The equation m = 1. 4p represents the mass, m, in grams, of


p polished stones.

Answers

Answer 1

We know that the total mass of 5 polished stones would be 7 grams according to this equation

Sure! The equation m = 1.4p represents the mass, m, in grams, of p polished stones.

This means that if you know the number of polished stones, p, you can use this equation to calculate their total mass, m, in grams. For example, if you have 5 polished stones, you can plug in p = 5 and solve for m: m = 1.4 x 5 = 7 grams.

So the total mass of 5 polished stones would be 7 grams according to this equation.

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Answer 2

Based on the equation, the number of grams which the mass increase for every 7 polished stones is: D. 9.8 g.

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

Based on the information provided above, a linear equation that models the mass in grams is given by;

y = mx + c

m = 1.4p

By substituting the given parameter (x = 7 polished stones), we have the following:

m = 1.4(7)

m = 9.8 g

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Equation M = 1. 4p Represents The Mass, M, In Grams, Ofp Polished Stones.

Related Questions

The circumstances if the base of the cone is 12π cm. If the volume of the cone is 96π, what is the height

Answers

Answer:8

Step-by-step explanation:

The thickness of paper manufactured at a manufacturing company is roughly symmetrical with a mean of 0. 0039 inch and a standard deviation of about 0. 00001 inch. A marketing manager wants to divide the values of the thickness of paper by 0. 0001 to make the values easier to manage.



What are the mean and standard deviation of the thickness of paper after dividing by 0. 0001?



The mean is ?


inch.



The standard deviation is ?


inch

Answers

The mean of the thickness of paper is 39 inches, and the standard deviation is 0.1 inches.

To find the mean and standard deviation of the thickness of paper after dividing by 0.0001, you should follow these steps:

1. Divide the mean by 0.0001:
Mean after dividing = 0.0039 inches / 0.0001
Mean after dividing = 39 inches

2. Divide the standard deviation by 0.0001:
Standard deviation after dividing = 0.00001 inches / 0.0001
Standard deviation after dividing = 0.1 inches

The mean of the thickness of paper after dividing by 0.0001 is 39 inches, and the standard deviation is 0.1 inches.

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The weekly demand for wireless mice manufactured by Insignia Consumer Electronic
Products group is given by
p(x) = -0.005x + 60, where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly cost
function associated with producing these wireless mice is given by
C(x) = -0.001x^2 + 18x + 4000
Where C(x) denotes the total cost in dollars incurred in pressing x wireless mice (a) Find the production level that will yield a maximum revenue for the manufacturer. What will
be maximum revenue? What price the company needs to charge at that level? (b) Find the production level that will yield a maximum profit for the manufacturer. What will be
maximum profit? What price the company needs to charge at that level?

Answers

The production level that will yield maximum revenue is 6000 units, the maximum revenue is $180,000, and the price the company needs to charge at that level is $30. The production level that will yield maximum profit is 5250 units, the maximum profit is $59,250, and the price the company needs to charge at that level is $37.25.

To find the production level that will yield maximum revenue, we need to determine the quantity demanded that maximizes the revenue. The revenue function is given by

R(x) = xp(x) = x(-0.005x + 60) = -0.005x^2 + 60x

To find the maximum value of R(x), we need to take the derivative of R(x) and set it equal to zero

R'(x) = -0.01x + 60 = 0

x = 6000

So the production level that will yield maximum revenue is 6000 units.

To find the maximum revenue, we can plug this value into the revenue function

R(6000) = -0.005(6000)^2 + 60(6000) = $180,000

To find the price the company needs to charge at that level, we can plug the production level into the demand function

p(6000) = -0.005(6000) + 60 = $30

To find the production level that will yield maximum profit, we need to determine the quantity that maximizes the profit function. The profit function is given by

P(x) = R(x) - C(x) = -0.005x^2 + 60x - (-0.001x^2 + 18x + 4000) = -0.004x^2 + 42x - 4000

To find the maximum value of P(x), we need to take the derivative of P(x) and set it equal to zero

P'(x) = -0.008x + 42 = 0

x = 5250

So the production level that will yield maximum profit is 5250 units.

To find the maximum profit, we can plug this value into the profit function

P(5250) = -0.004(5250)^2 + 42(5250) - 4000 = $59,250

To find the price the company needs to charge at that level, we can plug the production level into the demand function

p(5250) = -0.005(5250) + 60 = $37.25

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Can you guys help me on this algebra work? thankscompare b(x) = 6x^2 to f(x)compare m(x) = -1/3x^2 - 4

Answers

b(x) = 6x² and m(x) = -1/3x²- 4 have similarities and differences as quadratic functions with different coefficients and signs.

How do b(x) and m(x) compare?

We can look at the similarities and differences to compare b(x) = 6x² and m(x) = -1/3x² - 4

Similarities:

Both b(x) and m(x) are quadratic functions, which means they have an x² term.

They both have a constant term, with b(x) having a constant of 0 and m(x) having a constant of -4.

Differences:

The coefficients of the x² term are different: b(x) has a coefficient of 6, while m(x) has a coefficient of -1/3.

The signs of the coefficients are different: b(x) has a positive coefficient, while m(x) has a negative coefficient.

Overall, b(x) and m(x) have some similarities in their form as quadratic functions, but their coefficients and signs are different, which means they will have different shapes and behaviors.

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This wooden frame is made of three planks of wood attached with glue and nails. The wood will be painted with emulsion paint which takes 80ml of paint per metre of wood. Calculate the amount of paint needed to cover all the wood

Answers

amount of paint needed to cover all the wood in the frame, we need to first determine the total length of the wood in meters. Let's assume that each plank of wood is 1 meter long, so the total length of wood in the frame is 3 meters.

Next, we need to calculate the amount of paint required per meter of wood. The problem states that 80ml of emulsion paint is needed per meter of wood. So, we can multiply 80ml by 3 meters to get the total amount of paint needed for the entire frame.

80ml/meter x 3 meters = 240ml
Therefore, we need 240ml of emulsion paint to cover all the wood in the frame.
It is important to note that this calculation assumes that only one coat of paint will be applied to the wood. If multiple coats are desired, the amount of paint required will need to be adjusted accordingly.

In conclusion, to paint the wooden frame made of three planks of wood attached with glue and nails, we would need 240ml of emulsion paint.

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Solve (d-8) (6d-3) using the box method show work

Answers

6d^2 - 51d + 24

that's it

...............................

A random sample of 13 $1 Trifecta tickets at a local racetrack paid a mean amount of $52. 23 with a sample standard deviation of $3. 35. Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50? Use a 10% significance level and assume the distribution is approximately normal.



What is the critical value?

Answers

The critical value for the given problem is 1.282.

To determine if there's sufficient evidence that the average Trifecta winnings exceed $50, follow these steps:

1. State the hypotheses:
  H0: µ ≤ $50 (null hypothesis)
  H1: µ > $50 (alternative hypothesis)

2. Choose the significance level:
  α = 0.10

3. Calculate the test statistic (t-score):
  t = (sample mean - population mean) / (sample standard deviation / √sample size)
  t = ($52.23 - $50) / ($3.35 / √13)
  t ≈ 2.15

4. Determine the critical value:
  Using a t-distribution table or calculator, find the critical value for a one-tailed test with 12 degrees of freedom (13-1) and α = 0.10. The critical value is 1.282.

5. Compare the test statistic to the critical value:
  Since the test statistic (2.15) is greater than the critical value (1.282), we reject the null hypothesis.

In conclusion, there is sufficient evidence to conclude that the average Trifecta winnings exceed $50 at a 10% significance level.

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Complete question:

A random sample of 13 $1 Trifecta tickets at a local racetrack paid a mean amount of $52. 23 with a sample standard deviation of $3. 35. Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50? Use a 10% significance level and assume the distribution is approximately normal.What is the critical value?

Below is attached t-table image:

Analyzing Solution Sets to Linear Equations with the Variable on Both Sides

2x + 5 = 3 + 2(x + 1)

Answers

Answer: it will need to be rewritten so that the variable is only on one side of the equation

Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator

You start by distributing from the 2 into the parentheses for x which will become 2x and 2. Next you may start canceling out. get either 2x and cancel it out with the other you should at this point then have X+5=3+1 combine like terms.

1. Paula has x cups of food in a container to feed her dogs. She pours 1. 5 cups of food into their bowls. There is now 5. 25 cups left in the container. Which equation would be used to solve this problem?



a. 1. 5 - x = 5. 25


b. 5. 25 - x = 1. 25


c. X - 1. 5= 5. 25


d. X + 1. 5= 5. 25




2. A box of donuts cost $9. You want to send donuts to the local nursing home. Set up an equation to find how many boxes you can send if you have $72.



a. 72 = 9 + b


b. 72 = 9 - b


c. 72 = 9b


d. 72 = 9/b




3. Jordan is purchasing a board to build a bookcase. He wants to divide the board into 1. 75 foot sections and he needs 6 sections. Which equation can be used to solve this problem?



a. B/1. 75 = 6


b. 1. 75b = 6


c. B - 1. 75 = 6


d. B + 1. 75 = 6

Answers

The correct option for each individual question is c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.

1. Total food = poured food + remaining food

Keep the values in formula

x = 1.5 + 5.25

Rearranging the equation

x - 1.5 = 5.25

Thus, correct option is c. X - 1. 5= 5. 25

2. Cost of one box × number of boxes = total cost

9 × number of boxes = 72

Let us represent the number of boxes as b. So,

9b = 72

Hence, correct option is c. 72 = 9b.

3. Length of each section × number of sections = total length of bookcase sections

Let us represent total length of bookcase sections as B

1.75 × 6 = B

Rearranging the equation

B/1.75 = 6

So, the correct option is a. B/1. 75 = 6.

Thus, correct option are c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.

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Solid metal support poles in the form of right cylinders are made out of metal with a
density of 6.3 g/cm³. This metal can be purchased for $0.30 per kilogram. Calculate
the cost of a utility pole with a diameter of 42 cm and a height of 740 cm. Round your
answer to the nearest cent. (Note: the diagram is not drawn to scale)

Answers

Answer:Therefore, the cost of a utility pole with a diameter of 42 cm and a height of 740 cm is approximately $1957.43.

Step-by-step explanation:First, we need to calculate the volume of the cylinder-shaped utility pole:

The radius of the pole is half the diameter, so it's 42 cm / 2 = 21 cm.

The height of the pole is 740 cm.

The volume of a cylinder is given by the formula V = πr²h, where π is approximately 3.14, r is the radius, and h is the height.

Substituting the values we have, we get V = 3.14 x 21² x 740 = 1,034,462.4 cm³.

Now we can calculate the mass of the pole:

The density of the metal is 6.3 g/cm³, which means that 1 cm³ of the metal has a mass of 6.3 g.

The volume of the pole is 1,034,462.4 cm³, so its mass is 6.3 x 1,034,462.4 = 6,524,772.72 g.

Next, we convert the mass to kilograms and calculate the cost:

1 kg is equal to 1000 g, so the mass of the pole in kilograms is 6,524,772.72 g / 1000 = 6524.77 kg.

The cost of the metal is $0.30 per kilogram, so the cost of the pole is 6524.77 kg x $0.30/kg = $1957.43.

Which function is increasing and has a domain of (1,infiniti)?



A. F(x) = log(x - 1) + 2


B. F(x) = -log(x - 2) + 1


C. F(x) = -log(x - 1) + 2


D. F(x) = log(x - 2) + 1

Answers

The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.


To determine the increasing function with the specified domain, let's analyze each option:

A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.

B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.

C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.

D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.

The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.

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!!I need help seriouslyyy!!

Answers

The average cost per day for the four service is $3.23 per day

What is average cost?

Average cost refers to the per-unit cost of production, which is calculated by dividing the total cost of production by the total number of units produced.

Therefore average cost = total cost/ number of unit

total cost = $108

average cost for the three services = $108/3

= $36

total average cost = $36+$54.30

= $90.30

therefore average cost for a day will be average cost for a month over 28day i.e 7days ×4

= 90.30/28

= $3.23 per day

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Find the perimeter of a square that has a side length of 4.3x + 2 inches.

Answers

The calculated perimeter of the square from the side length is 17.2x + 8

Finding the perimeter of a square from the side length

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

A square that has a side length of 4.3x + 2 inches.

Using the above as a guide, we have the following:

Perimeter = 4 * side length

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

Perimeter = 4 * (4.3x + 2)

When teh brackets are opened, we have

Perimeter = 17.2x + 8

Hence, the perimeter is 17.2x + 8

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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. solve this one using the elimination method.

Answers

The solution to this system of equations are x = -5 and y = 8.

How to solve these system of linear equations?

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

x + y = 3                .........equation 1.

x - 3y = -29                .........equation 2.

By subtracting equation 2 from equation 1, we have:

(x - x) + (y - (-3y) = 3 - (-29)

y + 3y = 3 + 29

4y = 32

y = 32/4 = 8

x = 3 - y

x = 3 - 8

x = -5

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A set of 9 books has 5,481 pages.
How many pages would be in each
book, if each book has the same
number of pages.

Answers

Answer:

609 pages

Hope this helps!

Step-by-step explanation:

9 books = 5481 pages

1 book = ? pages

9 books ÷ 9 = 1 book  so  5481 pages ÷ 9 = 609 pages

1 book has 609 pages.

Help pls. And please actually answer the question

Answers

Start with the base graph: y = |x|

Translate the graph one unit to the right: y = |x - 1|

---We use a minus/negative/subtraction sign when dealing with horizontal translations because it is the opposite of the way we want to go. If the translation occurs within parenthesis/absolute value bars, we always do the opposite of what we think we should.

Translate the graph one unit down: y = |x - 1| - 1

---If the translation occurs to the y-value/vertically, we use the expected operation/sign. If the translation occurs outside of parenthesis, we use the same operation/sign as the translation (+ for up, - for down).

Answer: y = |x - 1| - 1

Hope this helps!

Answer:

y=|x-1|-1

Step-by-step explanation:

The function for a v shaped graph is an absolute value function: y=|x|

Subtracting 1 from the absolute value y=|x|, we move the graph 1 unit right of the x axis

Subtracting 1 from the whole equation, y=|x-1|, we move the graph 1 unit down the y axis

So, the equation would be y=|x-1|-1

Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)

Answers

The area of the triangle is (a-6, b-12) square units 6 sq unit.

What is the triangle?

A triangle is described as  a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.

This means that the sum of the interior angles of a triangle is equal to 180°

Now that we have  the points they make a 3-4-5 triangle.

The two legs are 3 and 4, so the hypotenuse has to be 5.

We  could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5

We then calculate the area

Area =1/2 b*h

Area = 1/2(3*4)

Area =  6 sq unit

The area of the triangle is (a-6, b-12) square units 6 sq unit.

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If p and q are real numbers in the function f(x)=x4+5x3+px2+qx+30 and f(1)=0, which equation is true?

Answers

p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.

If we substitute x = 1 in the given function, we get:

f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]

= 1 + 5 + p + q + 30

= p + q + 36

We are given that f(1) = 0. Therefore, we have:

p + q + 36 = 0

This is the equation that is true. From this equation, we can say that p + q = -36.

Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.

Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:

f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]

Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]

Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]

We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.

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Helpppppppppppppppppppppppp

Answers

Answer:

Point in the original figure: (5,4)

Point in the final figure: (0,-2)

Step-by-step explanation:

hope this works and helps! :)

The inventory at the end of the year was understated by $14,750:

(A) Did the error cause an overstatement or an understatement of the gross profit for the year? Why?

(B) Which items on the balance sheet at the end of the year were overstated or understated as a result of the error?

Answers

The error caused an understatement of the gross profit for the year, as the cost of goods sold was overstated by $14,750.

The error in inventory caused an understatement of the inventory value on the balance sheet, which in turn caused an overstatement of the cost of goods sold. This is because the cost of goods sold is calculated by subtracting the cost of the ending inventory from the cost of goods available for sale.

Therefore, an understatement of the ending inventory leads to an overstatement of the cost of goods sold, which ultimately results in an understatement of the gross profit. None of the other items on the balance sheet are directly affected by the error in inventory.

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Domain of the rational function.
(5x^2)/(1-x)

Answers

Answer:

(-∞, 1) ∪ (1, ∞)

Step-by-step explanation:

1 - x = 0

-x = -1

x = 1

In interval notation, the domain is (-∞, 1) U (1, ∞)

The demand function for an exclusive wool blanket is given byp=D(x)=33-2√x dollars, where x is in thousands of blankets. Findthe level of production for which the demand is elastic

Answers

To maximize the company's profit, we need to find the profit function and then differentiate it with respect to the quantities produced by each plant to find the optimal values.

The profit function is given by:

π = TR - TC

where TR is the total revenue and TC is the total cost.

Using the demand function p = 40 - 0.04q, we can express the total revenue as:

TR = p * q = (40 - 0.04q) * q = 40q - 0.04q²

The total cost is the sum of the costs of each plant, so we have:

TC = C1 + C2 = 6.7 + 0.03q1² + 7.9 + 0.04q2² = 14.6 + 0.03q1² + 0.04q2²

Substituting these expressions into the profit function, we get:

π = 40q - 0.04q² - 14.6 - 0.03q1² - 0.04q2²

To find the optimal values of q1 and q2, we differentiate the profit function with respect to each quantity and set the derivatives equal to zero:

∂π/∂q1 = 40 - 0.06q1 - 0.04q2 = 0

∂π/∂q2 = 40 - 0.03q2 - 0.04q1 = 0

Solving these equations, we get:

q1 = 357.14

q2 = 285.71

So each plant should produce 357.14 and 285.71 units of the item, respectively, in order to maximize the company's profit.

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Triangle Z Y X is shown with its exterior angles. Point Z extends to point L, point X extends to point N, and point Y extends to point M.
Analyze the diagram to complete the statements.

The m∠MXN is
the m∠YZX.

The m∠LZX is
the m∠ZYX + m∠YXZ.

The m∠MYL is
180° − m∠ZYX.

Answers

The completed statements, obtained from the relationship between the exterior angles of a triangle and supplementary angles are;

The m∠MXN is greater than m∠YZX

The m∠LZX is equal to m∠ZYX + m∠YXZ

The m∠MYL is equal to 180° - m∠ZYX

What are supplementary angles?

Supplementary angles are angles that form a linear pair and when added together are equivalent to 180°

The exterior angle of a triangle theorem indicates, that we get;

m∠MXN = m∠YZX + m∠ZYX

Therefore; m∠MXN > m∠YZXm∠LZX = m∠ZYX + m∠YXZ

∠MYL is a supplementary angle to the angle ∠ZYX

Therefore; m∠MYL + m∠ZYX = 180°

m∠MYL = 180° - m∠ZYX

The completed statements are therefore;

m∠MXN is greater than m∠YZX

m∠LZX equal to m∠ZYX + m∠YXZ

m∠MYL equal to 180° - m∠ZYX

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Please Answer ASAP! PLEEEASE
Answer Fully Please And Fill IN THe Blanks!
also you will get allot of points

Answers

It is a fifth order polynomial

The constant term is -7

The leading term is [tex]x^5/7[/tex]

The coefficient of the leading term is [tex]1/7[/tex]

What is the leading term of a polynomial?

The term with the highest degree—i.e., the term with the largest power of the variable—is the leading term. The leading coefficient is the leading term's coefficient.

We frequently rearrange polynomials so that the powers are descending or ascending because of the definition of the "leading" term. We can see that the leading term in the expression here is [tex]x^5/7[/tex].

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Can someone explain ._.

Answers

The mark-up value percentage is 25 %

Given data ,

The markup amount is the selling price minus the cost price, so:

Markup = $8630 - $6900 = $1730

The markup percentage is the markup amount divided by the cost price, expressed as a percentage:

Markup percentage = (Markup / Cost price) x 100%

Markup percentage = ($1730 / $6900) x 100%

Markup percentage = 0.25 x 100%

Markup percentage = 25%

Hence , the markup percentage is 25%

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Robert got home from school at twenty-seven minutes to four in the afternoon. He decided to bake muffins as an after-school snack. The muffins were ready at two minutes to four in the afternoon. How long did it take to prepare and bake the muffins?

Answers

Assuming that the muffins were actually ready at two minutes to five in the afternoon, we can determine that it took Robert approximately 38 minutes to prepare and bake the muffins.

To arrive at this conclusion, we can use the following logic:

Robert got home from school at 3:33 PM (twenty-seven minutes before 4:00 PM).

The muffins were ready at 4:58 PM (two minutes before 5:00 PM).

Therefore, the time between when Robert got home and when the muffins were ready is 85 minutes (58 minutes + 27 minutes).

Since Robert decided to bake the muffins immediately upon arriving home, it took him 85 minutes to prepare and bake them.

Of course, this assumes that Robert did not take any breaks or perform other activities during the time between getting home and the muffins being ready. In reality, the actual time it took to prepare and bake the muffins may have been longer or shorter depending on various factors, such as the recipe, equipment used, and Robert's baking experience.

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Steve bought 10 gallons of gas at the gas station with the highest price. how much more than cole did he pay for gas?

please help, thank you.​

Answers

Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

To answer this question, we need to know the prices of gas at both gas stations. Let's assume that Cole bought 10 gallons of gas at the gas station with the lowest price, and that the price difference between the two gas stations is $x per gallon.

If we denote the price per gallon of gas at the gas station where Cole bought gas as "c", then the total amount Cole paid for gas is:

10c

If we denote the price per gallon of gas at the gas station where Steve bought gas as "s", then the total amount Steve paid for gas is:

10s

The difference between the two amounts is:

10s - 10c

But we know that Steve bought gas at the gas station with the highest price, so we can assume that s = c + x.

Substituting this expression for s into the equation above, we get:

10s - 10c = 10(c + x) - 10c = 10x

So Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

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A particle moves along the x-axis so that its position at time t>0 is given by


X(t) = (t^2 - 9)/(3t^2 + 8)


A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2


B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.


C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).


D) What position does the particle approach as t approaches infinity?

Answers

The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]

The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]

A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:

[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]

[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]

[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]

[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]

Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]

B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:

[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]

Since v(2) is positive, the particle is moving away from the origin at time t = 2.

C) The acceleration of the particle is given by the derivative of its velocity with respect to time:

[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]

[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]

[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]

Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]

D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:

[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]

As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:

[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]

So the particle approaches the point x = 1/3 as t approaches infinity.

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For 50 points can you help me with this I really need help.

Answers

The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.

What is a reflection transformation?

A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.

The coordinate points of the image after the specified reflections can be presented as follows;

Original   [tex]{}[/tex]Reflection across the x-axis   Reflection across the y-axis   y = -x

(0, 15)      [tex]{}[/tex] (0, -15)                                      (0, 15)                                   (-15, 0)

(1,  15)      [tex]{}[/tex] (1, -15)                                       (-1, 15)                                   (-15, -1)

(1, 13)      [tex]{}[/tex]  (1, -13)                                       (-1, 13)                                    (-13, -1)

(3, 15)      [tex]{}[/tex] (3, -15)                                      (-3, 15)                                   (-15, -3)

(3, 12)      [tex]{}[/tex] (3, -12)                                      (-3, 12)                                   (-12, -3)

(1, 10)      [tex]{}[/tex]  (1, -10)                                      (-1, 10)                                     (-10, -1)

(1, 8)      [tex]{}[/tex]   (1, -8)                                        (-1, 8)                                      (-8, -1)

(3, 10)      [tex]{}[/tex](3, -10)                                      (-3, 10)                                    (-10, -3)

(3, 7)      [tex]{}[/tex]  (3, -7)                                       (-3, 7)                                      (-7, -3)

(1, 5)      [tex]{}[/tex]  (1, -5)                                        (-1, 5)                                      (-5, -1)

(1, 2)      [tex]{}[/tex]  (1, -2)                                        (-1, 2)                                      (-2, -1)

(4, 4)      [tex]{}[/tex] (4, -4)                                       (-4, 4)                                      (-4, -4)

(5, 7)      [tex]{}[/tex] (-5, 7)                                       (5, -7)                                      (-7, -5)

(7, 8)      [tex]{}[/tex] (7, -8)                                       (-7, 8)                                      (-8, -7)

(6, 5)     [tex]{}[/tex]  (6, -5)                                      (-6, 5)                                      (-5, -6)

(8, 6)     [tex]{}[/tex]  (8, -6)                                      (-8, 6)                                      (-6, -8)

(9, 9)     [tex]{}[/tex]  (9, -9)                                      (-9, 9)                                      (-9, -9)

(11, 10)     [tex]{}[/tex] (11, -10)                                   (-11, 10)                                    (-10, -11)

(10, 7)     [tex]{}[/tex]  (10, -7)                                   (-10, 7)                                     (-7, -10)

(12, 8)     [tex]{}[/tex]  (12, -8)                                   (-12, 8)                                    (-8, -12)

(13, 6)     [tex]{}[/tex]  (13, -6)                                   (-13, 6)                                    (-6, -13)

(11, 5)      [tex]{}[/tex]  (11, -5)                                    (-11, 5)                                     (-5, -11)

(14, 4)      [tex]{}[/tex] (14, -4)            [tex]{}[/tex]                       (-14, 4)                                     (-4, -14)

(12, 3)     [tex]{}[/tex]  (12, -3)                                   (-12, 3)                                     (-3, -12)

(9, 4)      [tex]{}[/tex]  (9, -4)                                    (-9, 4)                                       (-4, -9)

(7, 3)      [tex]{}[/tex]  (7, -3)                                     (-7, 3)                                       (-3, -7)

(10, 2)    [tex]{}[/tex]  (10, -2)                                   (-10, 2)                                     (-2, -10)

(8, 1)      [tex]{}[/tex]  (8, -1)                                      (-8, 1)                                       (-1, -8)

(5, 2)     [tex]{}[/tex]  (5, -2)                                     (-5, 2)                                      (-2, -5)

(2, 0)     [tex]{}[/tex]  (2, 0)                                      (-2, 0)                                      (0, -2)

The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.

Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.

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Question 2 of 10
What are the dimensions of AB?
A. 3x2
B. 3x3
C. 2x3
D. 2 x 2

Answers

Answer:

Based on the image, we can see that matrix A is a 3x2 matrix, and matrix B is a 2x3 matrix. In order to multiply matrices A and B, the number of columns in matrix A must match the number of rows in matrix B.

Since matrix A has 2 columns and matrix B has 2 rows, we can multiply them together, resulting in a 3x3 matrix. Therefore, the answer is B. The dimensions of AB are 3x3.

I DONT NEED BRAINLEST JUST STAY FUN AND SAFE

Ans. (c) 2X3

Dimension of matrix is given by row x column

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