The number of sides in a circle is 0.
The number of angles in a circle is 0.
What is the Radius of a circle?
Any circular object's radius is the measurement from the center to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.
It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.
The angle formed by any two-circle radii is known as the central angle. The arc length, or the distance between the two places where the two radii cross the circumference, and the radius length must be determined in order to determine the central angle.
So, we can say that:
Since a circle is made up of arcs, which form a continuous line that joins at both ends, it has no sides. The distance between each circle's component components and its center is equal. A side must have two angles, one on either side of the line, and a line.
Hence,
The number of sides in a circle is 0.
The number of angles in a circle is 0.
To learn more about Circles, visit;
brainly.com/question/23636799
#SPJ4
write code to assign x and y coordinates to currcoord, and store currcoord in locations. input first receives an x value, then a y value. input example: 12 32 88 2 -1 -1
It will be feasible to create a coordinate code that looks like this using the knowledge of the Python computational language:
Writing coordinate code in python:
def __init__(self, x, y):
self.x = x
self.y = y
def getX(self):
directly
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
class Coordinate(object):
def __init__(self,x,y):
self.x = x
self.y = y
def getX(self):
return self.x
def getY(self):
return self.y
def __str__(self):
return '<' + str(self.getX()) + ',' + str(self.getY()) + '>'
def __eq__(self, other):
if other.x == self.x and other.y == self.y:
return True
else:
return False
def __repr__(self):
return "Coordinate"+ str((self.x, self.y))
Learn more about python codes here;
https://brainly.com/question/27818319
#SPJ4
8. A table holds 4 cheese pizzas, 4 pepperoni
pizzas, and 2 supreme pizzas. How can
you write a ratio that compares part of
the pizzas to the total?
Answer: I don't know
Step-by-step explanation:
You got this pal!
What are the 3 types of solutions to a system of linear equations?.
The 3 types of solutions to a system of linear equations are Unique Solution, No Solution and Infinitely Many Solutions.
In the given question we have to find the 3 types of solutions to a system of linear equations.
The 3 types of solutions to a system of linear equations are:
(1) Unique Solution: There is only one solution to a linear equation including one variable. The one and only position at which LHS and RHS are similar on substitution is the unique solution of a linear equation.
(2) No Solution: The system of linear equations has no solution if the graphs of the linear equations are parallel. There is no point in this situation when no lines cross one another.
(3) Infinitely Many Solutions: There are infinite solutions to a 2 linear equation. There is a set of infinite solution points for the linear equation system when each equation's L.H.S changes to its R.H.S
To learn more about system of linear equations link is here
brainly.com/question/19549073
#SPJ4
If you have 675 cm? of material to make a box with a square bottom and an open top, find the largest possible volume of this box_ base edges = W height h
The largest possible volume of this box is 1687.5 cm³ with a base edge of 15 cm and a height of 7.5 cm
Let w = length of the base edge
h = height of the box
A box with a square bottom and an open top is to be made from 675 cm² of material. Hence,
675 cm² = w² + 4wh
4wh = 675 cm² - w²
h = (675 cm² - w²)/4w
The volume of the box is the product of the area of the square base and its height. Hence,
V = w²h
Substitute the expression of h to the equation of volume.
V = w²(675 cm² - w²)/4w
V = (675/4)w - (1/4)w³
To obtain the largest volume possible, the first derivative of the volume should be equal to zero.
V'(w) = 0
V = (675/4)w - (1/4)w³
675/4 - (3/4)w² = 0
Simplify and solve for the value of w.
675/4 - (3/4)w² = 0
(3/4)w² = 675/4
w² = 225
w = 15
length of the base edge = 15 cm
Solve for the value of h.
h = (675 cm² - w²)/4w
h = (675 cm² - (15)²)/4(15)
h = 7.5 cm
height of the box = 7.5 cm
Solve for the volume of the box.
V = w²h
V = (15 cm)²(7.5 cm)
V = 1687.5 cm³
Learn more about volume of rectangular prism here: brainly.com/question/23717073
#SPJ4
8.
Two airport shuttle trains leave the
main station at the same time, Shuttle
A returns to the station every 8 minutes.
Shuttle B returns to the station
every
10 minutes. In how many minutes
will Shuttles A and B leave the station
together for the second time?
Shuttles A and B leave the station together for the second time in 40 minutes.
What is LCM?The smallest number that can be divided by both numbers is known as the least common multiple (LCM) of two numbers
Given that, the two trains leave the station at the same time, but shuttle A returns every 8 minutes while shuttle B returns every 10 minutes.
To find the time when both trains will leave the station together for the second time, find the LCM of 8 and 10.
The LCM of 8 and 10 is 40.
Hence, Shuttles A and B leave the station together for the second time in 40 minutes.
Learn more about LCM:
https://brainly.com/question/20739723
#SPJ1
. the 49th parallel that separates the united states and canada is an example of what type of border?
The 49th parallel that separates the united states and Canada is an example of Antecedent border.
An antecedent border is one that existed before to the development of the cultural landscape and persisted even after inhabitants came in to occupy the surrounding region.A political border that existed before the area was occupied by the existing residents is known as an antecedent boundary. For instance, the colonists drew the border between the USA and Canada before they settled North America.Relict boundaries are historical boundaries that have been removed for political reasons but are still visible in the cultural environment. The majority of European borders are afterwards drawn, and we can see how well each one complies with major or minor divisions of natural and cultural areas.Thus this is the meaning Antecedent border.
Refer here to learn more about border: https://brainly.com/question/672409
#SPJ4
What is the equation of the line that passes through the point (-1, 3) and has a
slope of -3?
Answer:
y=-3x
Explanation:
3=-3(-1)+b
3=3+b
0=b
y=-3x
each side of a square is increased 3 inches. when this happens, the area is multiplied by 4. what is the side length of the original square?
The side length of the original square is 3.
Let s = side length of the original square
s + 3 = side length of the new square
Area of a square = s²
A = s²
A = (s+3)²
A = s² + 6s + 9
Area multiplied by 4 = 4 × s²
So,
s² + 6s + 9 = 4s²
4s² - s² - 6s - 9 = 0
3s² - 6s - 9 = 0
s² - 2s - 3 = 0
a = 1
b = -2
c = -3
s = -b ± √b² - 4ac / 2a
= -(-2) ± √(-2)² - 4(1)(-3) / 2(1)
= 2 ± √4+12/2
= 2± √16/2
= 2 ± 4/2
= 2+4/2 or 2-4/2
= 6/2 or -2/2
= 3 or -1
side length can not be negative
Therefore, s = 3
A = s²
A = (3)²
= 9
A = (s+3)²
= (3+3)²
= 36
Hence the side length of the original square is 3.
Learn more about Squares here:
brainly.com/question/25092270
#SPJ4
Which number line represents the solution set for the inequality 1/2 * x >= 4?.
The number line which represents the solution set for the inequality is second one.
What is number line?
In elementary mathematics, a number line may be a image of a graduated line that is visual illustration of the important numbers. each purpose of variety|variety} line is assumed to correspond to a true number, and each real to a degree.
Main body:
Start by solving for x.
-1/2x ≥ 4
Multiply each side by 2
-1x ≥ 8
then divide by -1....
but remember to flip your sign its a negative number.
x ≤ -8
hence, the second one is correct.
To know more about number line , visit:
https://brainly.com/question/12399107
#SPJ4
Find the Slope and Y-intercept of each line
Slope of graph is -4 and y- intercept is -8.
What is slope of graph?
In math, slope is employed to explain the gradient and direction of lines.
Main Body:
The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.
Select any two random points on the graph of the line (preferably with integer coordinates).Label them as A and B (in any order).Calculate the "rise" from A to B. While going vertically from A to B, if we have to go"up", then the rise is positive;
"down", then the rise is negative.
Calculate the "run" from A to B. While going horizontally from A to B, if we have to go"right", then the run is positive;
"left", then the run is negative.
Now, use the formula: slope = rise/run.hence slope of graph = -8/2 = 4.
And y intercept is point cutting y-axis , so it is -8.
To know more about slope of graph click on the link below
https://brainly.com/question/28135850
#SPJ1
a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. (T/F)
(F)alse
The given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes.is false.
What is a stiff equation
While integrating a differential equation numerically, one would expect the requisite step size to be relatively small in a region where the solution curve displays much variation and to be relatively large where the solution curve straightens out to approach a line with slope approaching to be zero. This is not always true in all the cases. In some cases in order for a numerical method to give a reliable solution to the differential system sometimes the step size is required to be at an very small level in a region where the solution curve is too smooth. The phenomenon is known as stiffness.
So, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.
Therefore, the given statement a stiff equation is a differential equation where some numerical solution approaches are numerically stable unless you use extremely small step sizes. is false.
To learn more about differential equations refer here
https://brainly.com/question/18760518
#SPJ4
a new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees fahrenheit and 425 degrees fahrenheit for each time, with the exception of the 90 minute - 425 degree combination. that combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. from 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. the quality of the finished product is evaluated for each roast. which of the following is true?
The explanatory variable is the quality of the finished lamb.
If the experiment is repeated, identical results will be expected.
The two cuts that are being roasted for each time-temperature combination are an example of replication.
There should be a control group (i.e. a group in which no treatment is given).
The response variable is the roasting temperature for the lamb.
The two cuts that are being roasted for each time-temperature combination are an example of replication.
Given,
In the question:
The best time-temperature combination for roasting a five-pound cut of lamb. the times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute - 425 degree combination.
Now, According to the question:
In the question it is given that From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. Here it is an act of copying the exact shape size of the lamb in all cuts, which is nothing but replication. Moreover, this replication can help in proper comparison.
which of the following is true?
Hence, The two cuts that are being roasted for each time-temperature combination are an example of replication.
Learn more about Temperature at:
https://brainly.com/question/14054025
#SPJ4
On the planet gepil, there are 6 dibble to every 10 toy. If farmer Kent ha 50 dibble on her quet farm how many yoy are on the farm your anwer may be your eaccute to the nearet tenth
If a farmer has 50 dibbles then the number of toys would be 84.
What are ratio and proportion?
A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls) One-quarter are boys, and three-quarters are girls.
For every 10 toys, there are 6 dibbles.
so for 50 dibble there will be = 10 * 50/6
= 500/6
= 83.33
≈ 84 toys
Hence, if a farmer has 50 dibbles then the number of toys would be 84.
To learn more about ratio and proportion, visit:
https://brainly.com/question/12024093
#SPJ4
Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
Answer:
Because the sum of the length of any two sides of a triangle is greater than the length of the third side
Step-by-step explanation:
Why we Cannot construct a triangle of given sides as 5 cm 5 cm and 10 cm?.
5+5=10 (not possible)
Context and sensory clues aid one in deciding whether or not something occurred. this is called __________. a. reality monitoring b. source monitoring c. misinformation effect d. source-monitoring error
Option-A is correct that is reality monitoring. One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as reality monitoring.
Given that,
One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as----
We have to fill the blank.
We know that
What is sensory context?sensory environment The auditory system adjusts to continuing, presumably irrelevant regularities in the acoustic environment in order to improve reactions to unexpected and possibly significant sounds, according to a prevalent theory in studies of sensory context.
We get,
The capacity to discern internally created information from external reality is known as reality monitoring.
Therefore, Option-A is correct that is reality monitoring. One can determine whether or not something happened with the use of context and sensory evidence. This is referred to as reality monitoring.
To learn more about evidence visit: https://brainly.com/question/16892173
#SPJ4
Is the following statement bicondional? A quadrilateral is a square if and only if it has four congruent sides and four right angles.
A) True b) False c) not enough information
The statement is true.
The quadrilateral is a square if and only if it has four congruent sides and four right angles.
Quadrilateral:
A closed quadrilateral has four sides, four vertices, and four angles. It is a type of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total interior angle of 360 degrees. The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not necessarily have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we can have different types of quadrilaterals.
To learn more about quadrilateral visit: https://brainly.com/question/13805601
#SPJ1
all of these are factors that influence whether an infant will show stranger wariness except .
All of the aforementioned are factors that influence whether an infant will show stranger wariness except: A. the infant's ability to regulate emotion.
What is stranger wariness?In Psychology, stranger wariness is sometimes referred to as stranger anxiety or stranger fear and it can be defined as any form of distress and apprehension that is typically experienced by infants (young children or babies) when they are around or within the proximity of individuals who are strange (unfamiliar) to them.
This ultimately implies that, stranger wariness simply refers to a form of distress and apprehension which an infant (young child or baby) experiences when exposed to strangers.
In this context, we can reasonably infer and logically deduce that the ability of an infant (young child or baby) to regulate emotion is not a factor that would influence whether an infant shows stranger wariness.
Read more on stranger wariness here: https://brainly.com/question/29552771
#SPJ1
Complete Question:
All of these are factors that influence whether an infant will show stranger wariness EXCEPT ______.
A. the infant's ability to regulate emotion
B. the overall temperament of the infant
C. the past experience of the infant
D. the situation in which the infant meets the stranger
15 ft
10 ft
20 ft
Find the area of the trapezoid
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=15\\ b=20\\ h=10 \end{cases}\implies A=\cfrac{10(15+20)}{2}\implies A=175~ft^2[/tex]
What do points in this app do for me?
Answer:
to post questions.
Step-by-step explanation:
The two triangles are similar, solve for x.
There are two triangles and both of them are similar, then the value of x will be equal to 4.5.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given diagram shown in the question,
Δ JKL is similar to Δ ABC.
Then,
10x + 9 = 54
Solve the equation for x,
10x = 54 - 9
10x = 45
x = 45/10
x = 4.5
To know more about an expression:
https://brainly.com/question/14083225
#SPJ1
the amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. what is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches?
80.8% of the time, the average yearly snowfall across the 25 years that were randomly chosen will be greater than 72.8 inches.
Describe the term Normal Distribution?When we are aware of the normal distribution of the data, we must utilize that normal distribution to calculate probabilities. That is, in order to determine the necessary area under the normal curve, we must use the mean and indeed the population standard deviation.As the question stated;
The z score is estimated as;
z = (x - μ)/σ
In which,
Mean μ = 70 inche
standard deviation σ = 10 inches.
n = 25
z = (72.8 - 70)/(10/√25)
z = 2.8/2
z = 1.40
Use z-score table to find the value;
P(x > 72.8 inches) = P(z > 1.40)
P(x > 72.8 inches) = 1 - P(z < 1.40)
P(x > 72.8 inches) = 1 - 0.9192
P(x > 72.8 inches) = 0.0808
Thus, 80.8% of the time, the average yearly snowfall across the 25 years that were randomly chosen will be greater than 72.8 inches.
To know more about the Normal Distribution, here
https://brainly.com/question/4079902
#SPJ4
The most intense rainfall on record was 75 mm in 2 min at Barst, Guadeloupe. At this rate, how much rain would you expect to fall in 1 h?
The amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of rainfall in 2 minutes = 75 mm
So , the amount of rainfall in 1 minute = amount of rainfall in 2 minutes / 2
= 75 / 2
= 37.5 mm
And , 1 hour = 60 min
So ,
The amount of rainfall in 1 hour = amount of rainfall in 1 minute x 60
= 37.5 mm x 60
= 2250 mm
Hence , the amount of rainfall in 1 hour at Barst , Guadeloupe is 2250 mm
To learn more about equations click :
https://brainly.com/question/10413253
#SPJ1
The number of newspapers sold decreases exponentially by x% each year.
Over a period of 21 years the number of newspapers sold decreases from 1763 000 to 58000.
Calculate the value of x.
In the exponential decrease function, the rate of decline is approximately 17.7%
Exponential FunctionAn exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828. An exponential curve grows, or decay depends on the exponential function. Any quantity that grows or decays by a fixed per cent at regular intervals should possess either exponential growth or exponential decay.
In this problem, we can write an exponential function as
58000 = 1763000(1 + x)⁻²¹
Solving for x
x = 0.1765
Converting this into percentage;
x = 0.1765 * 100 = 17.7%
The rate is 17.7%
Learn more on exponential function here;
https://brainly.com/question/2456547
#SPJ1
the difference between the squares of two numbers is 10. the difference between the two numbers is 2. what is their sum?
If the difference between the squares of two numbers is 10 and the difference between the two numbers is 2, their sum would be 5.
How to solve an equation?An equation is an expression that can be used to show the relationship between variables and numbers.
Let a and b represent the two numbers.
The difference between the squares of two numbers is 10. Hence:
a² - b² = 10
(a - b)(a + b) = 10 (1)
The difference between the two numbers is 2, hence:
a - b = 2
Substituting:
(a - b)(a + b) = 10
2(a + b) = 10
(a + b) = 5
Their sum is 5.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Cooper and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 10 apples and bananas altogether. Determine the number of apples, x, and the number of bananas, y, that Cooper bought.
Cooper bought 2 apples and 8 bananas.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = number of apples
y = number of bananas
If he bought a total of 10 apples and bananas altogether, then
x + y = 10
Rearranging, x = 10 - y (equation 1)
If each apple costs $1 and each banana costs $0.50, then the total cost of the apples and bananas he bought is $1x and $0.50y, respectively.
If he bought $6 worth of apples and bananas, then the total cost of the fruits is equal to $6.
$1x + $0.50y = $6
x + 0.5y = 6
Substitute equation 1 and solve for y.
x + 0.5y = 6
10 - y + 0.5y = 6
4 = 0.5y
y = 8
number of bananas = 8
Substitute the value of y to equation 1 and solve for x.
x = 10 - y
x = 10 - 8
x = 2
number of apples = 2
Learn more about algebraic expression and equation here: brainly.com/question/3927786
#SPJ4
What would be an appropriate way to assign digits in order to simulate flipping an unfair coin with P(H) = 0.3? *
Assign digits 1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a head. Assign 4 - 9 to be a tail.
Assign digits 0,1,2,3 to be a tail. Assign 4 - 9 to be a head.
Assign digits 0,1,2 to be a tail. Assign 3 - 9 to be a head.
Assign digits 0,1,2 to be a head. Assign 3 - 9 to be a tail
Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
Option (A) is correct.
What is probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
There are 10 chances to flip the coin.
If we assign digits 1, 2, and 3 to be as a head and if we assign 4 - 9 as a tail,
then we can get the probability of getting head
P(H) = 3/ 10 = 0.3.
Hence, Assign digits 1,2,3 to be a head. Assigning 4 - 9 to be a tail would be the most appropriate way.
To learn more about probability in statistics, visit:
https://brainly.com/question/13604758
#SPJ4
A flight from Baltimore to San Joe took 5 hour and covered 3,010 mile. What wa the plane’ average peed?
The plane's average speed is 602 miles/hour.
What is the average speed?
The overall distance the object covers in a given amount of time is its average speed. It can be calculated by:
Average Speed = (Total distance)/(Total Time)
Given, Total distance traveled = 3010 miles
Total time taken = 5 hours
Now, the average speed is given by:
average speed = (3010/5) miles/hour
= 602 miles/hour
Hence, the plane's average speed is 602 miles/hour.
To learn more about average speed
https://brainly.com/question/28538872
#SPJ4
a. conceptual warmup (25 points) think back to the navier stokes (n.s.) equations. (15 points) note: you do not need to solve the differential equation for problem. consider a thin layer of fluid flowing on a slope, as illustrated in figure. the fluid-solid interface is at y
∂v⃗ ∂t+(v⃗ ⋅∇⃗⃗) v⃗ +1ρ∇⃗ p=g. The viscosity leads to frictional forces within the fluid. Taking the viscosity into account in the Euler equation finally leads to the Navier-Stokes equation.
For the derivation of the Navier-Stokes equations we consider a fluid element and the forces acting on it. At first we will consider only the motion of the fluid in x-direction. The motion of the fluid element is influenced by the pressure forces acting on the front and back surface of the cubic volume element.
These pressure forces basically represent normal stresses and are therefore denoted in the following by the Greek symbol σ instead of p. We will see later that in addition to the pressure forces, viscosity-related forces also act perpendicular to the surfaces and contribute to the normal stress.
Learn more about Navier-Strokes equation at,
https://brainly.com/question/13388759
#SPJ4
Find the equation of the line
The linear equation on the given graph can be written as:
y = (-1/4)*x - 6
How to find the equation of the line?The general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
On the graph we can see that the line intercepts the y-axis at y = -6, then the value of b is -6, so we can write:
y = a*x - 6
To find the value of the slope we can use another point on the graph, we can see that the line passes through (-8, -4)
Replacing these values we get:
-4 = a*-8 - 6
-4 + 6 = -8a
2/-8 = a
-1/4 = a
The linear equation is:
y = (-1/4)*x - 6
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Let z* be the common (finite) optimal value of P and D. Suppose that I is a basic infeasible solution to P whose complementary dual basic solution is feasible. Is it possible that the common objective value of this pair of primal-dual basic solutions is z*? For the linear program: Minimize{x1 : 2x1 – X220, -2x1 +3x2 2-6, x>0}, consider the basic feasible solution with a basis comprised of the columns of x1 and the slack variable in the second constraint. Give the associated complementary dual basic solution. What can you say about this pair of primal-dual basic solutions?
Pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
Given that
Let z* be the common (finite) optimal value of P and D.
Suppose that I is a basic infeasible solution to P whose complementary dual basic solution is feasible.
Here, for linear program, we have to
Minimize {x1 : 2x1 - x2 [tex]\geq[/tex] 0, -2x1 + 3x2 [tex]\geq[/tex] - 6}, x1 [tex]\geq[/tex] 0
Stimulate equation 1 and equation 2:
[tex]2x_1 - x_2 = 0\\\\-2x_1 + 3x_2 = -6[/tex]
Canceling [tex]-2x_2[/tex] from both the equations, we get
[tex]2x_2[/tex] = -6
= [tex]x_2[/tex] = -3
So now,
[tex]2x_1 + 3 + S_1 = 0\\\\x_1 = -3-S_1/2[/tex]
Hence the answer is pair of primal-dual basic solutions is [tex]x_1 = -3-S_1/2[/tex].
To learn more about equations click here https://brainly.com/question/22688504
#SPJ4
