a) The system of inequalities that can be used to represent the situation is x + y ≤ 15 and 4x + 8y ≥ 80
b) One combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours is 10 hours babysitting and 5 hours as a library assistant.
To start, we know that Edith can work no more than 15 hours per week. Therefore, we can write the following inequality:
x + y ≤ 15
Next, we know that Edith earns $4 per hour babysitting and $8 per hour as a library assistant. We want her to earn at least $80 per week, so we can write the following inequality:
4x + 8y ≥ 80
This inequality states that the total amount Edith earns from both jobs (4x + 8y) must be greater than or equal to $80.
Now that we have two inequalities, we have a system of inequalities that can be used to represent the situation:
x + y ≤ 15
4x + 8y ≥ 80
To determine one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours, we can solve this system of inequalities.
Let's solve the first inequality for y:
y ≤ 15 - x
Now we can substitute this expression for y into the second inequality:
4x + 8(15 - x) ≥ 80
Simplifying and solving for x, we get:
-4x + 120 ≥ 80
-4x ≥ -40
x ≤ 10
To find the number of hours she should work as a library assistant, we can substitute x = 10 into our expression for y:
y ≤ 15 - x
y ≤ 15 - 10
y ≤ 5
So Edith should work no more than 5 hours as a library assistant per week.
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prove that if a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then: (a) the volume of the cylinder is 3 2 the volume of the sphere. (b) the surface area of the cylinder, including its bases, is 3 2 the surface area of the sphere.
To prove these statements, we will use the formulas for the volume and surface area of a sphere and a cylinder.
The volume of a sphere is given by the formula V = 4/3 πr³, where r is the radius of the sphere.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
(a) If a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then the height of the cylinder is 2r and the radius of the base is r. Therefore, the volume of the cylinder is
V = πr²(2r) = 2πr³.
Now, we can compare the volume of the cylinder to the volume of the sphere:
V_cylinder/V_sphere = (2πr³)/(4/3 πr³) = (2/4)(3/1) = 3/2.
Therefore, the volume of the cylinder is 3/2 the volume of the sphere.
(b) The surface area of a sphere is given by the formula A = 4πr².
The surface area of a cylinder, including its bases, is given by the formula
A = 2πrh + 2πr², where r is the radius of the base and h is the height of the cylinder.
If a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then the height of the cylinder is 2r and the radius of the base is r. Therefore, the surface area of the cylinder is
A = 2πr(2r) + 2πr² = 4πr² + 2πr² = 6πr².
Now, we can compare the surface area of the cylinder to the surface area of the sphere:
A_cylinder/A_sphere = (6πr²)/(4πr²) = (6/4) = 3/2.
Therefore, the surface area of the cylinder, including its bases, is 3/2 the surface area of the sphere.
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2.22 consider flipping coins until either two heads hh or heads then tails ht/th first occurs. by conditioning on the first coin toss, find the probability that ht/th occurs before hh.
The probability that ht/th occurs before hh, given that the first coin toss is H or T, is 1/4.
To find the probability that ht/th occurs before hh, by conditioning on the first coin toss is as follows: The sample space can be represented as T or H. 1) If the first toss is a T, then the following toss should be an H to obtain the sequence ht, which is what we want. The probability of this event is 1/2. If the second toss is T, we get the sequence tt, and the process repeats.
2) If the first toss is an H, then we need to obtain the sequence th. The probability of this event is 1/2. If we obtain the sequence hh, the process repeats. We now have two cases that must be considered: case 1: If the first toss is a tail, then the probability that ht occurs before hh can be calculated as follows:
P(ht occurs before hh|first toss is a T) = P(ht occurs before hh|TT)P(TT)+ P(ht occurs before hh|HT)P(HT)= 0 * 1/4 + (1/2) * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is a T, is 1/4. case 2: If the first toss is an H, then the probability that ht occurs before hh can be calculated as follows:
P(ht occurs before hh|first toss is an H) = P(ht occurs before hh|TH)P(TH)+ P(ht occurs before hh|HH)P(HH)= (1/2) * 1/2 + 0 * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is an H, is 1/4. Therefore, the probability that ht occurs before hh, given that the first coin toss is H or T, is 1/4.
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Question 18
5 pts
An airplane flying into a headwind travels 1176.00 miles in 4 hours and 54 minutes. On the return flight, the
distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both
remain constant.
plane speed = 282 mph; wind speed = 274 mph
plane speed = 267.00 mph; wind speed = 27.00 mph
plane speed = 282 mph; wind speed = 27.00 mph
plane speed = 244 mph; wind speed = 256 mph
plane speed = 244 mph; wind speed = 27.00 mph
Using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The distance travelled = 1176.00 miles
Time taken = 4 hours and 54 minutes = 4*60 + 54 = 294 minutes
The times taken for return flight = 4 hours = 240 minutes
Let,
x = speed of the plane
y = speed of the wind
In a headwind the speed reduces.
So the relative speed of the plane is (x-y)
distance = speed * time
1176 = (x-y) * 294
x-y = 4
Now for the return flight, the wind is tailwind and the speed increases.
So the relative speed of the plane is (x+y).
1176 = (x+y) * 240
x + y = 4.9
Now we have a system of equations.
x - y = 4
x + y = 4.9
Adding,
2x = 8.9
x = 4.45 miles/min = 4.45 * 60 miles/hour = 267 miles/hour
and
y = 4.9 - x = 4.9 - 4.45 = 0.45 miles/min = 0.45*60 = 27 miles/hour
Therefore using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
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Solve the equation:
27 - h = 14
H = [?]
Answer:
h=13
Step-by-step explanation:
have a good day
Answer:
13
Step-by-step explanation:
27-h=14
-h=14-27
-h=-13
To get rid of the negative sign, divide both sides by -1
Therefore h=13
pls answer thiss
give ismple working out
The third term of the arithmetic sequence presented is given as follows:
14.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the previous term.
From the sequence in this problem, the terms are given as follows:
First term of 22.Second term of 18.Third term of 14.Fourth term of 10, and so on...More can be learned about arithmetic sequences at https://brainly.com/question/6561461
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You deposit $200 in a bank account. Each year, the amount in your bank account increases 5% due to interest. What is the total in your bank account after 1 year?
Answer:
After one year, the amount in the bank account will be:
$200 + ($200 x 0.05) = $200 + $10 = $210.
Therefore, the total in the bank account after 1 year is $210.
The surface area of this rectangular prism is 76 square centimeters. What is the volume?
A cake that is 12 inches long, 9 inches wide, and 2 inches high is cut into 18 equal pieces.
What is the volume of each piece?
Answer:
The volume of the cake is:
12 inches x 9 inches x 2 inches = 216 cubic inches
Dividing the volume of the cake by the number of pieces, we get:
216 cubic inches / 18 = 12 cubic inches per piece
Therefore, the volume of each piece is 12 cubic inches.
Answer:
12 inches cubed
Step-by-step explanation:
First we have to find the total volume so we can split it up. We can do this by using the formula LWD = V, where l = length, w = width, and d = depth.
Here, the length is 12, the height is 2, and the depth is 9. We apply the formula:
(12)(2)(9) = 216
Now, we have to split it into 18 separate pieces. We can do this by dividing the total volume (216 inches cubed) by 18.
216/18 = 12
Therefore, each equal piece will be 12 inches cubed
in the science fiction section of the bookstore there are 19 bookcases each bookcase has 72 books in it how many science fiction books are there in the bookstore
Answer: 1,368 books
Explanation: To find the total number of science fiction books in the bookstore, you need to multiply the number of bookcases by the number of books in each bookcase. In this case, there are 19 bookcases, each containing 72 books:
19 bookcases × 72 books per bookcase = 1,368 books
So, there are 1,368 science fiction books in the bookstore.
Unit 4 Assessment- Geometry
The correct option is A. m∠X = 45° as the triangles ABC and XYZ are congruent.
What are congruent trianglesCongruent triangles are two triangles that have the same shape and size. In other words, if two triangles are congruent, then all their corresponding sides and angles are equal. Some methods that allow us to compare the lengths of corresponding sides and the measures of corresponding angles in the two triangles and determine whether they are equal includes: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or HL (hypotenuse-leg).
The angle m∠A corresponds to the angle m∠X given that the triangles ABC and XYZ are congruent.
In conclusion, the correct option for the congruent triangles is A. m∠X = 45°.
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HELP URGENT
A 0.2 kg cue ball moving at 10 m/s hits a 0.15 kg 8 ball at rest. The cue ball continues rolling forward at 1 m/s. What is the velocity of the 8 ball?
Answer:
We can use the principle of conservation of momentum to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system.
Initially, only the cue ball is moving, and the 8 ball is at rest. Therefore, the initial momentum of the system is:
p_initial = m1 * v1 + m2 * v2
= 0.2 kg * 10 m/s + 0.15 kg * 0 m/s
= 2 kg m/s
After the collision, the cue ball is rolling forward at 1 m/s, and the 8 ball is moving in some direction with some velocity v_final. Therefore, the final momentum of the system is:
p_final = m1 * v1 + m2 * v_final
According to the conservation of momentum principle, p_initial = p_final. Therefore,
2 kg m/s = 0.2 kg * 1 m/s + 0.15 kg * v_final
Solving for v_final, we get:
v_final = (2 kg m/s - 0.02 kg m/s) / 0.15 kg
= 13.33 m/s
Therefore, the velocity of the 8 ball after the collision is 13.33 m/s.
PLEASE SHOW WORK!!!!!!!!!
The angle between the cable and the ground is given by the trigonometric function tan⁻¹(7/4). Option E is the correct answer.
What is angle?When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol "" stands for the angle. The Latin word "Angulus" is where the term "angle" originated. The construction of an angle is a type of geometric shape made by connecting two rays at their termini.
The angle between the cable and the ground is given by the trigonometric function tangent.
Tan gives the relationship between opposite side and adjacent side.
Thus,
Tan A = 7/4
A = tan⁻¹(7/4)
Hence, the angle between the cable and the ground is given by the trigonometric function tan⁻¹(7/4). Option E is the correct answer.
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A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month?
$457.50
$460.00
$462.50
$572.50
Answer: C $462.50
Step-by-step explanation:
It's $462.50 because since $6 has a higher profit you would want to try and sell more of that product (The football). So $6 times 45 is 270. And the max number of balls the store can have is 80, 80 minus 45 is 35 so there can only 35 baseballs left. 35 times $5.50 is 192.50. Lastly, you add the two products, and you get 462.50.
The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's say the store sells x footballs and y baseballs.
The total number of balls sold can be expressed as x + y ≤ 80.
Also, we know that 35 ≤ x ≤ 45 and 40 ≤ y ≤ 55.
To maximize the profit, the store should sell the maximum number of footballs and baseballs that it can stock.
From the constraints, we see that the maximum number of footballs the store can sell is 45 and the maximum number of baseballs it can sell is 55, which together make a total of 100 balls.
However, this exceeds the 80-ball limit, so we need to adjust the numbers.
Let's say the store sells 45 footballs and y baseballs.
Then, y ≤ 35 since 45 + 35 = 80, which is the maximum number of balls the store can stock.
Similarly, let's say the store sells x footballs and 55 baseballs.
Then, x ≤ 25 since 25 + 55 = 80.
To find the maximum profit, we need to calculate the profit from selling 45 footballs and 35 baseballs, which will give the highest profit among the feasible combinations.
The profit from selling 45 footballs is 45 × $6 = $270.
The profit from selling 35 baseballs is 35 × $5.50 = $192.50.
The total profit is $270 + $192.50 = $462.50.
Therefore,
The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.
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Simplify. Express your answer using positive exponents. m9m4
Answer:
[tex] {m}^{9} {m}^{4} = {m}^{9 + 4} = {m}^{13} [/tex]
How do you find the surface area of this cone
Answer: 9.42477796077 square yards
Step-by-step explanation:
Cone Surface Area Calculation
surface area of cone slant height is 2 radius is 1
To find the surface area of a cone, we need to know the radius and slant height of the cone.
In this case, we are given that the radius (r) is 1, and the slant height (l) is 2. We can use the Pythagorean theorem to find the height (h) of the cone:
l^2 = r^2 + h^2
2^2 = 1^2 + h^2
4 = 1 + h^2
h^2 = 3
h = sqrt(3)
Now we can use the formula for the surface area of a cone:
A = πr^2 + πrl
Substituting the values we know:
A = π(1)^2 + π(1)(2)
A = π + 2π
A = 3π
So the surface area of the cone is 3π
3 times Pi = 9.42477796077
ChatGPT
.
Four fifths of the articles produced by a certain. firm are for export. Of the rest, 2/3 are guaranteed to one merchant, and 1/9 similarly to another merchant. What fraction of the total articles produced goes on the open market?
I need help with this.
According to the information, the scale that you would use for the pictogram would be 10 for each symbol.
Which scale is the best for the pictogram on the table?To choose the most appropriate pictogram for the information in the table, we must take the data into account. In this case, we must find a divisor number of all the numbers to take it as the value of the scale. In this case we can take 10, because it divides all the numbers as shown below:
80 / 10 = 840 / 10 = 470 / 10 = 760 / 10 = 6According to the above, 8 sports symbols, 4 reading symbols, 7 game symbols and 6 music symbols should be used to represent the values, taking into account that each symbol is equal to 10 units.
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Find the value of b.
Answer:
d
Step-by-step explanation:
Answer:
Step-by-step explanation:
This is a geometric means problem. 6 is the altitude, which belongs to both of those smaller triangles; thus, it is the geometric means. We set up the proportion like this:
[tex]\frac{8}{6} =\frac{6}{b+3}[/tex] and we cross multiply to solve.
8(b + 3) = 36 and
8b + 24 = 36 and
8b = 12 so
b = 3/2 or 1.5
Please ASAP Help
Will mark brainlest due at 12:00
Question
A small movie theater is arranged with 10 seats in the front row, 15 seats in the middle row, and 20 seats in the back row. The customers randomly pick seats as they enter the theater.
What is the probability that the first customer who enters the theater will sit a seat in the back row?
i need this in a fraction please.
The probability that the first customer will sit in a seat in the back row is 4/9.
What is customer ?A customer is a person or business that buys goods or services from another business.
There are a total of 45 seats in the theater. Out of those, 20 seats are in the back row.
So the probability that the first customer who enters the theater will sit in a seat in the back row is:
P(back row) = 20/45
Simplifying the fraction gives:
P(back row) = 4/9
Therefore, the probability that the first customer will sit in a seat in the back row is 4/9.
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work out b-a when a-b=5
(that's the question)
Answer:
b - a = -5
Step-by-step explanation:
I am not sure if I am right, but I am thinking -5
a = 0 and b - -5
a -b = 5
0 - (-5) = 5
5 = 5 If this is true, then
b - a would be
-5 - 0 = -5
-5 = -5
Helping in the name of Jesus.
Answer:
-5
Step-by-step explanation:
We know that a - b = 5,
so to find b - a, we can rearrange this equation as follows:
a - b = 5
a = b + 5
b = a - 5
Therefore, b - a = (a - 5) - a
= -5
So, b - a = -5.
Please ASAP Help
Will mark brainlest due at 12:00
Answer: -2
Step-by-step explanation:
Answer:
plot the point at -2
Step-by-step explanation:
i will mark branliest
Answer:
subtotal: $23.45
tip: $4.22
total: $27.67
Step-by-step explanation:
7.99+1.00+8.99+2.49+1.99+0.99=$23.45
23.45x0.18=$4.22
23.45+4.22=$27.67
Calculate the correlation coefficient of the following data:
X
1
4
8
6
2
y
9
16
22
24
12
Answer:
0.177
Step-by-step explanation:
A perfect correlation is 1. So .998 or even .863 is a good correlation.
since our decimal isn't close to that at all, we have a weak positive correlation.
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
f(x) = (x − 5)2 − 2
f(x) = (x − 4)2 − 1
f(x) = (x + 4)2 − 1
f(x) = (x + 5)2 − 2
The equation of the quadratic function is f(x) = (x + 5)² - 2
Define quadratic function?A quadratic function is a second-degree polynomial function of one variable, which can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable.
From the question, we have the table of values which represents a quadratic function f(x).
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where, Vertex = (h, k)
If we plot the graph according to the given table, the vertex will be,
(h, k) = (-5, -2)
Substitute, (h, k) = (-5, -2) in f(x) = a(x - h)² + k
So, we have, f(x) = a(x + 5)² - 2
Also, from the graph, we have the point (0, 23)
This means that
a(0 + 5)² - 2 = 23
25a = 25
a = 1
Substitute a = 1 in f(x) = a(x + 5)² - 2
f(x) = (x + 5)² - 2
Hence, the equation is f(x) = (x + 5)² - 2
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There are N people, numbered from 0 to N-1, playing a game. The K-th person is assigned the letter S[K]. At the beginning the 0th person sends a message, consisting of a single letter S[0], to the A[0]-th person. When the K-th person receives the message, they append their letter S[K] to the message and forward it to A[K]. The game ends when the 0th person receives the message. Find the final message
The final message would be "ABCE"
It prompts the user to enter the number of people (N), the letters assigned to each person (S), and the forwarding indices (A).
It initializes a message array with the first letter (S[0]).
It follows the forwarding chain until it reaches the 0th person. For each person K in the chain, it appends the corresponding letter (S[A[K]]) to the message.
It terminates the message with a null character (\0) and prints the final message.
The C program will be:
#include <stdio.h>
#include <stdlib.h>
#define MAX_N 100
int main() {
char S[MAX_N];
int A[MAX_N];
int N, K;
printf("Enter the number of people (N): ");
scanf("%d", &N);
printf("Enter the letter assigned to each person:\n");
for (K = 0; K < N; K++) {
printf("S[%d]: ", K);
scanf(" %c", &S[K]);
}
printf("Enter the forwarding indices:\n");
for (K = 0; K < N; K++) {
printf("A[%d]: ", K);
scanf("%d", &A[K]);
}
char message[MAX_N];
message[0] = S[0];
K = 0;
while (A[K] != 0) {
message[K+1] = S[A[K]];
K = A[K];
}
message[K+1] = '\0';
printf("Final message: %s\n", message);
return 0;
}
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A drawing has a collection of 5-pointed stars and 9-pointed stars. There
are a total of 10 stars in the drawing with a total of 66 points. Which
matrix can be used to represent this system of linear equations to
determine the number of 5-pointed and 9-pointed stars used in the
drawing?
203 QUESTONS
15 91101
9 5166
1111101
s 9166
Web and Windows
In the illustration, there are 2 9-point stars and 8 5-point stars.
Let x be the number of 5-pointed stars and y be the number of 9-pointed stars. Each 5-pointed star has 5 points and each 9-pointed star has 9 points, so the total number of points in the drawing is:
5x + 9y = 66
There are two variables in the equation, so we need another equation to solve for x and y. The problem states that there are a total of 10 stars in the drawing, so:
x + y = 10
We can represent this system of linear equations using a matrix:
[5 9] [x] [66]
[1 1] [y] = [10]
This is a matrix equation of the form Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix. We can solve for x and y by finding the inverse of the coefficient matrix A:
A^-1 = 1/(5-9) [-9 5]
[ 1 -1]
Multiplying both sides by A^-1, we get:
x = A^-1 b
x = 1/(5-9) [-9 5] [66]
[1 -1] [10]
x = [-3 8]
Therefore, there are 8 5-pointed stars and 2 9-pointed stars in the drawing.
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The number of guests in a hotel per day resembles a normal distribution with a mean of 220 and standard deviation of 30. One day, the z-score of the number of guests was 2.3. How many guests did the hotel have on that day?
The hotel had 289 guests on the day in question. The z-score is a measure of how many standard deviations a data point is away from the mean of the distribution.
In this case, we are given that the number of guests in a hotel per day follows a normal distribution with a mean of 220 and a standard deviation of 30, and that the z-score of the number of guests on a particular day was 2.3.
Using the formula for z-score, we have:
z = (x - mu) / sigma
where x is the number of guests on the given day, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.
Substituting the given values, we have:
2.3 = (x - 220) / 30
Multiplying both sides by 30, we get:
69 = x - 220
Adding 220 to both sides, we get:
x = 289
Therefore, the hotel had 289 guests on the day in question.
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give answers to these questions, and thereby flesh out a coordinate descent method. for (i), your solution should do something at least a bit more adaptive than merely picking a coordinate at random.
To flesh out a coordinate descent method : (i) One common approach is to choose coordinate with the largest gradient. (ii) One common approach is to use a line search, where we try out step sizes along the chosen coordinate and select the one that leads to the largest decrease in the function value. (iii) One common stopping criterion is to stop when the change in function value.
This can be done by computing the partial derivatives of the function with respect to each coordinate, and selecting the one with the largest absolute value. This approach is known as "greedy" coordinate descent, and it can help speed up convergence by focusing on the most important directions.
This approach can be more computationally efficient, since it doesn't require computing the gradient at each step. Another approach is to use a fixed step size, which can be simpler to implement but may not always lead to the best results.
By choosing the coordinate to optimize along, determining the step size, and setting a stopping criterion, we can develop a coordinate descent method that is well-suited to our particular optimization problem.
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PLEASE HELP!!!!
All I need to know is the area.
Answer:
A = 45 units²
Step-by-step explanation:
the lined figure is composed of a rectangle and a triangle
area of rectangle WFSC is calculated as
area = length × width
= FW × WC
= 2 × 9
= 18 units²
the area of Δ is calculated as
area = [tex]\frac{1}{2}[/tex] base × perpendicular height
= [tex]\frac{1}{2}[/tex] × FS × perpendicular length from N to base FS
= [tex]\frac{1}{2}[/tex] × 9 × 6
= 4.5 × 6
= 27 units²
total area (A) is then the sum of the 2 figures , that is
A = 18 + 27 = 45 units²