Use the parametric equations shown below to answer the following. x = (t^2)(sqrt3) y = 3t - (t^3)/3 (a) Use a graphing utility to graph the curve on the interval −3 ≤ t ≤ 3. a) Find dy/dx and d2y/dx2. b) Find the surface area generated by revolving the curve about the x-axis.
Answers
The value of parametric equations is dy/dx = (3 - t^2)/(2t√3) and d2y/dx2 = -√3(1 + t^2)/(4t^2).
To graph the curve defined by the parametric equations x = t^2√3 and y = 3t - t^3/3 on the interval -3 ≤ t ≤ 3, we can use a graphing utility such as Desmos or GeoGebra. Let's plot the curve first:
(a) To find dy/dx, we need to differentiate y with respect to t and divide it by dx/dt:
Given: x = t^2√3 and y = 3t - t^3/3
Differentiating both x and y with respect to t:
dx/dt = d/dt (t^2√3) = 2t√3
dy/dt = d/dt (3t - t^3/3) = 3 - t^2
Now, we can find dy/dx:
dy/dx = (dy/dt)/(dx/dt) = (3 - t^2)/(2t√3)
To find d2y/dx2, we need to differentiate dy/dx with respect to t and divide it by dx/dt:
Differentiating (3 - t^2)/(2t√3) with respect to t:
d(dy/dx)/dt = d/dt((3 - t^2)/(2t√3))
= (2t√3(-2t) - (3 - t^2)(√3))/(2t√3)^2
= (-4t^2√3 - 3√3 + t^2√3)/(12t^2)
Simplifying the expression:
d(dy/dx)/dt = (-3√3 - 3t^2√3)/(12t^2)
= -√3(1 + t^2)/(4t^2)
Therefore, dy/dx = (3 - t^2)/(2t√3) and d2y/dx2 = -√3(1 + t^2)/(4t^2).
(b) To find the surface area generated by revolving the curve about the x-axis, we can use the formula for the surface area of revolution:
A = 2π∫[a,b] y√(1 + (dy/dx)^2) dt
In this case, the curve is defined by x = t^2√3 and y = 3t - t^3/3. So, we need to find the integral of y√(1 + (dy/dx)^2) with respect to t from a = -3 to b = 3.
A = 2π∫[-3,3] (3t - t^3/3)√(1 + ((3 - t^2)/(2t√3))^2) dt
To evaluate this integral, numerical methods or graphing utilities can be used.
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Related Questions
We would like to estimate the proportion of uf students who owns a scooter to within 1% of the truth, with 95% confidence. We believe around 20% of students do. How many students should be sampled?.
Answers
We can estimate that (A) 3458 students should be sampled using proportions.
What are proportions?A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.So, we have the following confidence interval of proportions for a sample of n people who were surveyed with a probability of success of π and a level of confidence of.
π ± z√[π(1-π)/n]Where the z-score with a p-value of x is designated as 1+a/2.
The margin of error:
M = z√[π(1-π)/n]So, with respect to M = 0.01, the sample size is n.
Now solve:
M = z√[π(1-π)/n]0.01 = 1.96√[0.01(0.09)/n]0.01√n = 1.96√0.01(0.09)√n = [1.96√0.1(0.9)]/0.01(√n)² = ([1.96√0.1(0.9)]/0.01)²n = 3457.4Rounding off: 3458
Therefore, we can estimate that (A) 3458 students should be sampled using proportions.
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The complete question is given below:
We would like to estimate the proportion of UF students who own a scooter to within 1% of the truth, with 95% confidence. We believe around 10% of students do. How many students should be sampled? Group of answer choices
A. 3458
B. 34575
C. 38416
D. 3842
the owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. all measures are recorded in thousands of dollars. the summary output for the regression model is given below. anova df ss ms f significance f regression 11 21.2410567 1.93100515 23.20340372 9.2023e-14 residual 39 3.245610081 0.08322077 total 50 24.48666678 step 1 of 3: what is the coefficient of determination for this model, r2? round your answer to four decimal places.
Answers
The coefficient of determination for the model is 0.8675
How to determine the coefficient of determination for the modelFrom the question, we have the following parameters that can be used in our computation:
anova
df ss ms f significance f
regression 11 21.2410567 1.93100515 23.20340372 9.2023e-14
residual 39 3.245610081 0.08322077
total 50 24.48666678
The coefficient of determination for the model is calculated as
r² = 1 - RSS/TSS
From the table, we have
RSS = 3.245610081
TSS = 24.48666678
Substitute the known values in the above equation, so, we have the following representation
r² = 1 - 3.245610081/24.48666678
Evaluate
r² = 0.8675
Hence, the value of r² is 0.8675
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18+m=8 solve for m!!
Answers
Greetings from Brasil...
We have a 1st degree equation. Let us leave the variables in the 1st member and the numbers in the 2nd member
18 + M = 8 transferring the 18 in the 2nd member
M = 8 - 18
M = - 10The students in Sam’s school voted for their favorite subject. Sam displayed the results in the cirlce graph shown.
Which statements are true about the data in the graph? Check all that apply.
A circle graph titled Favorite Subject. Math is 24 percent, language arts is 20 percent, science is 18 percent, social studies is 16 percent, art is 14 percent, and other is 8 percent.
a. If 100 students were surveyed, 34 would choose math as their favorite subject.
b. If 200 students were surveyed, 28 would choose art as their favorite subject.
c. If 400 students were surveyed, 64 would chose social studies as their favorite subject.
d. If 100 students were surveyed, 38 would choose science as their favorite subject.
e. If 200 students were surveyed, more than half would choose science or social studies as their favorite subject.
Answers
The statements that are true about the data in the graph include the following:
B. If 200 students were surveyed, 28 would choose art as their favorite subject.
C. If 400 students were surveyed, 64 would chose social studies as their favorite subject.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
Assuming 200 students were surveyed at 14%, the number of students who would choose art as their favorite subject can be calculated as follows;
Number of students for arts = 14/100 × 200
Number of students for arts = 0.14 × 200
Number of students for arts = 28 students.
Assuming 400 students were surveyed at 16%, the number of students who would choose social studies as their favorite subject can be calculated as follows;
Number of students for social studies = 16/100 × 400
Number of students for social studies = 0.16 × 400
Number of students for social studies = 64 students.
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sorry ik its early but i gotta finish this LAST one
Answers
Step-by-step explanation:
14/15 , 4/5 , 2/3 , 8/15 ...
Change to common denominator:
14/15 , 12/15 , 10/15, 8/15 ...
The pattern is that the numerator decreases by 2 so the next in sequence is:
6/15 which reduces to 2/5
I will give brainliest if this is answerd in 10 min it is timed here it is:this is worth 100 pts
sort the units of measure into the appropriate system cups
customary system metric system miles
ounces
deciliters
kilometers
centigrams
______________ _____________
Answers
Answer:
customary system:
miles
ounces
metric system:
deciliters
kilometers
centigram
Step-by-step explanation:
Felix uses Supplier 1 about 74% of the time. Packages from Supplier1 are damaged about 9% of the time. Packages from Supplier 2 are damaged 12% of the time. One day a package is found that is damaged. Find the probability that it came from Supplier? Round your answer to 4 decimal places.
Answers
the probability that the package came from Supplier 1 given that it is damaged is approximately 0.6806 (rounded to 4 decimal places).
To solve this problem, we can use Bayes' theorem. Let's denote the events as follows:
A: The package came from Supplier 1.
B: The package came from Supplier 2.
D: The package is damaged.
We are asked to find the probability that the package came from Supplier 1 given that it is damaged, i.e., P(A|D). We can use Bayes' theorem to express this probability:
P(A|D) = (P(D|A) P(A) / P(D)
P(D|A) is the probability that the package is damaged given that it came from Supplier 1, which is 0.09 (9%).
P(A) is the probability that the package came from Supplier 1, which is 0.74 (74%).
P(D) is the probability that the package is damaged, which can be calculated using the law of total probability:
P(D) = P(D|A) P(A) + P(D|B) P(B)
P(D|A) P(A) is the probability that the package is damaged and came from Supplier 1.
P(D|B) is the probability that the package is damaged given that it came from Supplier 2, which is 0.12 (12%).
P(B) is the probability that the package came from Supplier 2, which is 1 - P(A) = 1 - 0.74 = 0.26 (26%).
Now we can calculate P(D):
P(D) = (0.09 0.74) + (0.12 0.26)
= 0.0666 + 0.0312
= 0.0978
Finally, we can substitute the values into Bayes' theorem:
P(A|D) = (0.09 0.74) / 0.0978= 0.0666 / 0.0978
=0.6806
Therefore, the probability that the package came from Supplier 1 given that it is damaged is approximately 0.6806 (rounded to 4 decimal places).
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If you square my age and subtract 28 times my age, the result is 60. What is my age?
Answers
My age is 2 years from the given condition.
Given that, if you square my age and subtract 28 times my age, the result is 60.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let x be my age.
Now, square my age is x²
28 times my age =28x
The square of my age and subtract 28 times my age, the result is 60.
x²-28x=60
⇒ x²-28x-60=0
⇒ x²+30-2x-60=0
⇒ x(x+30)-2(x+30)=0
⇒ (x+30)(x-2)=0
⇒ x=2
Hence, my age is 2 years from the given condition.
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how many triangles have these measures;
C=59 , b=67 , c=58
A- 0
B- 1 acute
C-1 obtuse
D-2
Answers
To determine the type and number of triangles based on the given measures, we can use the triangle inequality theorem and the properties of angles in triangles.
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, we have the measures of angles C, b, and c as 59, 67, and 58 respectively.
To determine the type of triangle, we need to check the relationship between these angles:
If all three angles are less than 90 degrees, the triangle is acute.If one angle is exactly 90 degrees, the triangle is right.If one angle is greater than 90 degrees, the triangle is obtuse.Now, let's analyze the given measures:
Angle C = 59 degrees: This angle is less than 90 degrees.Angle b = 67 degrees: This angle is less than 90 degrees.Angle c = 58 degrees: This angle is less than 90 degrees.Based on the measures of the angles, we can conclude that the triangle is acute.
Therefore, the correct answer is B - 1 acute triangle.
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I NEED HELP ASAP
The graph shows the movement of a car. Which statement describes the translation from point A to point B? Select all that apply.
Answers
The correct answer is D. Translation 2 units right and 4 units up
A) (x, y) -> (x - 3, y - 3): This represents a translation 3 units left and 3 units down.
B) (x, y) -> (x - 2, y - 4): This represents a translation 2 units left and 4 units down.
C) (x, y) -> (x - 3, y + 3): This represents a translation 3 units left and 3 units up.
D) Translation 2 units right and 4 units up: This represents a translation with the given direction and magnitude.
E) Translation 3 units left and 3 units down: This represents a translation with the given direction and magnitude.
To determine which statements describe the translation from point A to point B, you would need to analyze the graph and compare it to the translations provided in the options.
If the graph shows, for example, a movement 3 units left and 3 units down, then the correct statements would be A) and E).
Starting from point A, we can see that we need to move to the right by 2 units and up by 4 units to reach point B.
Therefore, the translation from point A to point B is:
(x, y) -> (x + 2, y + 4)
Option D "Translation 2 units right and 4 units up" correctly describes the translation. Option E "Translation 3 units left and 3 units down" does not correctly describe the translation, as it moves in the opposite direction.
Therefore, the correct answer is D.
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in a systematic sampling study, if the sampling frame has 2,000 names and the desired sample size is 50, then the skip interval should be
Answers
The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.
Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.
To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;
skip interval = population / target sample size
Substituting the given values;
skip interval = 2000 / 50
skip interval = 40
Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.
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where does x go in the fraction?
15/100 = ?/?
Answers
A graphic novel prints 12 issues per year, and a comic book prints 10 issues per year. The total number
of pages in all the issues of the graphic novel for one year is 32 more than the total number of pages in
all the issues of the comic book for one year. Each issue of the graphic novel has 18 fewer pages than
each issue of the comic book. Which system of equations can be used to find g, the number of pages in
each issue of the graphic novel, and c, the number of pages in each issue of the comic book?
Answers
Answer:
answer is che choi
Step-by-step explanation: wow ur in high school mathematics? i have this same question in middle school algrbra HHAHA
What is the image of (−8,6) after a reflection over the line y=−x?
Answers
After a reflection over the line y = -x, the image of (-8,6) is obtained (-6, 8).
What is the definition of reflection transformation?A reflection is known as a flip in geometry. A reflection is the mirror image of a shape. An image will reflect along a line known as the line of reflection.
Position changes during reflection may also result in translation. The reflection transformation can refer to the coordinate system (X and Y-axis).
Given the reflection of (-8,6) over the line y = -x.
When a point is reflected across the line y = -x, it's x and y coordinates change positions and are negated.
As a result, the reflection of (-8, 6) across the line y = -x is (-6, 8).
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The original price of a jacket was $45. It was on sale for $38. What was the percent of the discount?
Answers
Answer:
15.5% (or 16% rounded up)
Explanation:
Subtract the sale price from the original price first. This is the amount that was taken off.
$45-$38 = $7.00
To get the percentage, divide this discount amount by the original price.
$7.00/$45 = .155
Multiply by 100
.155 x 100 = 15.5%
Answer:
$7.00
Step-by-step explanation:
$45-38= $7.00
I hope this helps
In a sale, a microwave cost Php.2,999.99. It’s price has been reduced by Php 500.00 What was its price before the sale.
Answers
3. How many ways are there to elect a President, Vice
President, Secretary, and Treasurer, from a club
with 32 members?l
Answers
Answer:
Step-by-step explanation:
Answer: There are 863,040 possible ways
Step-by-step explanation: There are 32 members altogether in the club. So in order to elect a president from among all of them, if every one of them has a chance if being elected, there would be 32 possible chances for every single club member.
However, as long as one member has been elected as president, that leaves others with a 31 chance per person arrangement.
Therefore, all possible permutations of electing four officers from a club of 32 members can be expressed as
32! (Thirty two factorial) which can be simplified as
32 x 31 x 30 x 29 and that equals 863,040.
863,040 possible ways of electing four officers from a club of 32 members.
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have been working on this for the past 10 minutes . Can you guys help me ?
Answers
1. Proportional
Y is 5 times x
2. Not Proportional
Y is .5 times x
Answer:
x and y are not proportional in either table.
Step-by-step explanation:
x and y are not proportional in the first table. Notice that y = x/5 for x = 30, 25, 45 but not for x = 14. The relationship between x and y must be consistent.
x and y are not proportional in the second table. y = 2(4) = 8
and y = 3(5) = 15. In order for x and y to be proportional y = kx where k is constant. This is not happening in the second table.
give an example of a geometric formula that contains pi. what is the formula used for?
Answers
An example of a geometric formula that contains pi(π) is the formula for the circumference of a circle, which is
C = 2πr. This formula is used to calculate the distance around a circle.
What is a geometric formula?A geometric formula is a mathematical equation that describes a relationship between geometric figures or their properties.
Geometric formulas are used to calculate the area, perimeter, volume, surface area, and other properties of shapes such as circles, triangles, rectangles, spheres, cubes, and cylinders. For example, the formula for the area of a triangle is
A = 1/2 b×h, where b is the base of the triangle and h is its height.
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Rory, Phil, and Rickie are competing in a golf match. Their probabilities of winning the match are as follows:\text{P(Rory wins}) = 20\%P(Rory wins)=20%start text, P, left parenthesis, R, o, r, y, space, w, i, n, s, end text, right parenthesis, equals, 20, percent\text{P(Phil wins}) = 0.05P(Phil wins)=0.05start text, P, left parenthesis, P, h, i, l, space, w, i, n, s, end text, right parenthesis, equals, 0, point, 05\text{P(Rickie wins}) = \dfrac34P(Rickie wins)=43start text, P, left parenthesis, R, i, c, k, i, e, space, w, i, n, s, end text, right parenthesis, equals, start fraction, 3, divided by, 4, end fractionPut the following events in order from least to most likely.
Answers
The least likely event is Phil winning, followed by Rory winning, and the most likely event is Rickie winning. In order from least to most likely, the events can be arranged as follows: Phil wins, Rory wins, and Rickie wins.
Phil has the lowest probability of winning at 0.05 (5%), followed by Rory with a probability of 0.20 (20%), and finally, Rickie with a probability of 0.75 (75%). In this golf match, the probabilities represent the likelihood of each player winning. Phil has the lowest probability of winning at 0.05 (5%). This means that out of every 100 matches played, Phil is expected to win only about 5 times. Rory has a slightly higher probability of winning at 0.20 (20%), indicating that he is more likely to win compared to Phil. Out of every 100 matches, Rory is expected to win around 20 times. Finally, Rickie has the highest probability of winning at 0.75 (75%), making him the most likely to win among the three players. Rickie's higher probability suggests that he has a strong chance of winning the match, with approximately 75 wins out of every 100 matches played.
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Dean Willis earns $315.75 per weck. The Social Security tax rate is 6.2% and Medicare tax is 1.45% of gross pay. How much is the deduction from his pay check for Social Security and Medicare?
Answers
The total deduction from Dean's paycheck for Social Security and Medicare is $24.11.
What is a percentage?
A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or a ratio, and is denoted by the symbol "%".
To find the deduction from Dean's paycheck for Social Security and Medicare, we need to calculate the total amount of tax that he owes based on his gross pay.
First, we can calculate the Social Security tax by multiplying Dean's gross pay by the tax rate:
Social Security tax = $315.75 x 6.2% = $19.54
Next, we can calculate the Medicare tax by multiplying Dean's gross pay by the tax rate:
Medicare tax = $315.75 x 1.45% = $4.57
To find the total deduction from Dean's paycheck, we can add the two amounts:
Total deduction = $19.54 + $4.57 = $24.11
Hence, the total deduction from Dean's paycheck for Social Security and Medicare is $24.11.
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What is the value of (2/5)^3
Answers
The value of the exponent (2/5)^3 is \(\frac{8}{125}\)
In the above question, it is given that
(2/5)^3
The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2^3) signifies 2 x 2 x 2 = 8.
We need to solve it and then find the value of the exponent
(2/5)^3
= \(\frac{2}{5}\) x \(\frac{2}{5}\) x \(\frac{2}{5}\)
= \(\frac{2 . 2. 2}{5 . 5 . 5}\)
= \(\frac{8}{125}\)
Therefore the value of the exponent (2/5)^3 is \(\frac{8}{125}\)
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What is the slope of the line that passes through the points (-11, 5) and (17,-9)? *
A. -2
B. -1/2
C. 7
D. 2.
Answers
Answer:
-1/2
Step-by-step explanation:
y2-y1/ x2-x1
-9-5/ 17-(-11)
-14/ 28
-1/2
If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is what other kind of prime, whose namesake—the first woman to win a prize from the Paris Academy of Sciences, for work on elasticity—used them to investigate Fermat's Last Theorem?
Answers
If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is a Sophie Germain prime.
Sophie Germain was a French mathematician who used these primes to investigate Fermat's Last Theorem, a famous mathematical conjecture that was finally proved in 1994 by Andrew Wiles. A safe prime is a prime number of the form 2p+1, where p is also a prime number, and it is called "safe" because it has some cryptographic properties that make it useful in certain encryption schemes. In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.
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2. Graph each inequality on a number line:
5x + 15 < 0
Answers
Answer:
x < -3
Step-by-step explanation:
1. To put this inequality on a number line, we first must solve it.
Step 1: Subtract 15 from both sides.
\(5x + 15 - 15 < 0 - 15\) \(5x < -15\)Step 2: Divide both sides by 5.
\(\frac{5x}{5} <\frac{-15}{5}\) \(x < -3\)2. Now that we know x < -3, let's graph it!
Since it's less than, we make the number line point to the left, and we make the circle open.
please solve this fast
Write the following equation in standard form. Identify the related conic. x' + y2 - 8x - 6y - 39 = 0
Answers
The standard form of the equation is (x' - 8x) + (y - 3)^2 = 48
To write the equation in standard form and identify the related conic, let's rearrange the given equation:
x' + y^2 - 8x - 6y - 39 = 0
Rearranging the terms, we have:
x' - 8x + y^2 - 6y - 39 = 0
Now, let's complete the square for both the x and y terms:
(x' - 8x) + (y^2 - 6y) = 39
To complete the square for the x terms, we need to add half the coefficient of x (-8) squared, which is (-8/2)^2 = 16, inside the parentheses. Similarly, for the y terms, we need to add half the coefficient of y (-6) squared, which is (-6/2)^2 = 9, inside the parentheses:
(x' - 8x + 16) + (y^2 - 6y + 9) = 39 + 16 + 9
(x' - 8x + 16) + (y^2 - 6y + 9) = 64
Now, let's simplify further:
(x' - 8x + 16) + (y^2 - 6y + 9) = 8^2
(x' - 8x + 16) + (y - 3)^2 = 8^2
(x' - 8x + 16) + (y - 3)^2 = 64
Now, we can rewrite this equation in standard form by rearranging the terms:
(x' - 8x) + (y - 3)^2 = 64 - 16
(x' - 8x) + (y - 3)^2 = 48
The equation is now in standard form. From this form, we can identify the related conic. Since we have a squared term for y and a constant term for x (x' is just another variable name for x), this equation represents a parabola opening horizontally.
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a normalized binary number consists of three parts. these are:
Answers
Main Answer: A normalized binary number typically consists of three parts:
Sign bitExponentMantissaSupporting Question and Answer:
What is a sign bit in a normalized binary number?
The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.
Body of the Solution: A normalized binary number typically consists of the following three parts:
Sign bit: This is the leftmost bit of the number and indicates whether the number is positive or negative. A value of 0 indicates a positive number, while a value of 1 indicates a negative number.Exponent: This is the next set of bits that represent the exponent of the number in binary form. The exponent represents the power to which the base (2) is raised to obatain the actual value of the number. Mantissa: This is the remaining bits that represent the fractional part of the number in binary form. The mantissa contains the significant digits of the number, which are multiplied by the base raised to the exponent power to obtain the actual value of the number.Final Answer: A normalized binary number typically consists of three parts:
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at a middle school, 40% of the seventh-grade students are boys. What is the ratio of seventh-graders girls to seventh-grade students
Answers
The ratio of seventh-graders girls to seventh-grade students is 3 : 5
What is the ratio of seventh-graders girls to seventh-grade studentsFrom the question, we have the following parameters that can be used in our computation:
40% of the seventh-grade students are boys
This means that
60% of the seventh-grade students are girls
So, we have
Girls to Students = 60% : 100%
Simplify
Girls to Students = 3 : 5
Hence, the ratio is 3 : 5
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6.1.11 suppose we have a statistical model {fθ : θ ∈ [0, 1]} and we observe x0. is it true that 8 1 0 l(θ | x0) dθ = 1? explain why or why not.
Answers
No, it is not true that ∫_0^1 l(θ | x0) dθ = 1. The integral of the likelihood function l(θ | x0) over the parameter space [0, 1] does not necessarily equal 1.
The likelihood function l(θ | x0) measures the probability of observing the data x0 given the parameter value θ. It is a function of the parameter θ, and not a probability distribution over θ.
Therefore, the integral of the likelihood function over the parameter space does not have to equal 1, unlike the integral of a probability density function over its support.
In fact, the integral of the likelihood function over the parameter space is often referred to as the marginal likelihood or the evidence, and is used in Bayesian inference to compute the posterior distribution of the parameter θ given the data x0. The marginal likelihood is given by: ∫_0^1 l(θ | x0) p(θ) dθ
where p(θ) is the prior distribution of the parameter θ. The marginal likelihood is used to normalize the posterior distribution so that it integrates to 1:
p(θ | x0) = l(θ | x0) p(θ) / ∫_0^1 l(θ | x0) p(θ) dθ
In conclusion, the integral of the likelihood function over the parameter space does not necessarily equal 1, and is used in Bayesian inference to compute the posterior distribution of the parameter θ given the data x0.
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3х + y = 17
4х – у = 18
Answers
Answer:
x=5 and y=2
Step-by-step explanation:
Let's solve your system by substitution.
3x+y=17;4x−y=18
Step: Solve 3x+y=17 for y:
3x+y=17
3x+y+−3x=17+−3x(Add -3x to both sides)
y=−3x+17
Step: Substitute−3x+17 for y in 4x−y=18:
4x−y=18
4x−(−3x+17)=18
7x−17=18(Simplify both sides of the equation)
7x−17+17=18+17(Add 17 to both sides)
7x=35
7x
7
=
35
7
(Divide both sides by 7)
x=5
Step: Substitute 5 for x in y=−3x+17:
y=−3x+17
y=(−3)(5)+17
y=2(Simplify both sides of the equation)