5p+3
Step-by-step explanation:
-p-2-4p+5
-p-4p-2+5
-5p+3
1. Find the coordinates of the center and the measure of the radius for a circle whose equation is
(x - 8) + (y + 4) = 12
Answer:
the center of this circle is (8, -4) and the radius is 2√3.
Step-by-step explanation:
Compare this equation
(x - 8) + (y + 4) = 12 Don't forget to type in the " ^ " symbol to indicate exponentiation.
(x - 8)^2 + (y + 4)^2 = 12
to the standard equation of a circle with center at (h, k) and radius r:
(x - h)^2 + (y - k)^2 = r^2
In this way we learn that h = 8, k = -4 and r^2 = 12 (or r = 2√3).
Then the center of this circle is (8, -4) and the radius is 2√3.
Need help please thank you
Answer:
y = 4x+1
Step-by-step explanation:
The average American gets a haircut every 43 days. Is the average smaller for college students? The data below shows the results of a survey of 13 college students asking them how many days elapse between haircuts. Assume that the distribution of the population is normal. 36, 42, 40, 45, 33, 31, 47, 47, 39, 41, 33, 48, 32 What can be concluded at the the α = 0.05 level of significance level of significance? For this study, we should use Select an answer The null and alternative hypotheses would be: H 0 : ? Select an answer H 1 : ? Select an answer The test statistic ? = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 3 decimal places.) The p-value is ? α Based on this, we should Select an answer the null hypothesis. Thus, the f conclusion is that ... The data suggest the population mean number of days between haircuts for college students is not significantly lower than 43 at α = 0.05, so there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43. The data suggest the population mean is not significantly lower than 43 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is equal to 43. The data suggest the populaton mean is significantly lower than 43 at α = 0.05, so there is sufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43.
The data suggest that the population mean is not significantly different from 43 at α = 0.05.
To determine whether the average number of days between haircuts for college students is smaller than the average for the average American (43 days), we can conduct a one-sample t-test. Here are the steps and results:
Step 1: Formulate the null and alternative hypotheses:
Null hypothesis (H0): The population mean number of days between haircuts for college students is equal to 43.
Alternative hypothesis (H1): The population mean number of days between haircuts for college students is smaller than 43.
Step 2: Calculate the test statistic:
We can calculate the test statistic using the formula:
t = (x- μ) / (s / √n)
where x is the sample mean, μ is the hypothesised population mean (43), s is the sample standard deviation, and n is the sample size.
Using the given data, the sample mean x is calculated to be 39.923, the sample standard deviation s is 6.106, and the sample size n is 13.
Substituting these values into the formula, we get:
t = (39.923 - 43) / (6.106 / √13) = -0.808
Step 3: Calculate the p-value:
The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) if the null hypothesis is true. We can use the t-distribution to calculate the p-value.
Using a t-table or a statistical software, we find that the p-value for t = -0.808 with 12 degrees of freedom is approximately 0.438.
Step 4: Make a decision:
Comparing the p-value (0.438) to the significance level α (0.05), we find that the p-value is greater than α.
Therefore, we fail to reject the null hypothesis.
Based on the results, we conclude that there is insufficient evidence to conclude that the population mean number of days between haircuts for college students is lower than 43. The data suggest that the population mean is not significantly different from 43 at α = 0.05.
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6) Examples (a) j5 points Give an example of an infinite field such that 4-a -o for alle € F. (b) [5 points) Give an example of an infinite, non-commutative ring R such that for all a we have that 2a=0.
(a) An example of an infinite field such that 4-a -o for all e F is F_2.
Here, the only elements of the field are 0 and 1, and we have 1 + 1 = 0,
which is equivalent to 4 - 1 - 1 = 2 - 1 - 1 = 0. Therefore, for all a e F_2, 4 - a - a = 0, so F_2 satisfies the given condition.
(b) An example of an infinite, non-commutative ring R such that for all a we have that 2a = 0 is the ring of 2x2 matrices over the field F_2 (as defined in part (a)). If we identify the matrix \begin{pmatrix}a&b\\c&d\end{pmatrix} with the element ad + bc of F_2, then R becomes a ring.
Note that R is not commutative since the product of two matrices is not necessarily equal to the product of their entries, and that 2a = 0 for all matrices \begin{pmatrix}a&b\\c&d\end{pmatrix} in R since \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&1\\0&0\end{pmatrix} = \begin{pmatrix}0&a\\0&c\end{pmatrix} and \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}0&0\\1&0\end{pmatrix} = \begin{pmatrix}b&0\\d&0\end{pmatrix} have entries that are equal to 0 in F_2. Therefore, R satisfies the given condition.
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The characteristics of the Liberty Company bond is listed below. How much is the annual interest payment? Coupon rate 10.20% Yield to maturity 10.55% Face value $1,000 Market price $850 $101.75 O $102.00 $105.50 O $120.00
The Liberty Company bond has the following characteristics:
Coupon rate: 10.20%
Yield to maturity: 10.55%
Face value: $1,000
Market price: $850, $101.75, $102.00, $105.50, or $120.00
The question asks for the annual interest payment.
To calculate the annual interest payment, we need to multiply the coupon rate by the face value of the bond. The coupon rate represents the annual interest rate as a percentage. In this case, the annual interest payment can be calculated as 10.20% of the face value, which is $1,000.
Therefore, the annual interest payment for the BCompany bond is $1,000 * 10.20% = $102.00.
Note: The market price of the bond is provided, but it does not affect the calculation of the annual interest payment. The market price represents the current market value of the bond and may vary depending on various factors such as supply and demand in the market.
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Which equation represents a circle with a center at -3, -5) and a radius of 6 units?
O (x - 3)2 + (-5)2 = 6
0 (x - 3)2 + (-5)2 = 36
O (x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Mark this and retum
Save and Exit
Next.fm
Submit
Answer:
(x+3)²+(y+5)² = 36
Step-by-step explanation:
The general equation of a circle is expressed as;
(x-a)²+(y-b)² = r² where;
(a, b) is the centre of the circle
r is the radius of the circle
Given
Centre (-3, -5)
a = -3 and b = -5
radius r = 6units
Substitute
(x-a)²+(y-b)² = r²
(x-(-3))²+(y-(-5))² = 6²
(x+3)²+(y+5)² = 36
hence the required equation is (x+3)²+(y+5)² = 36
The equation of a circle that represents a circle with a center at (-3, -5) and a radius of 6 unit is (x + 3)² + (y + 5)² = 36
Equation of a circleThe general equation of a circle is expressed as follows:
(x-a)²+(y-b)² = r²
where
r = radius of the circlea and b are the centre of the circleTherefore,
a = -3
b = -5
r = 6
Hence,
(x - (-3))² + (y - (-5))² = 6²
(x + 3)² + (y + 5)² = 36
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waht is the answer for this? −35−85+5−25
PEMDAS
-140
-35-85=-120
-120+5-25
-120+5=-115
=-115-25
-115-25=-140
-140
Please Answer!! Will give brainly!!
Answer:
480 - 12.25d = 50
What is the equation of the following line please help
Answer:
C
Step-by-step explanation:
what is the absolute value of -l8|
Answer:
-8 i think
Hope you get it right
Answer:
the absolute value of -l8| is 8
Step-by-step explanation:
Absolute value means the opposite
Consider an RC circuit in which the resistance R = 2, the capacitance C = 0.5 F, and the electromotive force E (t) = te-2t V. What is the differential equation governing the variation of c?
The differential equation governing the variation of the charge (c) in the given RC circuit is 2(d^2q/dt^2) + (1/0.5)(dq/dt) = d(E(t))/dt, where q represents the charge, t represents time, and E(t) represents the electromotive force of the circuit. This equation describes the relationship between the charge, current, and voltage in the RC circuit.
To compute the differential equation governing the variation of the charge (c) in the given RC circuit, we can start by using Kirchhoff's voltage law (KVL) and the relationship between charge, capacitance, and voltage.
Kirchhoff's voltage law states that the sum of the voltages in a closed loop in a circuit is equal to zero. In this case, the voltage across the resistor (VR) and the voltage across the capacitor (VC) must sum up to the electromotive force (E) of the circuit.
The voltage across the resistor can be calculated using Ohm's Law: VR = IR, where I is the current flowing through the circuit.
The voltage across the capacitor can be calculated using the formula: VC = (1 / C) ∫Idt, where ∫Idt represents the integral of the current over time.
Combining these equations, we have:
E(t) = VR + VC
E(t) = IR + (1 / C) ∫Idt
Differentiating both sides of the equation with respect to time, we get:
d(E(t)) / dt = d(IR) / dt + d((1 / C) ∫Idt) / dt
Since the resistance R and the capacitance C are constant values, their derivatives with respect to time are zero.
d(E(t)) / dt = R(dI / dt) + (1 / C)(I)
Substituting I with dq / dt, where q represents the charge c, we get:
d(E(t)) / dt = R(d^2q / dt^2) + (1 / C)(dq / dt)
Simplifying the equation, we obtain the differential equation governing the variation of c:
R(d^2q / dt²) + (1 / C)(dq / dt) = d(E(t)) / dt
In summary, the differential equation governing the variation of the charge (c) in the given RC circuit is:
2(d^2q / dt²) + (1 / 0.5)(dq / dt) = d(E(t)) / dt
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the diagram shows a triangle.
2s
40°
2s
What is the value of s?
Answer:
s would be 20
Step-by-step explanation:
because 2 x 10 = 20 so you then would add the second 20 to the first 20 and get 40
Kianna says that Elena’s house is actually a reflection of her house across the y-axis.
Is Kianna right?
Answer: Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).
Step-by-step explanation: