Saturday

January 21, 2017
Total # Posts: 105

**Calculus (Definite Integrals - Force) Please Help**

A cylindrical oil storage tank 12 feet in diameter and 17feet long is lying on its side. Suppose the tank is half full of oil weighing 85 lb per cubic foot. What's the total force on one endof the tank?

*March 12, 2012*

**CALCULUS**

A cylindrical oil storage tank 12 feet in diameter and 17feet long is lying on its side. Suppose the tank is half full of oil weighing 85 lb per cubic foot. What's the total force on one endof the tank?

*March 12, 2012*

**Calculus (Definite Integrals - Work)**

Recall that work is defined to be force times distance, and that the weight (force) of a liquid is equal to its volume times its density. A fish tank has a rectangular base of width 2 feet and length 6 feet and sides of height 5 feet. If the tank is filled with water weighing ...

*March 12, 2012*

**Calculus (Definite Integrals - Arclength)**

Using the trapezoid rule with n = 8 to approximate the arc length of the graph of y = 2x^3 - 2x + 1 from A(0,1) to B(2,13) you get (to three decimal places): A.) 6.900 B.) 13.896 C.) 14.093 D.) 13.688 E.) 13.697

*March 12, 2012*

**Calculus**

Using the trapezoid rule with n = 8 to approximate the arc length of the graph of y = 2x^3 - 2x + 1 from A(0,1) to B(2,13) you get (to three decimal places): A.) 6.900 B.) 13.896 C.) 14.093 D.) 13.688 E.) 13.697

*March 12, 2012*

**CALCULUS**

In Seattle on September 30, the temperature hours after midnight was given by the function y=60 + 12sin((pi/x)(x-11)) What was the average temperature over the period from 8 A.M. until 10 P.M.?

*February 29, 2012*

**Calculus (Definite Integrals)**

How many definite integrals would be required to represent the area of the region enclosed by the curves y=(cos^2(x))(sin(x)) and y=0.03x^2, assuming you could not use the absolute value function? a.) 1 b.) 2 c.) 3 d.) 4 e.) 5

*February 29, 2012*

**Calculus (Area Between Curves)**

Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859

*February 29, 2012*

**Calculus (Area Between Curves)**

Thank you, I was just really unsure of my answer!

*February 29, 2012*

**Calculus (Area Between Curves)**

Find the area of the region IN THE FIRST QUADRANT (upper right quadrant) bounded by the curves y=sin(x)cos(x)^2, y=2xcos(x^2) and y=4-4x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859 Based on my calculations, I would say that the answer is e.) 0.37859. I ...

*February 29, 2012*

**math**

x = 2 5/6 or 17/6 ((5 13/21) - (2 11/14))

*February 29, 2012*

**Calculus (Area Between Curves)**

I got the same thing. Working out the other answers, they were either negative or obviously too large of an area for the given bounds, thank you Nade!

*February 29, 2012*

**Calculus (Area Between Curves)**

Find the area of the region bounded by the curves y=x^(-1/2), y=x^(-2), y=1 and y=3. You get: a.) 1/2(sqrt(3)) + 4/3 b.) 2(sqrt(3)) - 8/3 c.) 1/2(sqrt(3) - 32/3 d.) 2(sqrt(3)) - 32/3 e.) 8/3 - 2(sqrt(3))

*February 29, 2012*

**logic application**

4, 5, and 9. This way, you have all five odd numbers and 4+5+9=18 and 4+6+8=18 are of equal sums. Is this what you were looking for?

*February 29, 2012*

**Calculus (Area Between Curves)**

Thank you Nade for making this correction! I went back and graphed the functions with pencil to see if I could figure a rough estimate for the area. I found that these function make an odd trapezoid shape. The area of the solid trapezoid portion of the graph is 15 and then ...

*February 29, 2012*

**Calculus (Area Between Curves)**

Find the area of the region bounded by the curves y^2=x, y-4=x, y=-2 and y=1 (Hint: You'll definitely have to sketch this one on paper first.) You get: a.) 27/2 b.) 22/3 c.) 33/2 d.) 34/3 e.) 14

*February 29, 2012*

**Calculus (Antiderivatives)**

Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the above

*February 18, 2012*

**Calculus (Integrals)**

Evaluate the following expression: d/dx (integration sign: upper=1 and lower= -3) (2t^3 + 3)dt = I am given the following options: 2t^3 + 3 56 5 -28.0 None of the above

*February 15, 2012*

**Calculus (Integrals and Derivatives)**

Evaluate the following expression: d/dx (integration sign: upper=1 and lower= -3) (2t^3 + 3)dt = I am given the following options: 2t^3 + 3 56 5 -28.0 None of the above Would the result of the expression be 0 or 5???

*February 15, 2012*

**Calculus**

Evaluate the following expression: d/dx (integration sign: upper=1 and lower= -3) (2t^3 + 3)dt = I am given the following options: 2t^3 + 3 56 5 -28.0 None of the above Would the result of the expression be 0 or 5???

*February 15, 2012*

**Calculus (Antiderivatives)**

Thank you for the apology, no hard feelings!

*February 11, 2012*

**Calculus (Antiderivatives)**

Please, if you don't have anything helpful to contribute, save both of us some time. Please, this problem is really getting to me and I don't want any jokes or non-serious answers, thank you.

*February 11, 2012*

**Calculus (Antiderivatives)**

What is the antiderivative of the followring expression? x^(-1/2) sin(2x^(-3/2)) After trying to figure out this problem, I have the suspicion that the antiderivative cannot be found using substition method, would this assumption be correct?

*February 11, 2012*

**Calculus (Antiderivatives)**

What is the antiderivative of the following expression? 3x(x^2 + 7)^3

*February 11, 2012*

**Calculus (Antiderivatives)**

What is the antiderivative of? (x^2 - 4) / (x - 2)

*February 10, 2012*

**7th grade Lang. Art**

Tamper Both meddling and tampering concern getting involved where you are not supposed to.

*February 8, 2012*

**Physics**

Okay, I figured this was the answer. Not to mention, mathematically, the calculation would be W = (10)(9.8)(cos90)(10) But, cos90 = 0, so the calculation shows that the man does 0 J of work. If the question had concerned him picking up the sack vertically, then work would have...

*February 8, 2012*

**Physics**

A man carries a 10 kg sack of groceries in his arms with a force of 50 N as he walks forward a distance of 10 m. How much work has he done? Is this a trick question?

*February 8, 2012*

**business math**

I don't think your entire question was posted.

*February 8, 2012*

**Calculus (Parts A and B done, just help with C)**

I did notice this when I took the derivative for part A of the volume. But it seemed too simple to just plug in this value, I wanted to make sure that I was certain about the placement. Thank you!!!

*January 17, 2012*

**Calculus (Parts A and B done, just help with C)**

The radius, r, of a sphere is increasing at a constant rate of 0.05 meters per second. A. At the time when the radius of the sphere is 12 meters, what is the rate of increase in its volume? B. At the time when the volume of the sphere is 36pi cubic meters, what is the rate of ...

*January 17, 2012*

**Calculus**

A piece of elastic is attached to two nails on a flat board, with a button attached to the midpoint of the elastic. The nails are 5 cm apart. You stretch the elastic by pulling the button along the board in a direction that is perpendicular to the line between the nails. A. ...

*January 15, 2012*

**Calculus ~ Related Rates**

A man 2 meters tall walks at the rate of 2 meters per second toward a streetlight that's 5 meters above the ground. At what rate is the tip of his shadow moving?We've already set this up part of the way. We know that dx/dt = - 2 meters per second, and we're looking...

*January 5, 2012*

**Calculus (Tangent Line Approximation - EDIT)**

Just wanted to make one more clarification, the equation is supposed to be (1 + x)^n.

*December 22, 2011*

**Calculus (Tangent Line Approximation)**

Use tangent line approximation to derive an estimate for (1 + x)n , when x is near 0, and n is any real number.

*December 22, 2011*

**Calculus (Normal Line, please check my work)**

I think I may be understanding what you are saying. So, to put this in very simple turns, rather than assuming that -1 / (4/0) was just undefined, I should have taken it out farther; for example, dividing by a fraction is the same as multiplying by its reciprocal, which would ...

*December 17, 2011*

**Calculus (Normal Line, please check my work)**

I apologize if I seem like I don't understand what you are trying to explain, but you have really confused me on what I thought was a more simple problem. I would really appreciate it if you could check my original answer using differentiation, instead, as this is the ...

*December 17, 2011*

**Calculus (Normal Line, please check my work)**

Where did you get infinity? Using differentiation, I found that: dy/dx = (-4cosx) / (9(-siny)) When I put (pi, 0) into this equation, the denominator is 0, making the slope of the tangent line undefined. And since the slope of the normal line is -1/(slope of the tangent line...

*December 17, 2011*

**Calculus (Normal Line, please check my work)**

Using strictly the derivative (because wolfram isn't working for me), how can you prove that the slope of the normal line is 0?

*December 17, 2011*

**Calculus (Normal Line, please check my work)**

For the tangent line at (pi, 0), I find that the slope is 4/0, which is undefined. So, wouldn't this make the slope of the normal line undefined as well??? Did I miss something?

*December 17, 2011*

**Calculus (Normal Line, please check my work)**

The slope of the line normal to the graph of 4 sin x + 9 cos y = 9 at the point (pi, 0) is: Derivative: 4cosx - 9siny(dy/dx) = 0 (dy/dx) = (-4cosx) / (-9siny) (dy/dx) = (4) / 0 Normal line = -1 / (4/0) Does this mean that the slope of the normal line is undefined, or did I do ...

*December 17, 2011*

**Calculus**

Find the point on the graph of y = x^2 + 1 that’s closest to the point 8, 1.5. Hint: Remember the distance formula.

*December 16, 2011*

**Calculus (Optimization)**

Nevermind, that 4.42 was a mistake and my very original answer of 1.105940354 was absolutely correct!!! This is the right answer, I know it!

*December 16, 2011*

**Calculus (Optimization)**

Okay, so does this change my original answer of approximately 1.64 to 4.42??? The 4.42 came from putting your new values in the quadratic equation.

*December 16, 2011*

**Calculus (Optimization)**

Now I'm lost, I don't get why you changed the signs.

*December 16, 2011*

**Calculus (Optimization)**

I rechecked and found that 3x^2-22x+28 has the correct signs. Knowing this equation and the values I found from the quadratic equation, would you say that the 1.639079157 term is correct? (The 2.69 square inches came from squaring the 1.639079157).

*December 16, 2011*

**Calculus (Optimization)**

I think that you might have gotten the equation wrong, I think that it should be: 3x^2 - 22x + 28. When I put this equation into the quadratic equation, I got 5.694254177 and 1.639079157. So the squares that need to be cut out should have an area of approximately 2.69 square ...

*December 16, 2011*

**Calculus (Optimization, Still Need Help)**

I just wanted to correct something for my equation, it should be: V = (14 - 2x)(8 - 3x)(x), which simplifies to V = 112x - 44x^2 - 4x^3. Take the derivative: V' = 112 - 88x - 12x^2 Now all I need are the roots, any help? I think I found one around 1.10594, possibly?

*December 16, 2011*

**Calculus (Optimization)**

A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a small square from each corner and bending up the sides. What size square should be cut from each corner for the box to have the maximum volume? So far I have: V = (14 - 2x...

*December 16, 2011*

**Calculus**

Pretty sure I figured it out, 4/27. I found this by simplifying: ((1/3pi (h - 2/3 h))(4/9 r^2)) / (1/3 pi r^2 h)

*December 16, 2011*

**Calculus**

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible volume, what fraction...

*December 16, 2011*

**Calculus (Optimization)**

Both of you, thank you very much!!! I arrived at the correct answer width = 18 and length = 36, but I just got that answer by chance and wasn't sure how I could prove (mathematically) that it was indeed correct, your explanations helped tremendously!

*December 16, 2011*

**Calculus (Optimization)**

The U.S. Post Office will accept a box for shipment only if the sum of the length and girth (distance around) is at most 108 inches. Find the dimensions of the largest acceptable box with square ends.

*December 16, 2011*

**Physics (Really need help with this)**

An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion. a. What is the period and frequency of the pendulum’s motion? b. How many seconds out of phase with the displacements shown would graphs of the ...

*December 12, 2011*

**Physics (Please Help)**

An astronaut lands on an alien planet. He places a pendulum (L = 0.200 m) on the surface and sets it in simple harmonic motion. a. What is the period and frequency of the pendulum’s motion? b. How many seconds out of phase with the displacements shown would graphs of the ...

*December 12, 2011*

**Calculus**

True or False: Consider the following statement: A differentiable function must have a relative minimum between any two relative maxima. Think about the First Derivative Test and decide if the statement is true or false. I want to say that its true and that the question is ...

*December 10, 2011*

**Calculus**

Nevermind, I figured it out. Since the function is odd it must be symmetric about the origin, so: concave up: -5 < x < -3 and 0 < x < 3 and x > 5 concave down: x < -5 and -3 < x < 0 and 3 < x < 5

*November 19, 2011*

**Calculus**

Suppose you know that f(x) is an odd functon on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5. List ALL intervals on which the functon f(x) is concave up and ALL...

*November 19, 2011*

**Spanish**

I would just like to know if these sentences are grammatically sound. Esta es la receta para empanadas de pera de Chile. Estos son los ingredientes: Dos tazas de peras secas Dos tazas de agua Tres cuartos tazas de azucar Una cucharilla de canela Una cucharilla de clavo Dos ...

*November 18, 2011*

**Calculus (Continuity and Differentiability)**

I think that I may have confused you about the graph that I am dealing with. I know that if a corner is present in an original function, then it will not be differentiable at that point. I thoroughly understand this point. Now, the graph that I am given is the graph of the ...

*November 12, 2011*

**Calculus (Continuity and Differentiability)**

Okay, perhaps I shouldn't have given a function to work with. This proble does not given me a function, just a graph of a derivative. This graph has two straight sections, one going downward from the top left and the other increasing toward the top right. These segments ...

*November 12, 2011*

**Calculus (Continuity and Differentiability)**

Alright, I think I'm getting it more now. So, the function is in fact continuous at all points? But is it also differentiable at x = 2? Since I am given the graph of the derivative and x = 2 does produce a value, would it be considered differentiable? I also know that if I...

*November 12, 2011*

**Calculus (Continuity and Differentiability)**

Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it possible, impossible, or certain that the function...

*November 12, 2011*

**Find the Zeros (Thank you!)**

Thank you Damon. The first time I posted this question, someone gave me the answer 3.1216 for the positive zero. But when I double-checked the answer, it didn't work correctly. I figured something was up and wanted to clarify the answer. 3.161593987 works beautifully in ...

*November 11, 2011*

**Find the Zeros**

Find the three zeros for the following function on the interval -5 </= x </= 5 (1 + 50sin(x)) / (x^2 + 3)

*November 11, 2011*

**Calculus**

How did you come up with 3.1216 positive. I've tried to come up with this number but I can't figure it out. Also, it doesn't make 1 + 50 sin(x) = 0.

*November 11, 2011*

**Calculus**

Thank you, this helps tremendously!

*November 11, 2011*

**Calculus**

Find the three zeros for the following function on the interval -5 </= x </= 5 (1 + 50sin(x)) / (x^2 + 3)

*November 11, 2011*

**Calculus (Derivatives)**

Show the steps to get the derivative function of -500/x by evaluating the limit. By limit, they are referring to the equation, lim h -> 0 (f(x + h)-f(x))/h

*November 9, 2011*

**Calculus**

Okay, I know that the derivative functon of the function -500/x is 500/x^2, but I am having a hard time getting to this result using limit notation. Could someone show or explain the steps used in limit notation to get the derivative of 500/x^2?

*November 9, 2011*

**Calculus (Derivatives)**

Using the product rule, find the derivative of the following function: (x^1/2 cscx sinx).

*November 7, 2011*

**Calculus (Derivatives)**

Okay. So, 500/x^2 would be the simplified equation for the derivative, and from here I can figure that the limit is 5,000,000 as h approaches 0. Is this correct?

*November 1, 2011*

**Calculus (Derivatives)**

What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...

*November 1, 2011*

**Calculus (Derivatives)**

Two particles are moving in straight lines. The displacement (in meters) of particle 1 is given by the function e^(4cos(t)) , where t is in seconds. The displacement (in meters) of particle 2 is given by the function -(t^3)/(3) - (t^2)/(2) + 2 , where t is in seconds. Find the...

*October 29, 2011*

**Calculus (Derivatives)**

A tray of lasagna comes out of the oven at 200°F and is placed on a table where the surrounding room temperature is 70°F. The temperature T (in °F) of the lasagna is given by the function T(t) = e^(4.86753 - t) + 70, where t is time (in hours)after taking the ...

*October 29, 2011*

**English Language**

Could you please explain to me how it is used incorrectly? You aren't giving much reasoning behind your answer, you're just giving me an answer.

*October 27, 2011*

**English Language**

Sorry, according to my lesson, my antecedent deduction was correct and your verb tense argument was wrong.

*October 27, 2011*

**English Language**

Okay, so it should be more along the lines of "he has made money giving lectures," in order to show that he currently possesses the money.

*October 27, 2011*

**English Language**

So, according to your link, the verb tenses for this sentence are appropriate. Thus, the pronoun "it" in the subordinate clause needs to be replaced with a more descriptive word or group of words like "his argument." Would this be true?

*October 27, 2011*

**English Language**

What is the error in this sentence? "Dr. Smith had argued that the cure for insomnia could be found in the seeds of apples, and although it was not true, he had made money giving lectures." This statement: A. Includes a shift in tense B. Includes a pronoun with no ...

*October 27, 2011*

**Calculus (Continuity)**

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0 </= x </= pi/3 4sin^2(x), if x > pi/3 A. 0 B. 1 C. 2 D. 3 E. 4 I know that since the function is continuous, it should be equal to 1 at 0 and 3 at...

*October 22, 2011*

**Calculus (Continuity)**

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0 </= x </= pi/3 4sin^2(x), if x > pi/3 A. 0 B. 1 C. 2 D. 3 E. 4 I know that since the function is continuous, it should be equal to 1 at 0 and 3 at...

*October 22, 2011*

**Calculus (Limits)**

No, its not a typo, it is supposed to be x^2 - 2a + a^2. Thank you for the reassurance, I figured that this was the most logical choice!

*October 22, 2011*

**Calculus (Limits)**

Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f? I. lim f(x) exists as x approaches a II. f(a) exists III. f(x) is continuous at x = a. A. None B. I, II, and III C. I ...

*October 22, 2011*

**Calculus (Limits)**

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true? I. g(x) = 1 at least once II. lim g(x) = g(3.5) as x aproaches 3.5. III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right A. I ...

*October 22, 2011*

**Calculus**

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true? I. g(x) = 1 at least once II. lim g(x) = g(3.5) as x aproaches 3.5. III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches from the right A. I ...

*October 22, 2011*

**Calculus**

Let f be defined as follows, where a does not = 0, f(x) = {(x^2 - 2a + a^2) / (x-a), if x does not = a 5, if x = a Which of the following are true about f? I. lim f(x) exists as x approaches a II. f(a) exists III. f(x) is continuous at x = a. A. None B. I, II, and III C. I ...

*October 22, 2011*

**Calculus (Discontinuity)**

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump discontinuities. Okay, I presume that the [ ] brackets denote the greatest integer function (int () ). Once I graphed the function ...

*October 15, 2011*

**Calculus**

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. Okay, I presume that the [] brackets denote the greatest integer function (int () ). Once I graphed the...

*October 14, 2011*

**Calculus (Discontinuities)**

Suppose, f(x) = { (x - 1)^2 / x + 1 if x < 2 (x^2 - 2x - 8)/(x - 4) if 2 </= x < 4 (1 / (x - 3)) + 5) if 4 </= x Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump discontinuities. When I graphed this ...

*October 14, 2011*

**Calculus**

I'm not sure I understand your answer completely. I now understand that since the function is in greatest integer brackets, that it can only be one of three answers (-1, 0, or 1), but from here, you lose me. Where are the discontinuities located and how can I describe the ...

*October 14, 2011*

**Calculus**

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. Okay, I presume that the [] brackets denote the greatest integer function (int () ). Once I graphed the...

*October 14, 2011*

**Calculus**

Given f(x) = (x^4 + 17) / (6x^2 + x - 1) Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. From the work that I have done so far, I know that there are two discontinuiities, one at x = -1/...

*October 14, 2011*

**Spelling Errors, Sorry "Discontinuity"**

Sorry, it should be "Discontinuity."

*October 13, 2011*

**Calculus (Any Help At All Is Really Appreciated)**

Suppose g(x) = { 1 / (x-2) if x < 1 2x - 3 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontuity C.) has an infinite discontuity D.) has a removable discontuity E.) None of the above

*October 13, 2011*

**Calculus**

Suppose g(x) = { 1 / (x - 2) if x < 1 2x - 4 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontinuity C.) has an infinite discontinuity D.) has a removable discontinuity E.) None of the above

*October 13, 2011*

**Calculus**

Suppose g(x) = { 1 / (x-2) if x < 1 2x - 3 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontuity C.) has an infinite discontuity D.) has a removable discontuity E.) None of the above

*October 13, 2011*

**Physics**

Cheryl runs a race on a 400.0 m circular track. She starts running east of the starting line and then circles the track and falls, stopping 1.00 m west of the starting line. Her time is 80.0 s. What was her average velocity? I believe that it would be -1.25 x 10^-2 m/s, is ...

*October 12, 2011*

**calculus**

Thank you Reiny, this is what I found when I graphed the function. The reason that these other graphs are not showing the third intercept is because they are zoomed in too closely to observe it.

*October 8, 2011*

**calculus**

No, I meant roots on a graph. More specifically, the number of times the graph passes through the x-axis (so, I suppose all cases where y=0). When I graphed the function on a graphing calculator, I believe I found three. There is a sort of parabolic part and then what appears ...

*October 8, 2011*