exercise 3.3 let x be an element of the standard form polyhedron p {x e i ax = b, x o}. prove that a vector d e rn is a feasible direction at x if only if ad = 0 and di 0 for every i such that xi = o.
Answers
Vector d is a feasible direction at x if and only if ad = 0 and di is not equal to 0 for every i such that xi = 0.
To prove that a vector d is a feasible direction at x if and only if ad = 0 and di is not equal to 0 for every i such that xi = 0, we need to show both the implications.
First, let's assume that d is a feasible direction at x. This means that there exists a positive scalar t such that x + td also satisfies the constraints of the polyhedron. Therefore, we have:
(ax + tad) = b
ax + tad = b (since a is a row vector)
ad.t = 0 + 0 + ... + 0 (sum over all i such that xi = 0)
Since ad.t = 0, we can conclude that ad = 0, because t is a positive scalar. Moreover, since x + td satisfies the constraints of the polyhedron, we have ax + ad.t = b, which implies that ax = b. Thus, di must be non-zero for every i such that xi = 0, because otherwise ad would be zero.
Now, let's assume that ad = 0 and di is not equal to 0 for every i such that xi = 0. We need to show that there exists a positive scalar t such that x + td satisfies the constraints of the polyhedron. Let J be the set of indices such that xi > 0 and K be the set of indices such that xi = 0.
Since ad = 0, we can write d = (dJ, dK), where dJ is a subvector of d consisting of the components corresponding to the indices in J and dK is a subvector of d consisting of the components corresponding to the indices in K.
Since di is not equal to 0 for every i such that xi = 0, we can choose a positive scalar t such that xi + td i is greater than 0 for every i such that xi = 0. Therefore, x + td satisfies the constraints corresponding to the indices in K. Moreover, since ad = 0, we have:
(ax + ad.t)J = axJ + adJ.t = bJ
which implies that xJ + tdJ satisfies the constraints corresponding to the indices in J. Therefore, x + td satisfies all the constraints of the polyhedron, and d is a feasible direction at x.
Thus, we have shown that a vector d is a feasible direction at x if and only if ad = 0 and di is not equal to 0 for every i such that xi = 0.
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Related Questions
pleas help due to night
Answers
Answer:
72
Step-by-step explanation:
20+20+16+16=72, when they give you half of the sides, the sides opposite of it is the same.
Answer:
72
Step-by-step explanation:
When you are looking for perimeter you add all of the sides so 16+16 and 20+20 then add the sum of each side can I have brainliest please pretty please
what is a 8096 rounded to 1 significant figure
Answers
Answer:
Y Me Angry U Hungry Me And Me Angry Way Back together Me Y He Angry Me He Angry Me Angry:(
8 is the first non-zero digit leaving it the one used
A parallelogram is a four sided figure that has two pairs of parallel, opposite sides.
Answers
Given a parallelogram ABCD,
Since it is a parallelogram,
\(\begin{gathered} \bar{AB}=\bar{CD} \\ \bar{AD}=\bar{BC} \end{gathered}\)Also,
\(\bar{AB}\parallel\bar{CD}\)Therefore, the line segment parallel to CD passing through A , must fall on AB.
Guy is considering an investment that will pay $2,000 at the end of year 1; $1,500 at the end of year 2; $3,000 at the end of year 3; and, $400 at the end of year 4. rate for this investment is 6%, what would Guy be willing to pay today for this investment? If the current interest A) $6,900.00 B) $6,057.48 C) $5,989.00 D) $7,567.65 E) $7,134.54
Answers
Therefore, Guy would be willing to pay approximately $5,989.00 today for this investment based on the expected cash flows and the interest rate. The correct option is C) $5,989.00.
The formula for present value of a series of cash flows is given by:
\(PV = C1/(1+r)^1 + C2/(1+r)^2 + C3/(1+r)^3 + ... + Cn/(1+r)^n\)
Where:
PV is the present value,
C1, C2, C3, ..., Cn are the cash flows at different time periods,
r is the interest rate, and
n is the number of time periods.
In this case, the cash flows are $2,000, $1,500, $3,000, and $400, occurring at the end of year 1, year 2, year 3, and year 4, respectively. The interest rate (r) is 6%.
Substituting these values into the formula, we have:
\(PV = 2,000/(1+0.06)^1 + 1,500/(1+0.06)^2 + 3,000/(1+0.06)^3 + 400/(1+0.06)^4\)
Simplifying the expression:
\(PV ≈ 2,000/1.06 + 1,500/1.06^2 + 3,000/1.06^3 + 400/1.06^4\)
Using a calculator, we find that PV ≈ $5,989.00.
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WILL GOVE 50 POINTS AND BRAINLIEST PLZZZZZZZZZZZZZZZZZ HELP
Examine the diagram of a chloroplast.
Which choice best describes the function of the part labeled B?
enclosed space containing proteins used in ATP formation
membranes enclosing open space
layered stacks of membranes
fluid space that contains DNA, ribosomes, and other enzymes
Answers
Answer:
fluid space that contains DNA, ribosomes, and other enzymes
Step-by-step explanation:
B is points towards the "empty" space, meaning its Stroma.
Stroma defintion: involved in the synthesis of organic molecules from carbon dioxide and water or the fluid of the chloroplast surrounding the thylakoid membrane;
Let's look at the answer choices.
A. enclosed space containing proteins used in ATP formation
B. membranes enclosing open space
C. layered stacks of membranes
D. fluid space that contains DNA, ribosomes, and other enzymes
Obviously not C.
A is Synthase.
B is the whole thing.
It is D.
(BTW THIS IS MATH!! Not science!! Just in case you have more questions!)
Answer:
raw
Step-by-step explanation:
7440 divided by 60 long division show work
Answers
Answer:
124 with remainder 0 ( 124 R 0 )
Step-by-step explanation:
0124
_______
60 | 7440
0
__
74
60
___
144
120
___
240
240
___
0
Gregory's age is 5 years greater than [frac{1}{3{ Amandas age. Greogory is 17 years old. If Amandas age is denoted by x, which equation represents this situation and how old is amanda?
Answers
Answer:
36
Step-by-step explanation:
36 years
Amanda is 36 years old.
The equation formed is 17= × +5
51=+15
36=
Amanda’s age is denoted by x
Amanda is 36 years old.
112.2 in the standard form
Answers
Answer:
112
Step-by-step explanation:
Answer:
One hundred and twelve and two tenths
Step-by-step explanation:
PLSSSHELP ASAP Determine which integers in the set S:{−40, −10, 20, 40} will make the inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty false.
S:{−40, −10}
S:{−10, 20}
S:{20, 40}
S:{−40, 40}
Answers
Answer:
C) S: {20, 40}
Step-by-step explanation:
Given inequality:
\(\dfrac{1}{5}(m-5)\leq \dfrac{1}{10}(m-20)\)
To solve the inequality, multiply both sides by 10:
\(\implies \dfrac{10}{5}(m-5)\leq \dfrac{10}{10}(m-20)\)
\(\implies2(m-5)\leq m-20\)
Expand the left side:
\(\implies 2m-10 \leq m-20\)
Subtract m from both sides:
\(\implies m-10 \leq -20\)
Add 10 to both sides:
\(\implies m \leq -10\)
Therefore, the true solution set to the given inequality are values of m that are less than or equal to -10.
Therefore, the integers in the given set that make the inequality false are the values of m that are greater than -10:
S: {20, 40}Find the demand function for the marginal revenue function. Recall that if no items are sold, the revenue is 0. R'(x) = 0.06x2 – 0.05x + 152 p(x) = 0
Answers
The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
Given that,
We have to find for the marginal revenue function, locate the demand function.
Remember that the income is zero if no things are sold:
R'(x) = 0.06x² - 0.05x + 152
p(x) is what.
We know that,
MR = dTR/dx = 0.06x² - 0.05x + 152
Integrating the marginal revenue function , we get total revenue function,
MR = TR
= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x
= (0.06x³)/3 - (0.05x²)/2 + 152 x
TR = 0.02 x³ - 0.025 x² + 152 x
TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 152 x
P = ( 0.02 x³ - 0.025 x² + 152 x)/x
P = 0.02x² -0.025x + 152
Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.
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How many electrons in an atom can have each of the following quantum number or sublevel designations? (a) n -2,l-1 10 (b) 3d 28 (c) 4s 30
Answers
The maximum number of electrons that can have each of the given quantum number/sublevel designations are 10, invalid, and 30, respectively.
(a) n=2, l=-1 can't exist as l is always >=0. Therefore, the quantum number/sublevel designation is invalid.
(b) The 3d sublevel can hold a maximum of 10 electrons.
(c) The 4s sublevel can hold a maximum of 2 electrons, but when filled with 28 electrons, the 3d sublevel can hold a total of 18 electrons.
(a) The quantum number n represents the principal quantum number, which denotes the energy level of the electron. l represents the angular momentum quantum number, which determines the shape of the electron's orbital. As per the rules, l is always greater than or equal to 0. Therefore, the given quantum number/sublevel designation is invalid.
(b) In the 3d sublevel, there are five d orbitals, each of which can accommodate two electrons. Hence, the maximum number of electrons in the 3d sublevel is 10.
(c) The 4s sublevel can hold a maximum of 2 electrons, but when the 3d sublevel is filled with 28 electrons, it becomes energetically favorable for two electrons to occupy the 4s sublevel to maintain stability. Therefore, in this case, the 4s sublevel can hold a total of 30 electrons.
Therefore, the maximum number of electrons that can have each of the given quantum number/sublevel designations are 10, invalid, and 30, respectively.
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. Write an absolute value equation that represents these heights (in inches). Use h to represent the heights.
the two heights are 10in and 15in
Answers
The absolute value of the equation is "2.5".
What is absolute value?The absolute value serves as the modulus of a real number x, which can be written as |x|, and it is a non-negative value of x .
With the Closely circle on number lines , it can be deduced that both 10 and 15 were midpoints, then we can find the point as (10+150)/2 = 12.5.
Which implies that the moving from 10.5 and 15 will 2.5, hence the the distance between the poodle and the mid point is 2.5
If X suppose to be the reflection of the poodle height, then absolute value of the equation is "2.5".
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Determine the work done on this positive point charge between (i) x= 0 to x= 2nm (ii) x= 2nm to x= 4.5nm (iii) x= 4.5nm to x= 6.5nm (iv) x= 0 to x= 6.5nm
Answers
Total work done = Work done in interval (i) + Work done in interval (ii) + Work done in interval (iii). Total work done = qE * Δx(i) + qE * Δx(ii) + qE * Δx(iii)
To determine the work done on a positive point charge, we need to know the electric field and the displacement of the charge. Since you haven't provided the electric field, we'll assume it's a constant field of magnitude E.
(i) To find the work done on the charge between x=0 and
x=2nm, we need to calculate the force experienced by the charge and multiply it by the displacement. The force experienced by a positive charge in an electric field is given by F = qE, where q is the charge. The displacement is given by Δx = 2nm - 0.
The work done is given by W = F * Δx
= qE * Δx.
(ii) Similarly, for the second interval between x=2nm and
x=4.5nm, we calculate the force experienced by the charge using
F = qE, where q is the charge, and the displacement is
Δx = 4.5nm - 2nm.
The work done is given by W = F * Δx
= qE * Δx.
(iii) For the third interval between x=4.5nm and
x=6.5nm,
we use F = qE to calculate the force experienced by the charge and
Δx = 6.5nm - 4.5nm for the displacement.
The work done is given by W = F * Δx
= qE * Δx.
(iv) To find the total work done between x=0
and x=6.5nm, we sum up the work done in each interval:
Total work done = Work done in interval (i) + Work done in interval (ii) + Work done in interval (iii)
Total work done = qE * Δx(i) + qE * Δx(ii) + qE * Δx(iii)
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Total work done = Work done in interval (i) + Work done in interval (ii) + Work done in interval (iii). This calculation assumes a constant electric field of magnitude E and that the charge remains positive throughout the intervals. Hence, Total work done = qE * Δx(i) + qE * Δx(ii) + qE * Δx(iii).
To determine the total work done on a positive point charge between x-0 and x-6.5nm, we need to calculate the work done in each interval and then sum them up.
(i) For the interval between x-0 and x-2nm, the work done is given by:
Work done in interval (i) = qE * Δx(i),
where q is the charge, E is the magnitude of the constant electric field, and Δx(i) = 2nm - 0.
(ii) For the interval between x-2nm and x-4.5nm, the work done is given by:
Work done in interval (ii) = qE * Δx(ii),
where Δx(ii) = 4.5nm - 2nm.
(iii) For the interval between x-4.5nm and x-6.5nm, the work done is given by:
Work done in interval (iii) = qE * Δx(iii),
where Δx(iii) = 6.5nm - 4.5nm.
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Determine whether or not the following variable is a rank and give the units. Student ratings of a course on a 5-point Likert scale
B. The ratings are not ranks and have no units
C. The ratings are not ranks and the units are Likerts
D. The ratings are ranks and have no units
Answers
C. The ratings are not ranks and the units are Likerts.
In the context of student ratings of a course on a 5-point Likert scale, let's analyze the options further:
A. The ratings are ranks and have no units: In a ranking system, the responses would be ordered or ranked in a specific sequence. For example, if the students were asked to rank the course from best to worst, their responses would be assigned specific positions or ranks. However, in a Likert scale, the responses are not based on relative ranking but rather on levels of agreement or disagreement. Therefore, the ratings in this case are not ranks.
B. The ratings are not ranks and have no units: This option is accurate. The responses on a Likert scale do not represent ranks because they do not indicate a specific ordering or hierarchy. Each response on the 5-point Likert scale represents a different level of agreement or disagreement, rather than a rank.
C. The ratings are not ranks and the units are Likerts: This option is the most appropriate choice. Likert scales use response categories (e.g., strongly agree, agree, neutral, disagree, strongly disagree) instead of ranks. The units associated with this variable would be "Likerts" to indicate the scale used.
D. The ratings are ranks and have no units: This option is not applicable since the ratings on a 5-point Likert scale are not considered ranks.
Therefore, option C is the correct answer. The ratings on a 5-point Likert scale are not ranks, and the units associated with this variable are "Likerts" to represent the scale used.
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In the rectangular coordinate system the horizontal number line is called the.
Answers
Marcus traveled 45.5 miles in 3.25 hours. Part A How many feet did Marcus travel? (1 mile=5,280 feet)
Answers
Answer:780,780 I don't know if it is right though.....
Step-by-step explanation:
The number of feet Marcus did travel is 240240 feet.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, Marcus traveled 45.5 miles in 3.25 hours.
Here, speed = 45.5/3.25
= 14 miles per hour
We know that, 1 mile=5,280 feet
45.5 miles = 45.5×5,280
= 240240 feet
Now, 240240/3.25
= 73920 feet per hour
Therefore, the number of feet Marcus did travel is 240240 feet.
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Three more than a number j is at most 12
Answers
Answer:
j + 3 ≤ 12
Hope this helps :)
Solution, Explanation, & Check part below
Step-by-step explanation:
1. Isolate variable by doing the inverse operation which is subtracting 3 on both sides of the equation.
j + 3 ≤ 12
- 3 - 3
j ≤ 9
j can be any number that is less than 9 or equal to 9.
Check:
9 + 3 ≤ 12
12 ≤ 12
12 is equal to 12 ✓
The tower of an ancient fortress 141 feets tall and casts a shadow that is 258 feets long. What is the angle of depression that the sun makes with the ground to create the shadow?
Answers
The angle of depression that the sun makes with the ground is 28.66°
Angle depression:
In trigonometry, angle depression refers the angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given,
The tower of an ancient fortress 141 feets tall and casts a shadow that is 258 feet's long.
Here we need to find the angle of depression that the sun makes with the ground to create the shadow.
While we looking into the given question, we know that,
Height = 141 feet
Length = 258 feet.
Then as per the concept of angle of depression,
=> θ = tan⁻¹ (141/258)
When we simplify this, then we get the value of θ = 28.66.
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i will mark brainliesttt
In order to factor our polynomial must be written in ____________________.
Answers
In order to factor our polynomial must be written in a way that we will factor out the greatest common factor
What is a polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division.
A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.
To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.
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If a number is divided by 10, which number cannot be the reminder
Answers
Answer:
10
Step-by-step explanation:
from 99 to 91 give us reminder
so reminders in 91 will be 1
92 will be 2
93 will 3
and so on to the 99 will be 9
but in 100 will not be there any reminder so, 10 cannot be the reminder
Carmen has 28 a bag of markers. Each pen is 17 centimeters long. What is the combined length of pens the in meters?
Answers
If each pen is 17 centimeter long, then the combined length of pens in meters is 4.76meter.
If Carmen has 28 markers, and each marker is 17 centimeters long, then the total length of all the markers can be found by multiplying the number of markers by the length of each marker:
we get,
⇒ Total length = 28 × 17,
On Simplifying We get,
⇒ Total length = 476 centimeters
To convert this length to meters, we divide by 100,
On dividing ,
We get,
⇒ Total length = 476/100,
⇒ 4.76 meters
Therefore, the combined length of the markers is 4.76 meters.
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The given question is incomplete, the complete question is
Carmen has 28 markers in a bag, Each pen is 17 centimeters long. What is the combined length of pens the in meters?
HELP!!! WILL MARK BRAINLIEST!!! +15 POINTS!! REAL ANSWERS ONLY PLEASE!
Answers
Answer:
3rd option
Step-by-step explanation:
Answer:
it's the first option (x ≥ -4)
Step-by-step explanation:
Domain refers to the x range, which is the horizontal line. As we can that the point last touches from the left is -4 and it is a colored circle so that means that there is a line underneath. Then, it goes right so that means that x is larger and/or equal to -4.
x ≥ -4
Find the surface area of this cube
Answers
Answer:
512 in^3
Step-by-step explanation:
It would be length x height x width = AREA
8 x 8 x 8= 512 and since its 3d it will be 512^3
Which is the probability that a person goes to the movie theater _At Most_ 4 times a month?
A. 0.655
B. 0.345
Answers
Answer:
b
Step-by-step explanation:
four cards are dealt from a standard deck with 52 cards (w/o replacement), one at a time. what is the chance that a heart turns up on the fourth card, but not before? group of answer choices
Answers
The probability of getting a heart on the fourth card but not before that is 0.2278
The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.
The probability of not getting a heart in the first three cards can be calculated as follows:
(39/52) * (38/51) * (37/50) = 0.862
where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).
The probability of getting a heart on the fourth card can be calculated as follows:
13/49 = 0.265
where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).
So, the probability of getting a heart on the fourth card, but not before, can be calculated as:
0.862 * 0.265 = 0.2278
So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.
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Subtract the rational expression 1/x^2-x-6 - x/x+2.
Answers
Answer:
Step-by-step explanation:
x² - x -6 = x² + 2x - 3x - 3*2
=x(x + 2) - 3(x + 2)
= (x + 2 )(x - 3)
\(\frac{1}{x^{2}-x-6}+\frac{x}{x+2}=\frac{1}{(x +2 )(x - 3)}-\frac{x}{x + 2}\\\)
\(= \frac{1}{(x+2)(x-3)}-\frac{x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x(x-3)}{(x+2)(x-3)}\\\\=\frac{1-x^{2}+3x}{(x+2)(x-3)}\\\\\)
Suppose you have an isosceles triangle with a 90° angleIf the congruent sides each measure 9 feet, what is the length of the side across from the right angle?
Answers
Answer:
\(9\sqrt{2}\) feet
Step-by-step explanation:
Consider the attached figure.
An isosceles triangle is a triangle in which two sides are equal.
\(AB=BC=9\) feet
According to Pythagoras theorem,
square of hypotenuse is equal to sum of squares of other two sides.
\(AC^2=AB^2+BC^2\\AC^2=9^2+9^2\\AC^2=81+81\\AC^2=162\\AC=\sqrt{162}\)
\(AC=9\sqrt{2}\) feet
Find the value x 12. 1 , Not Selected 12. 4 , Not Selected Incorrect answer: 17. 6 6. 3
Answers
The value x 12. 1 is x=1 .The probability of guessing the correct answer is 12
Let's use the fact that the sum of the probabilities of all possible outcomes is equal to 1.
If the probability of guessing the correct answer is 12x, then the probability of not guessing the correct answer is 1 - 12x.
We are given that the probability of not guessing the correct answer is 32, so we can set up the equation:
1 - 12x = 32
Solving for x:
-12x = -12
x = 1
Therefore, the probability of guessing the correct answer is 12.
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The given equation has been solved in the table.
Answer option for step 2
Addition
Subtraction
multiplication
Division
Answer option for step 4
Addition
Subtraction
multiplication
Division
Answers
The operations used here are as follows:
Addition.
Division.
What are operations?The order of operations is a collection of rules that must be followed in a particular order while solving an equation.
The evaluation of any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division, is what we mean when we say "operations" in mathematics.
Here in the question,
For the 2nd step,
10 was added on both the sides of the equation.
So, addition was the property used.
For the 4th step,
3 was divided from both the sides of the equation.
So, division was the property used.
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If you spin the spinner, what is the probability of the pointer landing in the y section
Answers
Answer:
1/8
Step-by-step explanation: