Saturday

November 28, 2015
Number of results: 161,421

**Math**

Please help me with this problem: A bourbon that is 51 proof is 25.5% alcohol by volume while one that is 82 proof is 41% alcohol. How many liters of 51 proof bourbon must be mixed with 1.0 L of 82 proof bourbon to produce a 66 proof bourbon? Give answer to 3 decimal places. ...
*April 5, 2013 by Lorie*

**college math**

I posted this problem earlier, but I still can't figure it out. It is for extra credit. I was hoping if someone could please solve it. I would greatly appreciate it. A bourbon that is 51 proof is 25.5% alcohol by vol. while one that is 82 proof is 41% alcohol by vol. How many ...
*April 5, 2013 by Lorie*

**Philosophy**

I need help with this proof for my philosophy class. This proof is supposed to be done via indirect proof or conditional proof, so it is supposed to use AIP and IP or ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be...
*November 11, 2013 by Joy*

**Philosophy**

I need help with this proof for my philosophy class. This proof is supposed to be done via indirect proof or conditional proof, so it is supposed to use AIP and IP or ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be...
*November 11, 2013 by Joy*

**Philosophy**

I need help with this proof for my philosophy class. This proof is supposed to be done via indirect proof or conditional proof, so it is supposed to use AIP and IP or ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be...
*November 11, 2013 by Joy*

**math**

A bourbon that is 51-proof is 25.5% alcohol by volume while one that is 82-proof is 41% alcohol by volume. How many liters of 51 proof bourbon must be mixed with 1.0-L of 82 proof bourbon to produce a 66 proof bourbon? Give answer to three decimal places.
*April 4, 2013 by Lorie*

**Math**

What is wrong with the following proof. You must explain your answer in words. a>3 3a>3(3) 3a-a^2>9-a^2 a(3-a)>(3-a)(3+a) a>3+a 0>3 the problem with the proof is that the fourth step needs the sign to be reverse...but why? i looked at step 3 and there is ...
*January 26, 2008 by Wenny*

**Proof math problem help? Please help if you can!**

Let AB be the diameter of a circle, and let point P be a point on AB. Let CD be a chord parallel to AB. Prove that PA^2 + PB^2 = PC^2 + PD^2 It can be solved using geometry methods (no trig). Anyway, I figured out that PA^2 +PB^2 = 2OP^2 + 2OB^2. However, I cannot find right ...
*January 15, 2013 by Knights*

**Abstract Algebra**

If 2^n>n^2 and n>5, then 2^n+1>(n+1)^2 Proof: Assuming that 2^n>n^2 then I can say that 2*2^2>2*n^2 = 2^n+1>2n^2 If I can show that 2n^2>(n+1)^2 then I will be done by transitivity. So 2n^2>(n+1)^2? then 2n^2>n^2+2n+1? then n^2>2n+1, hence n^2-2n-...
*September 21, 2007 by Dina*

**communication**

In general, thesis or central idea is supported by claims; claims are supported by proof; and A.proof is supported by development,including details and examples B.proof is supported by the specific purpose C.proof is supported by solutions A?
*November 13, 2011 by Michelle*

**Coordinate geometry **

Our lesson coordinate geom already now analytic proof . HOW TO DO ANALYTIC PROOF ? PLEASE PLEASE HELP THANKS VERY MUCH
*February 5, 2014 by Joy*

**Math quiz**

Proof that half of 9 is 4.. uhm..it's proove instead of proof need a clue?
*September 27, 2006 by Rohit*

**math (geometry)**

how do you do this problem? If ZY=7XY then ZX=8XY It is a two colun proof
*October 23, 2006 by Troy*

**science**

when they talk about proof in regards to alcohol. how is proof determined. how do you proof alcohol.
*May 23, 2011 by DEEK*

**Coordinate Geometry: Ms.Sue or someone please help**

Hi! Can you please help me with this problem/proof? I'm not sure how to approach it. Thanks! Prove that a line perpendicular to a radius at the point where the radius meets the circle is tangent to the circle. Use coordinate geometry.Hi! Can you please help me with this ...
*October 28, 2013 by Anonymous*

**Coordinate Geometry: Ms.Sue or someone please help**

Hi! Can you please help me with this problem/proof? I'm not sure how to approach it. Thanks! Prove that a line perpendicular to a radius at the point where the radius meets the circle is tangent to the circle. Use coordinate geometry.Hi! Can you please help me with this ...
*October 28, 2013 by Anonymous*

**Proof reading**

Hello, my research paper is due Friday, and I am done with it. I need someone to proof read it and I was wondering anyone is willing to proof read 6-7 pages of text. I know thats alot to ask for, but I need a good grade on this. Is there anyone available tomorrow that think ...
*April 15, 2009 by Chopsticks*

**DISCRETE MATHS**

Prove that for every set S, Ø \subseteq( S. i need to Use vacuous proof. i know that vacuous proof is when the hypothesis is always False. but for this i find it very difficult please can you help me prove this? thanks.
*August 28, 2013 by Anonymous*

**Maths- very very simple**

can someone tell me what the title of this proof is? a^2+b^2=c^2 im writing a paper on the Pythagorean theorem and this is the proof I would use to explain it to someone but idk the name of it. PLEASE help me out here.
*February 14, 2013 by Corie*

**Language Proof and Logic(Philosophy)**

exercise 5.8 write an informal proof of Premises: LeftOf(a,b) | RightOf(a,b) BackOf(a,b) | ~Leftof(a,b) FrontOf(b,a) | ~RightOf(a,b) SameCol(c,a) & SameRow(c,b) conclusion BackOf(a,b) State if you use proof by cases.
*March 1, 2013 by Ashley*

**Math**

help please anyone? i'm having a hard time solvig these problems LOGIC CONDITIONAL PROOF. HOMEWORK HELP PLEASE!? A. 1. A -> (B -> C) 2. (C ^ D) -> E 3. -F ->(D ^ -E) / :. A -> (B -> F) B. 1. (A v B) -> -(C ^ D) 2. (-C v -D) -> (E <-> F) 3. (E <...
*January 17, 2013 by Moses*

**U.S. History**

please check this how did the Nationalists regard Shay's Rebellion? a. as proof that the states had too little power b. as an example of how governments abuse their power c. as proof that only a strong national government could prevent social disorder d. as a demonstration of ...
*January 24, 2009 by y912f*

**chem**

drbob you helped me with this problem the other day but i have a question. -i changed 500mL of ethanol to grams then to mol. i was wondering if i then used 1000mL or 500mL of water to change to kg? The "proof" of an alcoholic beverage is twice the volume percent of ethanol, ...
*February 13, 2008 by alicia*

**Philosophy**

I need help with this proof for my philosophy class. This proof is supposed to be done via conditional proof, so it is supposed to use ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be precise and the assignment is ...
*November 11, 2013 by Joy*

**Coordinate Geometry**

Hi! Can you please help me with this problem/proof? I'm not sure how to approach it. Thanks! Prove that a line perpendicular to a radius at the point where the radius meets the circle is tangent to the circle. Use coordinate geometry.Hi! Can you please help me with this ...
*October 28, 2013 by Anonymous*

**english**

when and where did Euclid write the proof of the pythagorean theorem. why did the proof was written.
*April 2, 2011 by 000*

**algebra proof**

Prove (ab)/b=a Proof 1. (ab)/b=(ab)x 1/b Is this property of reciprocal? or definition of division
*October 16, 2014 by Sweet Pea*

**Physics**

I'm trying to prove Kepler's equations the proof is in my book but I don't understand it (T1/T2)^2 = (s1/s2)^3 ok first what allows us to rewrite that formula as so??? (s1^3/T1^2)=(s2^3/T2^2) my book goes about the proof as m1 ((4 pi^2 r1)/T1^2) which I get but then where does...
*August 19, 2009 by QUESTION*

**Math/Algebra**

can someone please help me write a proof for the following: --a(-a)=a
*September 30, 2010 by SoConfused*

**math...help please!**

ok i REALLY am stumped. please help! it is a sequence problem here is the problem.... 120,60,30 __, __, __. if you could give me the rule for this problem and the next 3 numbers that would be so great!!!!!!
*September 18, 2007 by Rebekka*

**MATH**

Using the Law of Cosines for vectors, give a vector proof that if quadrilateral ABCD is a rhombus, diagonal AC bisects <BAD. As part of your proof include a carefully drawn figure a statement of what is given, and a statement of what you are proving. I need help with this. ...
*November 2, 2011 by Pam*

**English grammar**

Is it problems or problem? The possession of guns among law enforcement officials is at the core of the (problems or problem) of unnecessary force and the unwarranted killing of suspects. I appreciate all of your help. I'm just trying to proof reading a final draft. Thank you.
*April 24, 2008 by Suzi Q*

**informal Logic**

God must exist for there can be no other explanation for the order and complexity of the world. Some say there is no proof, but to me the proof is all around us. The conclusion of this argument is:
*June 12, 2015 by christopher*

**Calculus**

What is the simplest solution to the Brachistochrone problem and the Tautochrone problem involving calculus? (I know that the cycloid is the solution but I need a simple calculus proof as to why this is the case)
*May 27, 2010 by Sam*

**math help**

Thank you for helping me with the last problem Reiny and Bosnian. However, I have one more problem that I need help with please and I have no idea how work the problem. I used an on line calculator to get the answer. It didn't give an explanation on how to do the problem ...
*April 23, 2012 by Urgent Urgent Please*

**math**

can someone give me proof that a negative number times a negative number is a positive number I've always been told this in like seventh grade that it is but havne't been given any proof
*January 30, 2009 by Math*

**Pre-Calculus**

Can someone please help me with this problem? De Moivre’s theorem states, “If z = r(cos u + i sin u), then zn = rn(cos nu + i sin nu).” • Verify de Moivre’s theorem for n = 2. a. Provide a correct proof that includes written justification for each step.
*November 12, 2013 by Latrice*

**Trig Proofs**

Please Help: please solve this proof: cosx- cosy = -2sin(x+y/2)sin(x-y/2)
*April 27, 2009 by Kim*

**Logic- Formal Proof**

I need to solve a proof and I cannot figure it out. The instructions say only that I will have to use subproofs within subproofs. Premises: A or B A or C Conclusion: A or (B and C)
*November 9, 2011 by Megan*

**english**

I need someone to proof read my essay? are there any communities where i can get it proof read?
*March 20, 2009 by daniel*

**science**

The "proof" of an alcoholic beverage is twice the volume percent of ethyl alcohol, C2H5OH in water. The density of ethyl alcohol is 0.789g/ml and that of water is 1.00g/ml. A bottle of 100 proof rum is left outside on a cold winter day. a.) Will the rum freeze if the ...
*February 19, 2012 by Anonymous*

**chem**

The "proof" of an alcoholic beverage is twice the volume percent of ethanol, C2H5OH, in water. The density of ethanol is 0.789g/mL and that of water is 1.99g/mL. A bottle of 100-proof rum is left outside on a cold winter day. a) Will the rum freeze if the temperature drops to...
*February 12, 2008 by alicia*

**geometry**

1)given-AB=CD,CD=EF prove-AB-EF (in 5 steps that show why it is corect; i.e two-column proof) 2)Given-<2=<3, <4=<5 prove-<1 is supplementay to <6 (in 3 steps, with the two column proof) TWO-COLUMN PROOF LOOKS LIKE THIS.... STATEMENT: REASON: 1.AB=CD,CD=EF 1....
*November 9, 2008 by jessica*

**math- Triangle facts**

Explaining the isosceles theorem. Explain why the SAS Inequality theorem is also called the Hinge theorem. the steps for Indirect Proofs and using an indirect proof with an algebraic problem.
*February 14, 2008 by Rachel*

**math**

my topic is all about sums and differences of a rational algebraic expression this is the problem 3a/ax+ay + 2a/ax+ay another problem is a/4a+1 + 2/4a^2-7a-2 another is 3/a-b + 4/a+2b please anyone else who can answer my assignment please HELP ME!
*October 8, 2010 by jazmin*

**English**

Some ideas to write an argument about why the book 'follow the rabbit proof fence' is better than the movie 'rabbit proof fence'.
*June 27, 2012 by Ajay*

**chem**

calculate the number of grams of alcohol present in 1.70 L OF 75-Proof gin. The density of ethanol is 0.798 g/ml. Proof--> twice the % by volume of ethanol(C2H5OH) present.
*January 28, 2011 by help!*

**Math**

can you please check this problem for me, and if I happen to get it wrong. explain it? thank you =]]. -6x=54 this is the problem. -6x =54 +6 +6 x = 48 ?? is this right please respond. =]]
*January 7, 2008 by Taylor*

**Geometry**

Write a two-column proof. If point g is the centriod of triangle ABC and BG = 18. Find GE and BE. My work: ge is half so its 9. be equals 18 + 9 = 27 i need help on two column proof part
*November 27, 2015 by Anthony*

**Math logarithms**

The graph, y=lg x is rotated 90 degrees anticlockwise around the origin. What is the equation of the new graph? Please provide proof.
*April 30, 2014 by Yu*

**Geometry**

I don't know how to do this proof It is set up on a T chart In the figure below PQ = RS Prove PR=QS ______P________Q_____R________S______ Proof must be set up on a t chart starting with PQ=RS Given
*July 22, 2012 by Kim*

**math**

i need help on a proof, can anyone help? please HELP!!!! me on the difference between 3/4 and 1/3???????? You have to find the common denominator of 3 and 4, which can be 12. The first fraction becomes 9/12 and the second becomes 4/12. 9/12 - 4/12 = 5/12.
*January 2, 2007 by nicole*

**science someone please check my answers**

i just want to know if my answeres are correct! A.The problem = the main issue or subject being in vestigated in the study B.a method=a procedure, process, or approach used to investigate the problem C.a finding=a proven result obtained as a part of the investigation D.an ...
*May 12, 2010 by kayci*

**informal Logic**

God must exist for there can be no other explanation for the order and complexity of the world. Some say there is no proof, but to me the proof is all around us. The conclusion of this argument is: (Points : 1) God exists There is no other explanation of the order and ...
*June 12, 2015 by christopher*

**English **

Would someone be willing to proof read my English essay? I proof read it but I don't know if I got all the mistakes.
*June 4, 2015 by Marissa*

**Geometry**

Please help me! I have a proof that is very difficult
*December 8, 2007 by Ashley*

**Calculus I**

Show that the equation x^4 + 4x + c = 0 has at most two real roots. I believe we're supposed to prove this by proof of contradiction using Rolle's Theorem, but I'm not quite sure how to do this problem.
*March 5, 2012 by Emily*

**math**

Can someone please help me with this math problem. My teacher is looking for me to show my work, but I don't how to solve the problem to show my work. Please help!!! The problem is 2 1/2 + 3 1/4 + 3 5/8. Thank you for your help.
*August 24, 2010 by adore001*

**math**

Saying that 4<(sq.root of x)<9 is equivalent to saying what about x ? a. 0<x<5 b. 0<x<65 c. 2<x<3 d. 4<x<9 e. 16<x<81 Please help. Does this problem relate to 'x'values on the xy coordinate system ? If so please explain the concept here. If...
*July 26, 2010 by Cliff*

**chem**

An 80 proof brandy is 40.0% (v/v) ethyl alcohol. The "proof" is twice the percent concentration of alcohol in the beverage.How many milliliters of alcohol are present in 700mL of brandy?
*November 8, 2012 by tracy*

**Math**

Could someone please help me with this math problem. I am lost on trying to solve this math problem. Add. Simplify if possible. s+r/sr^2 + 2s+r/s^2r Thanks.
*May 16, 2010 by B.B.*

**Algebra II**

The problem is:Prove that the statement 1/5+1/5^2+1/5^3+...1/5^n=1/4(1-1/5^n) is true for all positive integers n. Write your proof in the space below. How do I start this? I have looked at the only example in the book but it did not help me. Any help in this would be great!!
*April 2, 2008 by Lucy*

**Algebra II**

The problem is:Prove that the statement 1/5+1/5^2+1/5^3+...1/5^n=1/4(1-1/5^n) is true for all positive integers n. Write your proof in the space below. How do I start this? I have looked at the only example in the book but it did not help me. Any help in this would be great!!
*April 5, 2008 by Lucy*

**U.S. History**

i need help with this quesiton How did the Nationalists regard Shay's Rebellion? a. as proof that the states had too little power b. as an example of how governments abuse their power c. as proof that only a strong national government could prevent social disorder d. as a ...
*January 23, 2009 by y912f*

**science,technology and the environment**

describe,compare and contrast induction and deduction as methods of science.using examples where appropriate.Identify and solve a problem using both induction and deduction.where appropriate illustrate why and how one would use experimentation and cycle of proof to solve the ...
*October 27, 2008 by adwoa*

**Calculus **

Hi there i am having some problems trying to do my calculus homework and i really need help on how to show the step to proof the volume of a sphere which is V= 4/3pirsquare. But I have to use triple integral to proof the volume of a sphere. Please help me and give me some good...
*November 25, 2009 by shylo*

**geometry**

ughh i need help i dnt like proofs we'll here it the instructions write a two column proof the segment addition postulate is useful for this proof also. remember that the transitive && substitution properties are common in proofs this one requires substitution.. given is rs=xy...
*September 24, 2009 by samm*

**Science - Chemistry**

A certain elixir is 92 proof. A proof is twice the volume percentage of alcohol in a blend. Ethanol's structural formula is CH3CH2OH with a molar mass of 46 grams/mole. The density is .79 g/ml. How many liters of elixir must one have in order to have 50 moles of carbon?
*September 29, 2011 by Ashley*

**mat115**

Please help with this math problem. The directions are Add. Must show work. 4 2/7 + 1 5/7 I appreciate your help with this math problem. Thanks so much.
*August 29, 2010 by adore001*

**4 grade math**

i need help on this problem. make 36/9 into a false number sentence? please! help me to understand this math problem thank you for your kindness.
*November 3, 2009 by samie*

**Math**

Dear Reader, Can you help me with my math problem on my homework please? There is nobody at my house who can help me yet. So when you get the chance can you help me with my problem? Thanks for reading. From, Portia1214
*March 8, 2012 by Portia*

**Science ...Urgent plz**

Describe, compare and contrast INDUCTION and DEDUCTION as methods of science – using examples where appropriate. Identity and solve a problem using both induction and deduction. Where appropriate illustrated why and how one would use experimentation/ “cycle of proof” to solve ...
*October 27, 2008 by Sheer12*

**Complex Number Proof**

Prove: If Z and W are complex numbers, then the conjugate of (Z+W) is equal to the conjugate of Z plus the conjugate of W. My thought is that this is kind of like the distributive property, but I'm not sure. It doesn't help that I haven't written a proof in over 10 years. Help...
*June 11, 2008 by Amy*

**Geometry**

I'm given a rhombus (BCDE) and I am supposed to make a proof. There is a diagonal across the rhombus from C to E. I am given that CE bisects angle BCD and BED. I am supposed to prove that BE is congruent to DE. If you could help me at least start writing the proof in list form...
*June 8, 2010 by Finn*

**Elementary Euclidean Geometry(Math)**

Little Joseph once said: I was once asked to prove that (PROOF ONE) in a right triangle, the sum of the squares of two sides equals the square of the third. Smart little rascal that I am, I proved it with ease. I was then asked to prove that (PROOF 2) if the sum of the squares...
*September 2, 2015 by Dav*

**Math Calculus**

This is all about the intermediate value theorme.. You wish to visit you sweetheart, but you don't want to go all the way over to their house if your sweetheart isn't home. What sort of "existence proof" could you do beforehand to decide whether it is worthwhile to make the ...
*September 24, 2008 by Desperate*

**math**

Please help solving this problem. Solve the following word problem: One poll reported that 48% of city residents were against building a new stadium. The polling service stated that the poll was accurate to within 3%. What is the minimum percent of city resident that oppose ...
*April 6, 2010 by bindiya farswani*

**Geometry**

Writing indirect proofs. Can someone please check for me. I am not sure If this is correct.Thanks much Given: triangle ABC angle B=120 degree Proof: Triangle A does not equal 60 degree Plan: Using an indirect proof, using the paragraph method My answer. Assume temporarily that...
*June 4, 2007 by DANIELLE*

**Analytical Proof**

The Theorum of Apollonius states in triangle ABC, if M is the midpoint of BC, then AB^2 + AC^2 = 2AM^2 + 2MC^2. Prove this theorum using analytic methods. http://www.google.com/search?hl=en&sa=X&oi=spell&resnum=0&ct=result&cd=1&q=Theorem+of+Apollonius+proof&spell=1
*December 6, 2006 by Raj*

**Please help trig proof**

((cotx+cscx)/(sinx+tanx))=cotxcscx Please prove left side equal to right side, only doing doing work on the left.
*December 16, 2013 by Potterhead*

**Algebra**

write the equation of the line passing through (-6, -9) and (0, -9). Can some one help me with this please. When I tried to solve this problem I got a slope of 0 and I do not know what to do from there I notice the y is constant, so there is zero slope. The equation of the ...
*April 26, 2007 by jessica*

**Math problem**

having problems working this problem out please solve 49 5/2
*March 11, 2012 by Lavern*

**Math**

Can you please helop with this problem? Solve this problem: -x/3 is greater than or equal to 2 Thank you
*September 7, 2010 by JulieAnne*

**math problem**

I have no clue about this problem please solve 8[-73-(-61-28)]
*January 22, 2012 by Clenisford J*

**Math**

Can someone please work out the steps in solving this elimination problem. Thank you. The problem is x + 2y = -7 x - 5y = 7
*April 17, 2014 by Tyler*

**Math 17**

What is the proof of theorem 2.23, where (b/a)+(d/c)=[(bc)+(ad)]/(ac). Thank you :)
*July 1, 2013 by Rob*

**English 1301**

I have a 1 paragraph exemplification paper that I would greatly appreciate having proof read. Can anyone help...please?
*October 28, 2010 by Tanicha*

**math**

HELP PLEASE! I don't understand how to do the problem! Please help thanks(: The problem is: your bike tire has a radius of 14 inches. If your tire makes 100 revolutions, how many feet does your bike travel? THANKS! :D
*April 25, 2012 by hannah*

**discrete math**

prove that if n is an integer and 3n+2 is even, then n is even using a)a proof by contraposition b)a proof by contradiction I'll try part b, you'll have to refresh me on what contraposition means here. Here is the claim we start with If n is an integer and 3n+2 is even, then n...
*September 27, 2006 by audryana*

**math**

please can someone help me with this problem. I am doing substitution. 3x + 4y = 0 y = x you have to substituted the y for x Then the same other problem with different number. y = x -6x + 8y = -2
*May 15, 2008 by Dj*

**math**

In this problem the letters x and y are each one digit numbers. Compare x+y O 19? Do I put any number for x and y ? please help. Your answer was no but how do I do this problem?
*September 22, 2010 by ann*

**Chemistry (again)**

I need help with this question: Suppose you bake two cakes and the the one with twice as much baking powder raises twice as much. Is this proof of the relation between concentration and reaction rate? See I know concentration has an affect on reaction rate but I am not sure if...
*April 23, 2007 by Chrissy*

**Math**

Could someone please help me with this math problem? Solve using the multiplication principle. Give the answer in set-builder notation. -4/5 less than or equal to -8x. I want to say that I multiply both sides by 5 but I'm not sure. I'm confused with this problem. Thanks.
*March 1, 2010 by B.B.*

**Math**

I am doing a scavenger hunt assigned by my sixth grade teacher and the beginning problem is 7<t please help me with the order of operations for this problem
*January 3, 2008 by Racheal*

**math problem**

having problem with this please help ∛3x+5+7=3
*March 9, 2012 by Lavern*

**math**

what is a proof of the pythagoarean theorem?
*July 14, 2011 by Chris*

**discrete math**

4m+5n^2=20 (proof by cares)
*September 12, 2015 by ben*

**English**

1. He can not solve the math problem. 2. He cannot solve the math problem. 3. He can't solve the math problem. 4. He could not solve the math problem. 5. He couldnot solve the math problem. 6. He couldn't solve the math problem. (Are they all grammatical? What about #5? Is it ...
*July 16, 2013 by rfvv*

**AP Physics**

Hello I was trying to find the proof of the formula x = x0 + v0t +.5at^2 were the zeros are subscripts My text book dosen't explain it that well. ok well it involves the formula for average velocity aver velocity = 2^-1(v0 + v) were the zero is a subscript and this is just ...
*June 13, 2009 by AP Physics*

**Math subject Calculus**

Hi there I am having some difficulties to solve this problem from my homework package and i don't understand how to approach this problem. Please help me by giving me advice on how to approach this problem. Let z = xsin(x/y), y does not equal zero. Show that the tangent plane ...
*October 24, 2009 by shylo*