Tutors Answer Your Questions about Linear Algebra (FREE)
Question 31746: Question reads:
Write the partial fraction decomposition of the rational expression:
-x/(x+6) (x+5)
Possible Answers:
(A) 5/x+6 + -6/x+5
(B) 6/11/x+6 + -5/11/x+5
(C) -6/x+6 + 5/ X+5
(D) -6/11?x+6 + 5/11/x+5
These are a lot of numbers. Please be specific when choosing an option.Thanks!
Click here to see answer by mukhopadhyay(490)  |
Question 31750: Question:
Solve the system:
x^2+y^2=64
x+y=8
(A) {[0,0), (8,-8)}
(B) {(0,8), (8,0)}
(C) {(8,-8), (-8,-8)}
(D) {(0,-8), (-8,0)}
Thank you very much!
Click here to see answer by venugopalramana(3286) |
Question 31753: Solve the system:
x^2+y^2=63
x^2-3y^2=27
a. (3 sqrt6,3) (3 sqrt6, -3)
b. (3 sqrt 6,3) (3 sqrt6,-3) (-3 sqrt6,3) (-3sqrt6,-3)
c. (1 sqrt62) (1,-62) (-1 sqrt62) (-1 -sqrt62)
d. (-3 sqrt6,3) (-3 sqrt6,-3)
Thanks a bunch!!!!!!!!
Click here to see answer by mukhopadhyay(490) |
Question 31752: The question is:
Find all the real and complex zeros of the polynomial
x^4+8x^3+16x^2-8x-17
(A) 4, -4, 1 -2i, 1+2i
(B) 1 -1, -4 -i, -4+i
(C) none of these
(D) 1, -1, -4 -2i, -4+2i
This is conufusing- thanks for your help!
Click here to see answer by stanbon(75887) |
Question 31686: I was given a homework sheet in class and have no idea what chapter it is from. Let A be an nxn matrix and suppose that v1 and v2 are nonzero vectors in R^n that satisfy  and  . Prove that the set {v1, v2} is linearly independent.
Thank you for your help.
Click here to see answer by venugopalramana(3286) |
Question 30238: Which equation below is the quadratic equation in standard form that results when you substitute u=x^-2 into the equation x^-4 -32+ 4x^-2 ?
POssible Answers:
(a) 1/u^2 - 4/u - 32=0
(b) u^2-4u-32=0
(c) u^4-4u^2-32=0
(d) u^-2 -4u +32=0
(e) 1/ u^2 + 4/u -32 = 0
Please be specific in which is the correct answer. Thanks!
Click here to see answer by mukhopadhyay(490) |
Question 32261: Given V=R^2 with "non-standard" operations: for u=(x1,y1) and v=(x2,y2)in R^2, and c(real number),
u(+)v=[(x1^1/3 + x^2^1/3)^3, (y1^1/3 + y2^1/3)^3] and
c(*)v=(c^3*x2, c^3*y2), where (*)and(+)anr non-standard operations,
I want to prove that V form a vector space, using 10 vector space axioms. But, I can't figure out how to handle the exponents (raised to the third power) in the operations...Also, I am confused about the "non-standard"...Can I still use some real number for x and y (like x=1, y=1)and 'c' when varifying the closure of the axioms? How exactly are "standard" and "non-standard" different when using the ten vector space axioms? For 'distributive property', could I use another vector w=(x3,y3)?
Would you help me with this problem???
Click here to see answer by venugopalramana(3286) |
Question 32528: I am trying to learn proofs. Question 32261 (on the site) is one I cannot solve, but I would like to learn. Can you share the solution? I cannot find the link to the solution. Thanks!
Question 32261: Given V=R^2 with "non-standard" operations: for u=(x1,y1) and v=(x2,y2)in R^2, and c(real number),
u(+)v=[(x1^1/3 + x^2^1/3)^3, (y1^1/3 + y2^1/3)^3] and
c(*)v=(c^3*x2, c^3*y2), where (*)and(+)anr non-standard operations,
I want to prove that V form a vector space, using 10 vector space axioms. But, I can't figure out how to handle the exponents (raised to the third power) in the operations...Also, I am confused about the "non-standard"...Can I still use some real number for x and y (like x=1, y=1)and 'c' when varifying the closure of the axioms? How exactly are "standard" and "non-standard" different when using the ten vector space axioms? For 'distributive property', could I use another vector w=(x3,y3)?
Would you help me with this problem???
Click here to see answer by venugopalramana(3286) |
Question 30774: The Question Reads:
List all of the potential rational zeros of the polynomial function. Do not attempt to find the zeros.
f(x) =2x^3+x^2+3x+8
The Answers to choose are:
(A) +2, +4, +8, +1/2, +7/2
(B) +2, +4, +8, +16, +7/2
(C) 0, +1, +2, +4, +1/2
(D) +1, +2, +4, +8, +1/2
Can you please help me!
Thank you!
Click here to see answer by venugopalramana(3286) |
Question 33004: Could you help me again? For some reason the chart doesnt show here, but Im hoping you can make it out & help me solve and explain the steps along the way, so hat I may understand it better. Thank you very much. :)
Fill in the chart given this linear equation:
3x + y = 10
x y
-2
-1
0
1
2
Dee
Click here to see answer by xcentaur(357) |
Question 33006: This is a descussion question that I totally dont get. Am I suppose to graph this? How am I suppose to set up the graph so it shows on the Discussion board?
Can someone help me solve this and explain how it was achueved?
Name the coordinate described here:
From the origin, the point is five places to the right and nine places down.
Thank you very much! :)
Dee
Click here to see answer by xcentaur(357) |
Question 33013: Find the midpoint between these points:
(2, 3) and (8, 1)
Can you explain how I am to achieve this?
Also...
Can you tell me if I did this correctly?
Solve for x:
2(x + 1) > 12
My answer:
Simplify left side and right side to get:
2x + 1= 12-3
2 + 1 + x = 12
x = 9
Thank you,Thank you Thank you
Dee
Click here to see answer by stanbon(75887) |
Question 32995: Hi I have a question about Vector space
My question is the reverse question of the question in the book (Problem 17)
Find the condition that make the solution set of consistent system Ax=b (m linear equations, n unknowns) form a subspace of Rn)
Click here to see answer by khwang(438) |
Question 33660: 1)An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out.
a)Find the function V that represents the volume of the box in terms of x.
Answer
b)Graph this function.
Show Graph here
c)Using the graph, what is the value of x that will produce the maximum volume?
Answer
2)The volume of a cylinder (think about the volume of a can) is given by V = pr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.
a)Write h as a function of r.
Answer
b)What is the measurement of the height if the radius of the cylinder is 2 centimeters?
Answer
Show work in this space
c)Graph this function.
Show graph here
Click here to see answer by venugopalramana(3286) |
Question 33699: 5)Logarithms:
a)Using a calculator, find log 10000 where log means log to the base of 10.
Answer:
b)Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:
log b a = loga/logb
Using this formula, find log 10000.
Answer:
Show work in this space
Click here to see answer by Nate(3500) |
Question 34258: Problem: Is it possible for the columns of a 4x3 matrix to be linearly dependent? if so, give an example and demonstrate the dependence. If not, prove it.
I understand what linearly dependent means, but I don't know what kind of a matrix we should use to prove it without coming up with a clear example with numbers. Please help.
Click here to see answer by venugopalramana(3286) |
Question 31747: Let P (n) represent the statment 2+6+10+...+(4n-2)=2n^2
In the proof that P (n) is true for all integers n, n>1, what term must be added to both sides of P (k) to show P (k+1) follows form p(k)?
(A) 4k+2
(B) P(k+1)
(C) 4k+6
(D) 4k-2
Thank you for your assistance!
Click here to see answer by venugopalramana(3286) |
Question 34491: 3) The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by
A is the amount of returned.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the compound period.
t is the number of years.
Suppose you deposit $10,000 for 2 years at a rate of 10%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer:
Show work in this space. Use ^ to indicate the power.
b) Calculate the return (A) if the bank compounds quarterly (n = 4).
Answer:
Show work in this space
c) Calculate the return (A) if the bank compounds monthly (n = 12).
Answer:
Show work in this space
d) Calculate the return (A) if the bank compounds daily (n = 365).
Answer:
Show work in this space
e) What observation can you make about the increase in your return as your compounding increases more frequently?
Answer:
f) If a bank compounds continuous, then the formula takes a simpler, that is
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding.
Answer:
Show work in this space
g) Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).
Answer:
Show work in this space
h) A commonly asked question is, “How long will it take to double my money?” At 10% interest rate and continuous compounding, what is the answer?
Answer:
Show work in this space
4) For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4.
a) Show coordinates in this space
Show work in this space
b) Show graph here
Click here to see answer by stanbon(75887) |
Question 34572: need help with the following:
1. The table below shows the comparison of the cost, in dollars, of a $100,000 life insurance policy for female nonsmokers at certain ages
Age, a Cost, C
31 170
32 172
33 176
34 178
35 182
Model the data with a linear function using age 32 and 35.
2. Using the line in Exercise 2, predict the cost of the life insurance for a female nonsmoker of age 40.
Click here to see answer by stanbon(75887) |
Question 35914: If a system of nonlinear equations contains one equation whose graph is a circle and another equation whose graph is a line, can the system have exactly one solution? If so, describe the graph of this situation...
Click here to see answer by Prithwis(166) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760
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