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Question 1162884: N lattice points in coordinate 8-space are chosen at random. The line segments joining all pairs of these N points are drawn. What is the smallest value of N that guarantees that the midpoint of at least one of the resulting line segments is itself a lattice point?
Click here to see answer by ikleyn(52775)

Question 1163713: Cost for copies is a linear function of the number of copies. If 100 copies cost $16.00, and 75 copies cost $13.00, write a formula for copy cost as a linear function of the number of copies. Then find how much it would cost to make 800 copies.
Click here to see answer by ikleyn(52775)

Question 1163923: Let w,x,y,z be vectors and suppose z=2x+3y and w=2x−2y−z.
A. Span(y)=Span(w)
B. Span(y,w)=Span(z)
C. Span(x,y)=Span(w)
D. Span(x,y)=Span(x,w,z)
Which is the correct answer(s)?
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Question 1163945: (x/x-1)+(x+2/x-2)+(5/3)=0
Solve the equation
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Question 1164017: From the sum of -4 and 11, subtract the sum of 25 and -4

Click here to see answer by josgarithmetic(39616)

Question 1164099: A company produces boxes that are 5m long, 4m wide and 3m high. The company wants to increase each dimension by the same amount so that the new volume is twice as big. How much in centimeters is the increase in dimension.
Click here to see answer by Alan3354(69443)

Question 1164240: Value of x and YZ if Y is between X and Z knowing xY = 12, YX=2x
Click here to see answer by Edwin McCravy(20054)

Question 1164472: Subtract (9x5 +4x4-x3+3) from (4x6 - 2x4 + 13)
Click here to see answer by josgarithmetic(39616)

Question 1164529: Suppose A is a square matrix. Prove that there is a symmetric matrix B and a skew-symmetric matrix C such that A = B + C. In other words, any square matrix can be decomposed into a symmetric matrix and a skew-symmetric matrix (Proof Technique DC).
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Question 1164526: Suppose A is an invertible n × n matrix. Must the system of equations A x = x have a unique solution? Explain your reasoning.
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Question 1164667: Write an equation in slope-intercept form for the line that satisfies each set of conditions. passes through ( - 4, 2), parallel to y =12x + 5.
Click here to see answer by josgarithmetic(39616)

Question 1164525: Find the values of x, y, and z so that matrix A =
1 2 x
3 0 y
1 1 z
is invertible.

Click here to see answer by Edwin McCravy(20054)

Question 1165047: would you prefer that your salary be modeled linearly or exponentially? Give reason and explain your answer
Click here to see answer by greenestamps(13198)

Question 1165251: Solve the linear system.
3x + y + 6z = 0
−6x − 16z = 4
8y − 17z = 17
using the following steps:
(i) find the LU-factorization of the coefficient matrix,
(ii) solve the lower triangular system Ly = b, and
(iii) solve the upper triangular system Ux = y.
Click here to see answer by Edwin McCravy(20054)

Question 1165295: Suppose A and B are n × n matrices. If A and B are invertible, then A B is
invertible. Suppose one or both of A and B are singular, what can you say
about the invertibility of A B? Explain your reasoning.
Click here to see answer by Edwin McCravy(20054)

Question 1165539: Find the slope and y-intercept of the equation: -2x+y=1
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Question 1165539: Find the slope and y-intercept of the equation: -2x+y=1
Click here to see answer by MathTherapy(10551)

Question 1165603: Suppose T : R2 → R2 is the transformation that reflects vectors across the line y = x. Find the eigenvalues and eigenvectors for this transformation.
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Question 1165602: Determine whether the transformation T : R3 → R2 is a linear transformation. 􏰂
T(x)=
x1
x1+x2+x3
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Question 1165601: Let matrix Determine whether multiplication by A is a one-to-one transformation.
A = 1 -1
2 0
3 -4
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Question 1165598: Suppose u and v are orthogonal vectors in R . If ∥u∥ = ∥v∥ = 1 then find d(u, v).
Click here to see answer by ikleyn(52775)

Question 1165600: In your own words describe the geometric effect of multiplying a vector x ∈ R2 by the matrix,
􏰂 cos^2 θ−sin^2 θ −2sinθcosθ 􏰃
2 sin θ cos θ cos^2 θ − sin^2 θ
Click here to see answer by ikleyn(52775)

Question 1165795: Using the properties of the Euclidean inner product, prove the parallelogram identity, a+b∥^2 +∥a−b∥^2 =2∥a∥^2 +2∥b∥^2
Click here to see answer by ikleyn(52775)

Question 1165929: Solve the following simultaneous equations
a. 2x+3y-z= 13
x -2y+2z=-3
3x+y +z =10
b. x-3y+z = -2
x+y-2z = 4
-2x+y+z= 12
Click here to see answer by Alan3354(69443)

Question 1166344: Let f(x) = cos^2 x and g(x) = sin^2 x. Write h(x) = cos(2x) as a linear combination of {f, g}
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Question 1166491: Write the equation of the line containing (4,0) and (0,-5)

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Question 1166668: In your own words describe the effect of multiplying a vector x ∈ R2 by the (10points) matrix,
A= -3/2 0
0 1/2
Click here to see answer by ikleyn(52775)

Question 1166666: In your own words describe the effect of multiplying a vector x ∈ R2 by the matrix,
A= -3/2 0
0 1/2
Click here to see answer by ikleyn(52775)

Question 1166671: Name any two points on a horizontal line that is 9 units above the x-axis. (Enter your answers as a comma-separated list of ordered pairs.)
Click here to see answer by ikleyn(52775)

Question 1166862: If you have 5 vectors in R5 and the vectors are linearly dependent, can it always be concluded they span R5? Explain.
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Question 1166866: Suppose A is a 3 × 3 matrix and consider the set
{I3,A,A2,A3,...,A9}. Explain why this set must be linearly dependent.
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Question 1166883: Solve the system of equations by graphing:
y=−6x−15
y=3x+3

Answer:
(x,y)
=

Click here to see answer by ikleyn(52775)

Question 1166879: Its several months before Christmas - New Year’s holiday season. Wholesalers for Barako’s Distilled Spirits have been busy taking orders and will soon be making deliveries to retailers to stock their shelves for the holiday season. During the next 2 weeks, Barako’s must decide on the quantities of its two principal products to be bottled and shipped.
The firm’s vice-president of sales, Sheilla Valdez, has negotiated contracts for minimum shipments to the firm’s customers. She has also created this year an attractive promotion campaign to attract new customers. Valdez expects that, as a result of the advertising program, the company’s sales during the holiday season will come close to those of the firm’s chief rival, Don John, whose aromatic cognac has been the top choice of discriminating holiday revelers for the past decade.
The following table indicates the minimum amounts that Valdez has contracted to supply the firm’s wholesalers. It also shows the maximum amounts that she believes the firm can sell this season - provided, of course, that the bottling plant has sufficient amounts of the necessary ingredients. This table also indicates the profit margins on the two products: a relatively low-price blend, New Rhythm and a premium product - Crown Alternate.
table row cell P r o d u c t end cell cell M i n i m u m space G a l l o n s end cell cell M a x i m u m space G a l l o n s end cell cell P r o f i t space M a r g i n comma space left parenthesis P h P divided by G a l l o n right parenthesis end cell row cell N e w space R h y t h m space left parenthesis N R right parenthesis end cell cell 30 comma 000 end cell cell 80 comma 000 end cell cell 2.50 end cell row cell C r o w n space A l t e r n a t e space left parenthesis C A right parenthesis end cell cell 15 comma 000 end cell cell 40 comma 000 end cell cell 4.00 end cell end table
The two products are concoctions of Dr. M. dela Torre, research chemist at Barako’s, who is in charge of quality control. Besides a standard alcohol base, which is available in unlimited quantities, New Rhythm and Crown Alternate include a blend of two secret ingredients, which give the products their distinctive flavors and appeal. The amounts of these two ingredients (in percentage by volume) in the two products are as follows:table row cell P r o d u c t end cell cell P e r c e n t a g e space b y space V o l u m e space o f space S e c r e t space I n g r e d i e n t space A end cell cell P e r c e n t a g e space b y thin space V o l u m e space o f space S e c r e t space I n g r e d i e n t space X end cell row cell N e w space R h y t h m space left parenthesis N R right parenthesis end cell cell 2.0 end cell cell 3.0 end cell row cell C r o w n space A L t e r n a t e space left parenthesis C A right parenthesis end cell cell 1.0 end cell cell 5.0 end cell end table

The amount of the two ingredients that the company has available for blending during the production period are limited to 2,000 gallons of ingredient A and 2,500 gallons of ingredient X.

Click here to see answer by ikleyn(52775)

Question 1166880: Its several months before Christmas - New Year’s holiday season. Wholesalers for Barako’s Distilled Spirits have been busy taking orders and will soon be making deliveries to retailers to stock their shelves for the holiday season. During the next 2 weeks, Barako’s must decide on the quantities of its two principal products to be bottled and shipped.
The firm’s vice-president of sales, Sheilla Valdez, has negotiated contracts for minimum shipments to the firm’s customers. She has also created this year an attractive promotion campaign to attract new customers. Valdez expects that, as a result of the advertising program, the company’s sales during the holiday season will come close to those of the firm’s chief rival, Don John, whose aromatic cognac has been the top choice of discriminating holiday revelers for the past decade.
The following table indicates the minimum amounts that Valdez has contracted to supply the firm’s wholesalers. It also shows the maximum amounts that she believes the firm can sell this season - provided, of course, that the bottling plant has sufficient amounts of the necessary ingredients. This table also indicates the profit margins on the two products: a relatively low-price blend, New Rhythm and a premium product - Crown Alternate.
Product, Minimum Gallons, Maximum Gallons, Profit Margin(PhP/gallon)
New Rhythm, 30,000, 80,000, 2.50
Crown Alternate, 15,000, 40,000, 4.00
The two products are concoctions of Dr. M. dela Torre, research chemist at Barako’s, who is in charge of quality control. Besides a standard alcohol base, which is available in unlimited quantities, New Rhythm and Crown Alternate include a blend of two secret ingredients, which give the products their distinctive flavors and appeal. The amounts of these two ingredients (in percentage by volume) in the two products are as follows:
Product, % by volume of secret ingredient A, % by volume of secret ingredient B.
new Rhythm, 2.0, 3.0
crown alternative, 1.0, 5.0

The amount of the two ingredients that the company has available for blending during the production period are limited to 2,000 gallons of ingredient A and 2,500 gallons of ingredient X.
a. formulate lp models
b. Determine the product amounts that Barako’s should produce during the production period and the Barako’s profits. (Use Graphical Analysis)

Click here to see answer by Theo(13342)

Question 1167344: David's Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Alex's Rental Car charges an initial fee of $36 plus an additional $28 per day. For what number of days is the total cost charged by both of them the same ?
Click here to see answer by Boreal(15235)

Question 1167395: Consider the n × n matrix A where
a(ij) [ 1 if i+j is even,
[ 0 if i+j is odd.
Find the rank and nullity of A.

Click here to see answer by ikleyn(52775)

Question 1167475: How does the rank of the following matrix depend on the value of t?
(1,1,t)
(1,t,1)
(t,1,1)
Click here to see answer by ikleyn(52775)

Question 1167652: Let vector space M22 have the inner product defined as tr(UTV). Find d(A,B) where
A=
| 2 6 |
| 9 4 |
and B=
| -4 7 |
| 1 6 |

Click here to see answer by ikleyn(52775)

Question 1167651: Let vector space M22 have the inner product defined as tr(U^T V ). Find ∥A∥ Where
A=
| -4 7 |
| 1 6 |
Click here to see answer by ikleyn(52775)

Question 1167648: Define the function
⟨A, B⟩ = a11b11 + a12b21 + a21b12 + a22b22 on the vector space M22. Show this function is not an inner product.
Click here to see answer by ikleyn(52775)

Question 1167704: Let vector space M22 have the inner product defined as tr(U^T V ). Find the angle (measured in degrees) between the vectors
A=
| 2 6 |
| 1 -3 |
B=
| 3 2 |
| 1 0 |
Click here to see answer by ikleyn(52775)

Question 1167701: Let vector space P2 have an inner product defined as
⟨p, q⟩ = ∫[-1 to 1] p(x)q(x) dx
Find d(1, x)
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Question 1168007: what are the coordinates of the point where the graph of the equation x+2y=8 crosses the Y axis
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