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A set X is said to be closed under multiplication if for every X1, X2 E X we have X1X2 E X. Let A be the union of all bounded subsets X CR that are closed under multiplication. Does inf(A) exist? If it does, find it.

Answers

Answer 1

Answer:

Answer:

inf(A) does not exist.

Step-by-step explanation:

As per the question:

We need to prove that A is closed under multiplication,

If for every $X_(1), X_(2)\in X$

$X_(1)X_(2)\in X$

Proof:

Suppose, x, y $\in A$

Since, both x and y are real numbers thus xy is also a real number.

Now, consider another set B such that:

B = {xy} has only a single element 'xy' and thus [B] is bounded.

Since, [A] represents the union of all the bounded sets, therefore,

$B\subset A$

⇒ xy $\in A$

Therefore, from x, y $\]in A$ , we have xy $\]in A$ .

Hence, set a is closed under multiplication.

Now, to prove whether inf(A) exist or not

Proof:

Let us assume that inf(A) exist and inf(A) = $\beta$

Thus $\beta$ is also a real number.

Let C be another set such that

C = { $\beta$ - 1}

Now, we know that C is a bounded set thus { $\beta$ - 1} is also an element of A

Also, we know:

inf(A) = $\beta$

Therefore,

$n(A)\geq \beta$

But

$\beta - 1$ is an element of A and $\beta - 1 \leq \beta$

This is contradictory, thus inf(A) does not exist.

Hence, proved.

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The world’s fastest flying insect is the dragonfly. It can fly 36 miles per hour. If a dragonfly flew in a straight path at this rate, what distance would it fly in 15 minutes? (1 hour = 60 minutes) *

Answers

The total number of distance the word fastest insect in 15 minutes would fly is 9 miles

How to determine the number distance it would fly

from the question, we have the following parameters that can be used in our computation:

Speed = 36 miles per hour

Time = 15 minutes = 1/4 hour

The distance it would fly is calculated as

Distance = Speed * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = 36 miles per hour * 1/4 hour

Evaluate

Distance = 9 miles

Hence, the number of distance it would fly is 9 miles

Answers

Step-by-step explanation:

If x is the kilograms of 30% chocolate, and y is the kilograms of 50% chocolate, then:

x + y = 200

0.30x + 0.50y = 0.46(200)

Solving the system of equations with substitution:

0.30x + 0.50(200 − x) = 0.46(200)

0.30x + 100 − 0.50x = 92

8 = 0.20x

x = 40

y = 200 − x

y = 160

The distributor needs 40 kg of 30% chocolate and 160 kg of 50% chocolate.

Final answer:

To obtain 200 kilograms of a 46% fat-content chocolate, the candy distributor needs to mix 40 kilograms of a 30% fat-content chocolate and 160 kilograms of a 50% fat-content chocolate.

Explanation:

This problem can be solved using a basic mixture problem method. Let's name the amount of the 30% fat-content chocolate as 'x' and the amount of the 50% fat-content chocolate as 'y'. The total weight of the resulting chocolate is provided in the problem, 200 kilograms, therefore we know that x + y = 200.

The total fat in the chocolates should be 46% of 200kg, or 92kg. This gives us another equation based on the fat content, 0.3x + 0.5y = 92.

Solving these two equations linearly, we find the values of x and y. The amount of 30% fat content chocolate (x) is 40 kilograms and the amount of 50% fat-content chocolate (y) is 160 kilograms.

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Caroline needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 2.75 hours and charged her $114 for parts. The total was $320.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.

Answers

2.75(x)+114=320.25
-114 -114
2.75(x)=206.25
/2.75. /2.75
X=75

It costs 75$ per hour

This is because we don’t know how much they charge per hour but we know the number of hours spend working on the computer, so you have to do 2.75(x) where x represents the cost per hour And we also know that the cost of the part is $114 so we have to add that to
(2.75(x)+114) the equation then finally you have to make the expression equal to 320.25 since we know the final cost so

2.75(x)+114=320.25

Final answer:

The equation to solve this problem is 114 + 2.75x = 320.25. Solving this equation, we find that the cost of labor per hour, represented by x, is $75.

Explanation:

The problem you're trying to solve involves the labor cost per hour of the technician who worked on Caroline's computer. From the problem, we know that the total cost of the repair was $320.25. This includes the cost of parts, which was $114, and the labor the technician invested, which we know took 2.75 hours but we aren't sure of the per hour cost. Let's denote this unknown cost as x. Therefore, our equation would be 114 + 2.75x = 320.25.

We can solve for x, the cost of labor per hour, by isolating this variable on one side of the equation. Firstly, subtract 114 from both sides: 2.75x = 320.25 - 114 which results in 2.75x = 206.25. Then, divide both sides by 2.75 to find x: x = 206.25/2.75 which equals $75. Therefore, the cost of labor per hour is $75.

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3 (2d-1) 2d= 4(d-2) + 5

Answers

Answer:

The answer will be 0=0. This means that the equation will always be true.

Final answer:

The question is a quadratic equation that can be solved by first simplifying, setting to equal zero, and finally using a method like factoring, completing the square, or the quadratic formula.

Explanation:

To solve the equation 3 (2d-1) 2d= 4(d-2) + 5, firstly, you'll need to distribute the expressions inside the brackets on both sides: 6d² - 3d = 4d - 8 + 5. Simplify to get 6d² - 3d = 4d - 3.

Next, set the equation to equal zero: 6d² - 3d - 4d +3 = 0, which simplifies further to 6d² - 7d + 3 = 0.

Now, you can solve this quadratic equation either by factoring, completing the square or using the quadratic formula (if it's difficult to factor).

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Finding the work done in stretching or compressing a spring. Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.

In this problem we assume that the force applied doesn't distort the metal in the spring.

A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

Final answer:

To find the force function of a spring using Hooke's Law, you first identify the spring constant 'k' using the given work done and extension. In this case, we found 'k' to be 137.5 N/m. Hence, the force function F(x) for the spring comes out to be 137.5x N.

Explanation:

The problem revolves around Hooke's Law, which is used to determine the force needed to stretch or compress a spring by a certain distance away from its equilibrium position. This law can be mathematically represented as F(x)=kx, where 'F(x)' represents the force applied, 'k' is the spring constant, and 'x' is the distance.

In this question, the work done (W) to stretch the spring is given as 11 J, and the extension (Δx) is 0.4 m (from 2 m to 2.4 m). The work done on a spring is calculated by the equation W = 1/2 * k * (Δx)^2. From this, you can solve for 'k' value. Once you have 'k', you can find the force function F(x) for the spring.

1. Calculate 'k' using the work done equation:

11 J = 1/2 * k * (0.4 m)^2 ➔ k = 137.5 N/m

2. Substitute 'k' in F(x):

F(x) = 137.5 N/m * x

Hence, the force function F(x) = 137.5x N is required to extend the spring by 'x' metres.

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Which linear equation can be derived from this proportion? $(x - 9)/(x - 3) = (2)/(5)$

A. 2x - 3 = 5x - 9
B. 2x - 9 = 5x - 3
C. 2x - 18 = 5x - 15
D. 2x - 6 = 5x - 45

Answers

9514 1404 393

Answer:

D. 2x - 6 = 5x - 45

Step-by-step explanation:

To make the linear equation, we can multiply the given equation by 5(x-3).

$(x-9)/(x-3)=(2)/(5)\n\n((x-9)(5)(x-3))/((x-3))=(2(5)(x-3))/(5)\n\n5(x-9)=2(x-3)\qquad\text{looks like }\textit{cross multiply}\n\n5x-45=2x-6\qquad\text{use the distributive property; matches D.}$

Answer:

The correct answer is D. 2x-6=5x-45

Step-by-step explanation:

I got it right on the Plato test.

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