I really need help ASAP. plz

Answer:

2 1/5

Step-by-step explanation:

4 3/5 - 2 2/5

I like to make them vertical

4 3/5

- 2 2/5

-----------------

2 1/5

Answer:

D. 7n = 28

Step-by-step explanation:

Let's substitute 4 for n in each equation to check if it the resulting equation is correct:

\(6+n=24\\ 6+4=24\\ 10\neq 24\rightarrow \text{Incorrect!}\)

\(5n=54\\5(4)=54\\20\neq54\rightarrow\text{Incorrect!}\)

\(12-n=16\\12-4=16\\8\neq16\rightarrow\text{Incorrect!}\)

\(7n=28\\7(4)=28\\28=28\rightarrow\text{Correct!}\)

Therefore the answer is D

Step-by-step explanation:

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when \(h=(-\infty,3)U(3,\infty)\) and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

\(x_{1}+hx_{2}=3\)

so

\(x_{1}=3-hx_{2}\)

Next we can substitute this into the second equation so we get:

\(5(3-hx_{2})+15x_{2}=k\)

We distribute the 5 into the first parenthesis so we get:

\(15-5hx_{2}+15x_{2}=k\)

and group like terms:

\(-5hx_{2}+15x_{2}=k-15\)

we factor x2 so we get:

\(x_{2}(-5h+15)=k-15\)

and solve for x2:

\(x_{2}=\frac{k-15}{-5h+15}\)

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

\(-5h+15= 0\)

and solve for h:

\(-5h= -15\)

\(h=\frac{-15}{-5}\)

\(h= 3\)

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

\(5x_{1}+15x_{2}=k\)

we start by factoring a 5 from the left side of the equation so we get:

\(5(x_{1}+3x_{2})=k\)

Next, we divide both sides of the equation into 5 so we get:

\(x_{1}+3x_{2}=\frac{k}{5}\)

we now compare it to the first equation:

\(x_{1}+hx_{2}=3\)

\(x_{1}+3x_{2}=\frac{k}{5}\)

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and \(\frac{k}{5}=3\)

when taking the second condition and solving for k we get that:

\(k=3(5)\)

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

a) These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).

a) To find all solutions to the equation z⁴ = 1, we can use De Moivre's theorem:

z⁴ = 1 = cos(0) + i sin(0)

We can rewrite this in polar form as:

z = cos(0/4 + 2kπ/4) + i sin(0/4 + 2kπ/4)

where k = 0, 1, 2, 3.

Simplifying the expression for z, we get:

z = cos(kπ/2) + i sin(kπ/2)

For k = 0, we get z = 1.

For k = 1, we get z = i.

For k = 2, we get z = -1.

For k = 3, we get z = -i.

These are the four solutions to the equation z⁴ = 1. We can plot these solutions on an Argand diagram by marking points at (1, 0), (0, 1), (-1, 0), and (0, -1).

b) To find all solutions to the equation z³ = 8, we can use De Moivre's theorem:

z³ = 8 = 8(cos(0) + i sin(0))

We can rewrite this in polar form as:

z = 2(cos(0/3 + 2kπ/3) + i sin(0/3 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = 2(cos(kπ/3) + i sin(kπ/3))

For k = 0, we get z = 2.

For k = 1, we get z = -1 + i√3.

For k = 2, we get z = -1 - i√3.

These are the three solutions to the equation z³ = 8. We can plot these solutions on an Argand diagram by marking points at (2, 0), (-1, √3), and (-1, -√3).

c) To find all solutions to the equation z³ = i, we can use De Moivre's theorem:

z³ = i = cos(π/2) + i sin(π/2)

We can rewrite this in polar form as:

z = (cos(π/6 + 2kπ/3) + i sin(π/6 + 2kπ/3))

where k = 0, 1, 2.

Simplifying the expression for z, we get:

z = cos(kπ/3) + i sin(kπ/3)

For k = 0, we get z = 1.

For k = 1, we get z = (-1 + i√3)/2.

For k = 2, we get z = (-1 - i√3)/2.

These are the three solutions to the equation z³ = i. We can plot these solutions on an Argand diagram by marking points at (1, 0), (-1/2, √3/2), and (-1/2, -√3/2).


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Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

Here are the angles in each quadrant with a common reference angle of 165°:

First quadrant: angle is 15° (subtract 165° from 180°)

Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)

Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)

Fourth quadrant: angle is 195° (subtract 165° from 360°)

Answer: answer is 5

Step-by-step explanation:

A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

The answers are -0.5, 2.2, 3.8, and 9.0

We need to evaluate the expression 3.8 + 0 + y for the given values of y.

Let x = 3.8 + 0 + y

The values of y are -4.3, -1.6, 0, and 5.2

Let's substitute the value of y in the expression and calculate the values of x.

Refer to the attached image for the values of the expression corresponding to the values of y.

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Answer:

-0.5, 2.2, 3.8, and 9.0

Step-by-step explanation:

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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The least positive number with this property is given as follows:

N = 280.

A number N gives remainder 0 when divided by 8, it gives remainder 0, when divided by 7 and it is an even multiple of 5, hence the number is multiple of these 3 numbers.

Before obtaining the number, we must obtain the least common multiple of 8, 7 and 5, factoring them by prime factors as follows:

8 - 7 - 5|2

4 - 7 - 5|2

2 - 7 - 5|2

1 - 7 - 5|5

1 - 7 - 1|7

1 - 1 - 1.

Hence:

lcm(8,7,5) = 2³ x 5 x 7 = 280.

280 is an even multiple of 5, as it is an even number, hence it is the least positive number N with the property in this problem.

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sinθ = t/o

cosθ = m/o

tanθ = t/m

cscθ = o/t

secθ = o/m

cotθ = m/t

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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The solution is :

Mean max speed = 157 m/sec.

Median max wind speed = 100 m/s.

Mode max wind speed = 75, 80, 85 and 115.

We have,

The amount of times an occurrence or value occurs is referred to as its frequency.

A frequency table is one that lists objects and shows how frequently they occur.

The frequency is represented by the letter 'f' in the English alphabet.

Arrange the given frequencies in the ascending order.

75, 75, 80, 80, 85, 85, 90, 100, 115, 115, 160, 165, 205, 450, 475.

Total frequencies 'n' = 15.

Part 1: Mean max speed: The number of duration or frequently applied events of a particular type in a unit of time, usually one second.

Mean max speed: (75 + 75 + 80 + 80 + 85 + 85 + 90 + 100 + 115 + 115 + 160 + 165 + 205 + 450 + 475)/15

Mean max speed: 2355/15 = 157.

Thus, the mean max speed of the wind is 157 m/sec.

Part 2: median max wind speed;

The median is the number in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.

median = (n + 1)/2 ....for odd number of frequencies.

median = (15 + 1)/2

median = 8th term

median = 100.

The  median speed of the wind is 100 m/s.

Part 3: mode max wind speed,

A mode is the value with the highest frequency in a specific set of values. It is the value which appears the most frequently.

Mode = 75, 80, 85 and 115.

Thus, given frequencies has 4 mode values.

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The correct question is-

The frequency table is given as-

Max Wind Speed

(mph)

-75

450

160

205-

475-

115

90

85

80

100

80-

75

165

115.

85

Find the mean max wind speed of the wind.

Find the median max wind speed of the wind.

Find the mode max wind speed of the wind.

Answer:

1/2

please mark me brainliest

Answer:

Step-by-step explanation:

Melonie,  k = 2*10,  is another way to look at this

I think you can get the answer now

k = 20 , if you're not sure

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

Answer:

The answer is below

Step-by-step explanation:

The model is not given, but I would attached a model and show you how to solve.

Solution:

An equation is a mathematical statement that makes two expressions to be equal to each other. Models can be used to represent equations through the use of various forms such as tiles model, balance scale model, cups and counter model, and so on.

From the model attached, we can form an equation. The equation is given as:

(5 * x) + (-1 * 9) = (-x * 3) + (1 * 20)

5x  + (-9) = -3x + (20)

5x - 9 = -3x + 20

collecting like terms:

5x + 3x = 20 + 9

Simplifying:

8x = 29

8x/8 = 29 / 8

x = 29 / 8

140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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Apollo Spas will need 46.035 liters of muriatic acid to service all 297 hot tubs.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To find the total amount of muriatic acid needed for all of the hot tubs, we can multiply the amount needed for one hot tub (155 mL) by the number of hot tubs (297) and convert the result to liters.

First, let's convert the volume of acid needed for one hot tub from milliliters to liters by dividing by 1000:

155 mL ÷ 1000 = 0.155 L

Now we can find the total amount of acid needed for all of the hot tubs:

0.155 L/hot tub x 297 hot tubs = 46.035 L

Therefore, Apollo Spas will need 46.035 liters of muriatic acid to service all 297 hot tubs.

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Answer:

280,000

Step-by-step explanation:

10^5=100,000

2.8 x 100,000=280,000

The integer that represents the change in temperature from morning to afternoon is 18.

The group of counting numbers that can be written without a fractional component includes zero and both positive and negative integers. An integer can, as was already established, be either positive, negative, or zero.

To find the change in temperature from morning to afternoon, we need to subtract the morning temperature from the afternoon temperature:

9.3 F - (-8.7 F) = 9.3 F + 8.7 F = 18 F

Therefore, the integer that represents the change in temperature from morning to afternoon is 18.

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Answer:

she makes $22.80 a day

Step-by-step explanation:

since she makes $0.57 per box and averages at 40 boxes a day, we multiply 40 and 0.57. 40 x 0.57 = 22.8, or $22.80.

hope this helped!

Answer:

MAR=180-165

=15 IS THE ANSWER

The quadratic function for the value of David's investment indicates;

(i) $45,000

(ii) 9.375 months

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The model of the value of the investment in the bank obtained from the amount of his retirement funds David invested in the bank can be presented as follows;

a = 45 + 75·t - 4·t²

Where;

a = The value of the investment in thousand of dollars after t months

t = The number of months of the investment

(i) The initial amount David invested can be found by plugging in t = 0, in the function for the amount David invested in the bank, as follows;

a = 45 + 75 × 0 - 4 × 0² = 45

The initial amount David invested is; a = $45,000

(ii) The number of months it takes for David investment to reach a maximum value can be found from the quadratic function as follows;

The number of months t(max) at the maximum amount is; t(max) = -75/(2 × (-4)) = 9.375

Therefore, it will take 9.375 months for David's investment to reach a maximum value

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The volume of the described solid is V = 16r³/3

Given,

A solid line S should be drawn between z=a and z=b. If S has a cross-sectional area of Px through x and is perpendicular to the x-axis, then A (x)

Volume of S = limₙ→∝ ∑i=₁ⁿ A(xi) Δx = \(\int\limits^b_a {A(x)} \, dx\)

The equation of circle x² + y² = r² where r is the radius of the circle.

Equation of upper semicircle yu= √(r²-x²)  and

Equation of lower semicircle yl = -√(r²-x²)

Area of cross-section A(x) = (yu² - yl²)

Substitute yu and yl values

A(x) = [√(r²-x²) - (-√(r²-x²) )]² = 4(r² -x²)        (1)

The limit for volume v varies from -r to r

Thus Volume v = ₋\(\int\limits^r_r {A(x)} \, dx\)

Substitute A(x) from (1)

V = ₋\(\int\limits^r_r {4(r^{2}-x^{2} ) } \, dx\)

⇒V = 4[r²x - x³/3 ]

⇒V = 4(r³ - r³/3) - 4(-r³ + r³/3) = 4[2 (r³ - r³/3)] = 16r³/3

The volume of the described solid S where the base is a circular disk or radius r and parallel cross sections perpendicular to the base are squares is V = 16r³/3

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The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Answer: P=60.16m

Step-by-step explanation: