Inverses of Functions 7. Find fᵒg and gᵒf, if they exist. f = {(-4,-5), (0, 3), (1,6)} and g = {(6, 1), (-5,0), (3,-4)}. 8. Find [gᵒh] (x) and [hg](x), if they exist. g(x) = x + 6 and h(x) = 3x². 9. Find the inverse of this relation. {(-5,-4), (1, 2), (3, 4), (7,8)} 10. Find the inverse of each function. Then graph the function and its inverse. g(x) = 3 + x

Answers

Answer 1

The inverse function is g⁻¹(x) = x - 3.

Let us begin with fᵒg, which stands for f composite g. To calculate this, we first need to apply the function g to the domain of f. f = {(-4,-5), (0, 3), (1,6)} and

g = {(6, 1), (-5,0), (3,-4)}.

So, g(-4) = 1, g(0) = 0, and g(1) = -4. Then,

fᵒg = {(-4,6), (0,-5), (1,1)}.

Now, let's calculate gᵒf, which stands for g composite f. To calculate this, we first need to apply the function f to the domain of

g. f = {(-4,-5), (0, 3), (1,6)} and g = {(6, 1), (-5,0), (3,-4)}.

So, f(6) is undefined, f(-5) = 3, and f(3) is undefined. Then, gᵒf is undefined.

8. Here, we have to calculate [gᵒh] (x) and [hg](x), if they exist.

g(x) = x + 6 and h(x) = 3x².So,

[gᵒh] (x) = g(h(x))

= g(3x²) = 3x² + 6.

Now, [hg](x) = h(g(x))

= h(x+6)

= 3(x+6)²

= 3(x² + 12x + 36).

9. To find the inverse of this relation, we have to swap the x and y values and solve for y.{(-5,-4), (1, 2), (3, 4), (7,8)} becomes {(-4,-5), (2,1), (4,3), (8,7)}.

10. g(x) = 3 + x

The inverse of this function can be found by swapping the x and y values. Then, solving for y:

x = 3 + y

y = x - 3

Therefore, the inverse function is g⁻¹(x) = x - 3.

We have learned about inverses of functions and how to calculate f composite g and g composite f. We have also learned how to find the inverse of a relation and how to find the inverse of a function and graph it.

To know more about the inverse function, visit:

brainly.com/question/25614985

#SPJ11


Related Questions

Polygons that are similar have the same shape, but are a different size. Select one: O True O False

Answers

True.Polygons that are similar have the same shape, but are of a different size.

The relationship between corresponding angles and the corresponding side lengths of similar polygons is that they are proportional to each other. So, if a shape is enlarged or reduced, but it retains the same shape, it is considered to be similar to the original shape. Therefore, the statement is true that polygons that are similar have the same shape, but are a different size.

Let us understand polygons in detail:A polygon is a closed figure that has many sides, and it is made up of line segments that are connected end-to-end. In the plane, a polygon can be classified as a simple polygon or a complex polygon. In simple polygons, no line segment intersects another line segment that is not an endpoint of the segment.

Any polygon that is not simple is known as a complex polygon. Similarly, polygons can be classified according to their number of sides, and they are named accordingly. Triangles, quadrilaterals, pentagons, hexagons, heptagons, octagons, and so on are the most frequent polygons.

To know more about Polygons visit:

https://brainly.com/question/17756657

#SPJ11

Pen A B C Length (1) 12 m 8 m 6 m Breadth (b) 2 m 3 m 4 m (i) Which pen would take most fencing? (ii) Which pen would you like to minimize the cost of fencing? ​

Answers

(i) Pen A would take the most fencing.

(ii) Pen C would be the preferred option to minimize the cost of fencing.

(i) For calculating the total fencing, we need to find the perimeter of each pen by using the formula

P = 2(l + b), where P is the perimeter, l is the length and b is the breadth.

Pen A: P = 2(12 + 2) = 28 m

Pen B: P = 2(8 + 3) = 22 m

Pen C: P = 2(6 + 4) = 20 m

Thus, Pen A requires the most fencing.

(ii) To minimize the cost of fencing, we should choose the pen with the smallest perimeter. Here, Pen C has the smallest perimeter, so it would minimize the cost of fencing.

for such more questions on cost

https://brainly.com/question/2292799

#SPJ8

) A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied tof on [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, If the Mean Value Theorem does not apply, enter DNE for the c value. CM f(x)=2x²-3x²-72x+6 (Separate multiple answers by commas.) on [-5,9]

Answers

According to the Mean Value Theorem, there exists at least one value c in the interval (-5, 9) such that f'(c) = -23.71. The approximate value of c is -24.14.

To check if the Mean Value Theorem (MVT) can be applied to the function f(x) = 2x² - 3x² - 72x + 6 on the interval [-5, 9], we need to verify two conditions:

The function f(x) must be continuous on the closed interval [a, b].The function f(x) must be differentiable on the open interval (a, b).

Let's check these conditions:

Continuity: The function f(x) is a polynomial, and polynomials are continuous for all values of x. Therefore, f(x) is continuous on the interval [-5, 9].Differentiability: The function f(x) is also a polynomial, and polynomials are differentiable for all values of x. Therefore, f(x) is differentiable on the interval (-5, 9).

Since both conditions are satisfied, we can conclude that the Mean Value Theorem applies to f(x) on the interval [-5, 9].

According to the Mean Value Theorem, there exists at least one value c in the interval (-5, 9) such that the derivative of f evaluated at c is equal to the average rate of change of f over the interval [-5, 9].

To find the value(s) of c, we need to find the derivative of f(x) and set it equal to the average rate of change.

f(x) = 2x² - 3x² - 72x + 6

Taking the derivative:

f'(x) = 4x - 6x - 72

Simplifying:

f'(x) = -2x - 72

Now, we calculate the average rate of change of f over the interval [-5, 9]:

Average rate of change = (f(b) - f(a)) / (b - a)

= (f(9) - f(-5)) / (9 - (-5))

= (2(9)² - 3(9)² - 72(9) + 6 - [2(-5)² - 3(-5)² - 72(-5) + 6]) / (9 - (-5))

= (162 - 243 - 648 + 6 - 50 + 75 + 360 + 6) / 14

= -332 / 14

= -23.71

We need to find the value(s) of c such that f'(c) = -23.71.

Solving -2c - 72 = -23.71, we find:

-2c = -23.71 + 72

-2c = 48.29

c ≈ -24.14

Therefore, according to the Mean Value Theorem, there exists at least one value c in the interval (-5, 9) such that f'(c) = -23.71. The approximate value of c is -24.14.

To know more about Mean Value Theorem, visit:

https://brainly.com/question/31033828

#SPJ11

lim (x,y)→(0,0)

x 2
+y 2

9xy

= A. −1 B. 1 C. 0 D. π E. does not exist mevcut değil

Answers

The limit does not exist. Therefore, the correct answer is (E) does not exist.

Given expression islim (x,y)→(0,0)

x 2
+y 2

9xy

We have to determine the limit of this expression as (x,y) tends to (0,0).

Let's evaluate the limit using polar coordinates:

Substituting x=r cos θ, y=r sin θ, the expression becomes:lim (r,θ)→(0,0)

(r cos θ) 2
+(r sin θ) 2

9(r cos θ)(r sin θ)

After simplification, the expression becomes:

lim (r,θ)→(0,0)

r cos θ sin θ
9

This limit depends on the choice of θ.

Therefore, the limit does not exist. Therefore, the correct answer is (E) does not exist.

Know more about limit here:

https://brainly.com/question/30679261

#SPJ11

4500-p² 4 The demand equation for a product is found to be a = price of the product in dollars and q is the quantity. a. Find the price elasticity of demand when the price is $40. b. Is the demand el

Answers

The demand equation for a product is a function that represents the relationship between the price of a product and the quantity demanded by consumers. The price elasticity of demand when the price is $40 is E= (40/Q) (dQ/dP) = (40/Q) (q/40) = 1 Therefore, demand is unit elastic.

The price elasticity of demand measures the responsiveness of the quantity demanded of a product to a change in its price.

It is a crucial concept in economics, particularly in understanding how consumers react to changes in prices.

To answer this question, we use the formula for price elasticity of demand:

E= (P/Q) (dQ/dP) where E is the elasticity,

P is the price of the product, Q is the quantity demanded, and

dQ/dP is the derivative of the quantity demanded with respect to the price.

Given the demand equation,

a = price of the product in dollars and q is the quantity.

Therefore, we can rewrite the equation as follows:

a = Pq Taking the derivative of both sides, we get:

da/dP

= q + P (dq/dP)  Solving for dq/dP,

we get: dq/dP

= (da/dP - q)/P

Plugging in the values, we get:

dq/dP

= (1q - 0)/40

= q/40

Hence, the price elasticity of demand when the price is $40 is

E= (40/Q) (dQ/dP)

= (40/Q) (q/40)

= 1

Therefore, demand is unit elastic.

The demand is unit elastic if the percentage change in quantity demanded is equal to the percentage change in price.

Therefore, a change in price will lead to an equal change in quantity demanded.

If the elasticity is greater than 1, the demand is elastic.

If the elasticity is less than 1, the demand is inelastic.

To know more about Equation  visit :

https://brainly.com/question/29538993

#SPJ11

e demand function for a particular product is given by the function \( D(x)=\frac{-2}{9} x^{2}+400 \). Find the consumers' surplus if \( x_{E}=30 \) units.

Answers

The consumer's surplus for [tex]\(x_E = 30\)[/tex] units is [tex]\(-\frac{2000}{3}\)[/tex] or approximately [tex]\(-666.67\)[/tex] units.

To find the consumer's surplus, we first need to determine the demand function. The demand function for a particular product is given by the function [tex]\(D(x) = \frac{-2}{9}x^2 + 400\),[/tex] where [tex]\(x\)[/tex] represents the quantity of the product.

The consumer's surplus represents the difference between what consumers are willing to pay for a product and what they actually pay. Mathematically, it can be calculated by finding the area between the demand curve and the price line for a given quantity.

Given that [tex]\(x_E = 30\)[/tex] units, the consumer's surplus can be calculated as follows:

The price line for [tex]\(x_E\)[/tex] units is determined by evaluating the demand function at [tex]\(x = x_E\):[/tex]

[tex]\[P(x_E) = D(x_E) = \frac{-2}{9}(30)^2 + 400\][/tex]

To find the consumer's surplus, we need to integrate the difference between the demand function and the price line over the range [tex]\([0, x_E]\):[/tex]

[tex]\[CS = \int_{0}^{x_E} (D(x) - P(x_E)) \, dx\][/tex]

Substituting the given demand function and the price line:

[tex]\[CS = \int_{0}^{30} \left(\frac{-2}{9}x^2 + 400 - \left(\frac{-2}{9}(30)^2 + 400\right)\right) \, dx\][/tex]

Simplifying:

[tex]\[CS = \int_{0}^{30} \left(\frac{-2}{9}x^2 + 400 + \frac{2}{9}(30)^2 - 400\right) \, dx\][/tex]

[tex]\[CS = \int_{0}^{30} \left(\frac{-2}{9}x^2 + \frac{2}{9}(30)^2\right) \, dx\][/tex]

[tex]\[CS = \int_{0}^{30} \frac{-2}{9}(x^2 - (30)^2) \, dx\][/tex]

[tex]\[CS = \frac{-2}{9} \int_{0}^{30} (x^2 - 900) \, dx\][/tex]

Integrating term by term:

[tex]\[CS = \frac{-2}{9} \left(\frac{x^3}{3} - 900x\right)\Bigr|_{0}^{30}\][/tex]

Evaluating the definite integral:

[tex]\[CS = \frac{-2}{9} \left(\frac{30^3}{3} - 900 \cdot 30 - 0^3 + 900 \cdot 0\right)\][/tex]

Simplifying further:

[tex]\[CS = \frac{-2}{9} \left(30000 - 27000\right)\][/tex]

[tex]\[CS = \frac{-2}{9} \cdot 3000\][/tex]

[tex]\[CS = -\frac{2000}{3}\][/tex]

Therefore, the consumer's surplus for [tex]\(x_E = 30\)[/tex] units is [tex]\(-\frac{2000}{3}\)[/tex] or approximately [tex]\(-666.67\)[/tex] units.

To know more about surplus visit-

brainly.com/question/31401628

#SPJ11

A contour map is shown for a function f(x,y) on the rectangle R=[−3,6]×[−1,4]. a. Use the midpoint rule with m=2 and n=3 to estimate the value of ∬R​f(x,y)dA. b. Estimate the average value of the function f(x,y). fave​≈ Hint

Answers

a. The estimated value of ∬R​f(x,y)dA is 105

b. The estimated average value of the function f(x, y) is 7.

a. The rectangle R=[−3,6]×[−1,4] is divided into m = 2 subintervals along the x-axis and n = 3 subintervals along the y-axis. Therefore, each subinterval has a width of Δx = (6 - (-3))/2 = 9/2 and a height of Δy = (4 - (-1))/3 = 5/3.

We can calculate the midpoint of each subrectangle using the formula:

[tex]x_i = x_min + (i - 0.5) * \Delta x\\y_j = y_min + (j - 0.5) * \Delta y[/tex]

where i = 1, 2, ..., m and j = 1, 2, ..., n.

Using the midpoint rule, the estimate of the double integral is given by:

∬R​f(x,y)dA ≈ Δx * Δy * ∑∑[tex]f(x_i, y_j)[/tex]

where the double summation is taken over all the midpoints (x_i, y_j) of the subrectangles.

Calculate the midpoints of the subrectangles.

[tex]x_1 = -3 + (1 - 0.5) * (9/2) = -3 + 4.5 = 1.5\\x_2 = -3 + (2 - 0.5) * (9/2) = -3 + 9 = 6\\y_1 = -1 + (1 - 0.5) * (5/3) = -1 + (1/2) * (5/3) = -1 + 5/6 = -1/6\\y_2 = -1 + (2 - 0.5) * (5/3) = -1 + (3/2) * (5/3) = -1 + 5/2 = 9/2\\y_3 = -1 + (3 - 0.5) * (5/3) = -1 + (5/2) * (5/3) = -1 + 25/6 = 19/6[/tex]

Evaluate the function at each midpoint.

[tex]f(x_1, y_1) = 2\\f(x_1, y_2) = -1\\f(x_1, y_3) = 0\\f(x_2, y_1) = 1\\f(x_2, y_2) = 3\\f(x_2, y_3) = 2[/tex]

∬R​f(x,y)dA ≈ Δx * Δy * ∑∑[tex]f(x_i, y_j)[/tex]

           = (9/2) * (5/3) * (2 + (-1) + 0 + 1 + 3 + 2)

           = (9/2) * (5/3) * 7

           = 15 * 7

           =  105

b. To estimate the average value of the function f(x, y), we can divide the double integral by the area of the rectangle R, which is A = Δx * Δy * m * n.

The average value is then given by:

f_ave ≈ (∬R​f(x,y)dA) / A

Now let's perform the calculations:

Step 1: Calculate the area of the rectangle.

A = Δx * Δy * m * n

 = (9/2) * (5/3) * 2 * 3

 = 15

Step 2: Calculate the average value.

f_ave ≈ (∬R​f(x,y)dA) / A

     = 105 / 15

     = 7

Therefore, the estimated value of ∬R​f(x,y)dA is 105 and the estimated average value of the function f(x, y) is 7.

To know more about estimated value, refer here:

https://brainly.com/question/32263011

#SPJ4

Let Y₁,..., Yn N(μ,0²). State the sampling distribution of Y = n=¹_₁ Y₁. -1 i=1 n1, Σ (Υ; – Υ)2. State the sampling distribution of S² = State the mean and variance of Y and S².

Answers

1. The sampling distribution of Y is a normal distribution with mean nμ and variance nσ².

2. The mean of the sampling distribution of S² is σ², and the variance is 2σ⁴ / (n-1).

In the given notation, Y₁, Y₂, ..., Yₙ are independent and identically distributed (i.i.d.) random variables following a normal distribution with mean μ and variance σ².

1. Sampling Distribution of Y = ∑(i=1 to n) Yᵢ:

The random variable Y represents the sum of n independent normal random variables. The sampling distribution of Y is also a normal distribution. The mean of the sampling distribution of Y can be obtained by the linearity of expectation:

E(Y) = E(∑(i=1 to n) Yᵢ) = ∑(i=1 to n) E(Yᵢ) = ∑(i=1 to n) μ = nμ

The variance of the sampling distribution of Y can be obtained by the linearity of variance:

Var(Y) = Var(∑(i=1 to n) Yᵢ) = ∑(i=1 to n) Var(Yᵢ) = ∑(i=1 to n) σ² = nσ²

Therefore, the sampling distribution of Y is a normal distribution with mean nμ and variance nσ².

2. Sampling Distribution of S²:

The random variable S² represents the sample variance calculated from a sample of n observations. The sampling distribution of S² follows a chi-square distribution with (n-1) degrees of freedom.The mean of the sampling distribution of S² is given by:

E(S²) = σ²

The variance of the sampling distribution of S² is given by:

Var(S²) = 2σ⁴ / (n-1)

Therefore, the mean of the sampling distribution of S² is σ², and the variance is 2σ⁴ / (n-1).

To know more about Mean refer here:

https://brainly.com/question/15323584#

#SPJ11

How does sample size affect determinations of statistical significance? The _________ the sample, the ________.
a. larger; greater probability that the variable has an effect
b. smaller; greater probability that the variable has an effect
c. larger; the more confident you can be in your decision to reject or retain the null hypothesis
d. smaller; the more confident you can be in your decision to reject or retain the null hypothesis

Answers

The larger; the sample, the greater probability that the variable has an effect. The correct option is (a).

When it comes to determining statistical significance, a larger sample size increases the statistical power of the analysis.

This means that with a larger sample size, there is a greater probability of detecting a true effect or relationship between variables.

This is because a larger sample size provides more information and reduces the impact of random variability.

Option (a) correctly identifies that a larger sample size leads to a greater probability that the variable has an effect. With a larger sample size, the analysis has more statistical power to detect and accurately estimate the effects or relationships being investigated.

A larger sample size also increases the precision of the estimates and reduces the sampling error, making the results more reliable and representative of the population. It allows for more accurate inference and increases the confidence in the findings.

Therefore, option (c) is also partially correct, as a larger sample size provides more confidence in the decision to reject or retain the null hypothesis.

In summary, a larger sample size improves the ability to detect effects and increases the confidence in the statistical analysis and decision-making process. The correct option is (a).

To know more about "Sampling error" refer here:

https://brainly.com/question/30765764#

#SPJ11

The graph shows the function f(x) = |x – h| + k. What is the value of k?

Answers

The calculated value of k is -2.5

How to determine the value of k?

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

The graph

(see attachment)

Also, we have

f(x) = |x - h| + k

From the graph, we have the vertex to be

(h, k) = (1, -2.5)

By comparison, we have

k = -2.5

Read mroe about functions at

https://brainly.com/question/27915724

#SPJ1

∫ x 11
30(− x 10
3
−5) 4
dx 5
1
(− x 10
3
−5) 5
+C b) 5
1
(− x 10
3
−5) 5
x+C (− x 10
3
−5) 4
x+C d) 4
1
(− x 10
3
−5) 4
+C

Answers

The correct option that represents the antiderivative of the given integral ∫ [tex](x^{11}/(30(-x^{10}/3 - 5))^4) dx[/tex] is option c)[tex](-x^{10}/3 - 5)^5/(5(-x^{10}/3 - 5)^5) + C.[/tex]

To find the antiderivative of the given integral ∫ [tex](x^{11}/(30(-x^{10}/3 - 5))^4)[/tex]dx, we can simplify the expression inside the integral first.

Let's rewrite the integral as ∫ [tex](x^{11}/(30(-x^{10}/3 - 5))^4)[/tex] dx.

Now, let [tex]u = -x^{10}/3 - 5.[/tex] Taking the derivative of u with respect to x, we get:

[tex]du/dx = -10/3 * x^{(10/3 - 1)}[/tex]

[tex]= -10/3 * x^{(7/3)}[/tex]

Next, we can rewrite the integral in terms of u:

∫ [tex](x^{11}/(30(-x^{10}/3 - 5))^4) dx[/tex] = ∫ [tex](x^{11}/(30u)^4) dx.[/tex]

Substituting u and du into the integral, we get:

∫ [tex](x^{11}/(30u)^4) dx[/tex] = ∫ [tex](x^{11}/(30(-x^{10}/3 - 5))^4) dx[/tex]

= -∫[tex](1/(30u)^4) du.[/tex]

Now, we can simplify further:

-∫[tex](1/(30u)^4) du[/tex]= -∫ [tex](1/(30(-x^{10}/3 - 5))^4) du[/tex]

= -∫[tex](1/(30(-x^{10}/3 - 5))^4) (-10/3 * x^(7/3)) dx[/tex]

= 10/3 ∫ ([tex]x^{(7/3)}/(30(-x^{10}/3 - 5))^4) dx.[/tex]

Finally, we can simplify the expression inside the integral:

10/3 ∫[tex](x^{(7/3)}/(30(-x^{10}/3 - 5))^4) dx[/tex] = [tex](10/3) * (-(x^{10}/3 + 5))^5/5 + C[/tex]

[tex]= (-1/3) * (-(x^{10}/3 + 5))^5 + C.[/tex]

To know more about integral,

https://brainly.com/question/31055649

#SPJ11

Complete question:

Solve the following integrals:

∫ x 11 30(− x 10 3 −5) 4 dx 5 1 (− x 10 3 −5) 5 +C

b)∫ 5 1 (− x 10 3 −5) 5 x+C (− x 10 3 −5) 4 x+C

d)∫ 4 1 (− x 10 3 −5) 4 +C

Jacobi wants to install an underground sprinkler system in her backyard the backyard is rectangular with side length 17 m and 26 m .the water pipe will run diagonally across the yard about how many metres of water pipe does Jacobi need .

Answers

The length of the pipe required would be 31.06 meters

The length of the pipe is the hypotenus of the triangle formed :

hypotenus = √opposite² + adjacent²

substituting the values into our equation:

length of pipe = √17² + 26²

length of pipe = √965 = 31.06

Therefore, the length of the pipe needed is 31.06 meters

Learn more on length : https://brainly.com/question/2217700

#SPJ1

Question Find dx2d2y​ if x2+3y2=−8

Answers

By using differentiation we can find that the value of dx²d²y is 3.

The equationis x² + 3y² = -8

Differentiate both sides of the equation with respect to x: 2x + 6yy' = 0

Differentiate the above equation with respect to x again:

2 + 6(y')² + 6yy'' = 0

Substitute y' = dy/dx into the equation:

2 + 6(dy/dx)² + 6yy'' = 0

Substitute the given equation x² + 3y² = -8 into the above equation:

2 + 6(dy/dx)² - 4x = 0

Differentiate the above equation once more with respect to x:

12(dy/dx)(d²y/dx²) - 4 = 0

Solve for d²y/dx²:

12(dy/dx)(d²y/dx²) = 4

Divide both sides by 12:

(dy/dx)(d²y/dx²) = 4/12

Simplify:

(dy/dx)(d²y/dx²) = 1/3

Therefore, the value of d²y/dx² is 1 divided by 3 times the derivative of y with respect to x.

learn more about Derivative here:

https://brainly.com/question/25324584

#SPJ4

Decide which of the following properties apply to the function. (More than one property may apply to a function. Select all that apply.) y = ln x The function is one-to-one. The domain of the function is (-0, 00). The function is a polynomial function. The graph has an asymptote. The function is increasing on its entire domain. The function is decreasing on its entire domain. The function has a turning point. The range of the function is (-00,00). 

Answers

The function y = ln x is a logarithmic function with a natural base, where the independent variable (x) is the argument of the logarithm and the dependent variable (y) is the exponent to which e (Euler's number) is raised to obtain the argument.

The function is one-to-one: A one-to-one function is a function where every distinct input has a distinct output, which means that there are no repeated values of f(x) on its domain.

If we graph the function, we can see that there is only one value of the function for each value of x, so it is a one-to-one function.The domain of the function is (-0, 00): The domain of a function is the set of all possible input values (x) for which the function is defined.

The logarithmic function is only defined for positive values of x, so the domain of ln x is (0, ∞).The function has an asymptote: An asymptote is a line that the graph of a function approaches but never touches.

The graph of y = ln x has a vertical asymptote at x = 0 because the function is undefined at x = 0, but approaches negative infinity as x approaches 0 from the right.

To know more about independent visit:

https://brainly.com/question/27765350

#SPJ11

Solve the following LP model using graphical method: Maximize Z=x−2y
s.t.


x−y≥0
x+2y≤4
x≥0
y≥−1

Answers

The optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2. To solve the given linear programming (LP) model using the graphical method, we need to graphically represent the feasible region and find the optimal solution by maximizing the objective function.

Step 1: Graph the Constraints

We start by graphing each constraint individually on a coordinate plane.

The first constraint is x - y ≥ 0, which represents the line y = x. We can draw this line on the plane.

The second constraint is x + 2y ≤ 4. To graph this, we can rewrite it as 2y ≤ -x + 4 and then solve for y, which gives y ≤ (-1/2)x + 2. We can plot this line on the graph as well.

The third constraint x ≥ 0 represents the x-axis, and the fourth constraint y ≥ -1 represents the horizontal line y = -1.

Step 2: Identify the Feasible Region

The feasible region is the area where all constraints are satisfied. It is the intersection of the shaded regions formed by the constraints.

Step 3: Identify the Optimal Solution

To find the optimal solution, we need to maximize the objective function Z = x - 2y. The objective function is represented by a line with a positive slope.

By sliding the objective function line parallel to itself from left to right or right to left, we can observe the points of intersection between the objective function line and the feasible region. The point that gives the maximum value of Z within the feasible region is the optimal solution.

Step 4: Determine the Optimal Solution

By visually inspecting the graph, we can see that the objective function line will intersect the feasible region at the corner point (2, 0). This is the optimal solution for the given LP model.

Therefore, the optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Other Questions
Part 1: After learning Philosophical Taoism, pick the Taoist concept that you think would be the most helpful to you in your life right now, or reflects your own personal philosophy.uselessnessnaturalness and spontaneitynon-actionintuitiontransmutabilitythe "uncarved block"Directions: Create an interesting and catchy TITLE! Please don't label it DB 3....let's get more creative!!Explain why you selected this concept above all others.Explain how you think this could be helpful to you (or others) now or in the future in terms of living a better life, finding peace or happiness?Explain how you might experience this concept or state of being in your life? I.e. give and example of how this concept could apply to a real modern situationIs this practice at odds with our culture and societal norms/beliefs or values?Part 3: Chapter from the Tao te Ching (pick your favorite "chapter") Theer are 81 very short chapters.After exploring some of the chapters of the Tao Te Ching online, find one chapter that you find particularly interesting and discuss the ideas. Make sure you include the number of the chapter and post all of the text from your chapter in the post.Explain how the text of your selected chapter reflects the ideas of Taoism. For example, if the chapter mentions "The Tao" specifically, then you would want to explain what that means. Other concepts that will come up are "wu wei" and "yin and yang." Explain to students, why you picked this chapter and how you believe it reflects one of the Taoist concepts this week consider how sociological researchers would investigate a (public) issue, and address the following:What question might researchers pose?What data might they attempt to gather to address this question and hypothesis?What type of study would this be? A contour map is shown for a function f(x,y) on the rectangle R=[3,6][1,4]. a. Use the midpoint rule with m=2 and n=3 to estimate the value of Rf(x,y)dA. b. Estimate the average value of the function f(x,y). fave Hint The graph shows the function f(x) = |x h| + k. What is the value of k? Q. 2 If the surface tensions of water and benzene at 20 C are 72, 28.8 dyne/ cm respectively. Find the interfacial tension? If the surface tensions of HO and C8H15OH at 20 C are 72, 17.0 dyne/ cm respectively while the interfacial tension was 10.7 dyne / cm. Calculate (i) cohesion work of C8H15OH (ii) adhesion work between HO and C8H15OH (iii) Predict if the C8H15OH will spread on the water surface or No Jacobi wants to install an underground sprinkler system in her backyard the backyard is rectangular with side length 17 m and 26 m .the water pipe will run diagonally across the yard about how many metres of water pipe does Jacobi need . Let Y,..., Yn N(,0). State the sampling distribution of Y = n=_ Y. -1 i=1 n1, (; )2. State the sampling distribution of S = State the mean and variance of Y and S. Make at least 3 suggestions according to the SWOT-PESTLE analysisin IT department How does sample size affect determinations of statistical significance? The _________ the sample, the ________.a.larger; greater probability that the variable has an effectb.smaller; greater probability that the variable has an effectc.larger; the more confident you can be in your decision to reject or retain the null hypothesisd.smaller; the more confident you can be in your decision to reject or retain the null hypothesis In the Project Opportunity Assessment, the first question is the aim of all questions.True/FalseA problem statement is an unstructured set of statements that describes the purpose of an effort in terms of what problem its trying to solve.True/False Show that the communalities in a factor analysis model are unaffected by the transformation A = AM Ex. 5.3 Give a formula for the proportion of variance explained by the jth factor estimated by the principal factor approach. He _____________ snacks most of time he is travelling. a. ate b. eaten c. eating d. eats 4500-p 4 The demand equation for a product is found to be a = price of the product in dollars and q is the quantity. a. Find the price elasticity of demand when the price is $40. b. Is the demand el Write a short two-page paper on ""blood diamonds"" and/or ""ethical diamonds."" Define each and explain the positives and negatives for this social sustainability issue. What should be the role of diamond producers? What is the role of operations managers in this industry? howto solve8. Consider the following elementary reactions (process) I) CO (g) + Cl2 (g) COCI2 (g) II) HCII (g) HCI (g) + 1 (g) What is the molecularity of each reaction and write the rate law expression Snow fields and glaciers have high ____________ and reflect 80to 90 percent of sunlight. Question A2 Square planar metal complexes typically undergo ligand substitution via an associative mechanism, due to their low coordination number. Below is a series of ligands listed in terms of the Part 2: Short answer questions. There are 5 questions each worth 2 marks. The total mark for Part 2 is 10 marks. n databases, derived attributes are often not represented. Give two reasons why you would include derived attributes in a database? Enter your answer here Of course Sir. We .......................................... the denim you are looking for. lim (x,y)(0,0)x 2+y 29xy= A. 1 B. 1 C. 0 D. E. does not exist mevcut deil