Mishaka
Most popular questions and responses by Mishaka
Calculus
Given a right circular cone, you put an upsidedown 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 upsidedown cone to have the largest possible
asked on December 16, 2011 
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
asked on January 15, 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,
asked on January 17, 2012 
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.
asked on December 16, 2011 
Calculus (Limits)
Let f be defined as follows, where a does not = 0, f(x) = {(x^2  2a + a^2) / (xa), 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,
asked on October 22, 2011 
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?
asked on March 12, 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
asked on January 5, 2012 
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
asked on October 29, 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.
asked on December 16, 2011 
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?
asked on March 12, 2012 
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
asked on December 16, 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
asked on December 12, 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
asked on December 17, 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
asked on October 29, 2011 
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?
asked on February 8, 2012 
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
asked on 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
asked on December 10, 2011 
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=44x. 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
asked on February 29, 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
asked on 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
asked on March 12, 2012 
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(x2)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
asked on November 12, 2011 
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=44x. You get: a.)1.8467 b.) 0.16165 c.) 0.36974 d.) 1.7281 e.) 0.37859
asked on February 29, 2012 
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
asked on October 14, 2011 
Calculus (Area Between Curves)
Find the area of the region bounded by the curves y^2=x, y4=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
asked on February 29, 2012 
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
asked on October 12, 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
asked on 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
asked on October 22, 2011 
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
asked on February 29, 2012 
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
asked on November 19, 2011 
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
asked on March 12, 2012 
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
asked on October 27, 2011 
CALCULUS
In Seattle on September 30, the temperature hours after midnight was given by the function y=60 + 12sin((pi/x)(x11)) What was the average temperature over the period from 8 A.M. until 10 P.M.?
asked on February 29, 2012 
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
asked on October 15, 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
asked on October 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.
asked on December 22, 2011 
Calculus (Discontinuities)
Suppose, f(x) = { (x  1)^2 / x + 1 if x < 2 (x^2  2x  8)/(x  4) if 2
asked on October 14, 2011 
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?
asked on February 11, 2012 
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 ()
asked on October 14, 2011 
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
asked on February 18, 2012 
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
asked on October 22, 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 ()
asked on October 14, 2011 
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))
asked on February 29, 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???
asked on February 15, 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
asked on 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???
asked on February 15, 2012 
calculus
How many roots does the graph of this function have? 4x^4  4^x I believe that it either has two or three roots.
asked on October 8, 2011 
Calculus
What is the limit of this function as x approaches 0? cos(x)  1 / x From what I gather, the limit is equal to 0, since on the right, the function approaches from negative values close to zero and on the left, it approaches 0 with positive values close to
asked on October 8, 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
asked on November 1, 2011 
calculus
What is the limit of the function as x approaches infinity? (x^4  7x + 9) / (4 + 5x + x^3) From what I know, the limit should be infinity since the greater exponent is in the numerator. However, I am only given the options: 0, (1/4), 1, 4, or Does not
asked on October 8, 2011 
calculus
What is the limit of the function as x approaches infinity? 4x^4  4^x Would the limit be positive infinity or negative infinity?
asked on October 8, 2011 
Find the Zeros
Find the three zeros for the following function on the interval 5
asked on November 11, 2011 
Calculus
Find the three zeros for the following function on the interval 5
asked on 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
asked on November 9, 2011 
Calculus (Any Help At All Is Really Appreciated)
Suppose g(x) = { 1 / (x2) 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
asked on 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
asked on October 13, 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
asked on November 18, 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?
asked on November 9, 2011 
Calculus (Derivatives)
Using the product rule, find the derivative of the following function: (x^1/2 cscx sinx).
asked on November 7, 2011 
Calculus
Let f be defined as follows, where a does not = 0, f(x) = {(x^2  2a + a^2) / (xa), 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,
asked on October 22, 2011 
Calculus (Antiderivatives)
What is the antiderivative of the following expression? 3x(x^2 + 7)^3
asked on February 11, 2012 
Calculus (Antiderivatives)
What is the antiderivative of? (x^2  4) / (x  2)
asked on February 10, 2012 
Calculus
Suppose g(x) = { 1 / (x2) 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
asked on October 13, 2011 
calculus
What is the limit of this function as x approaches infinity? 2^x + x^3 / x^2 + 3^x
asked on October 8, 2011

Calculus (Area Between Curves)
Thank you, I was just really unsure of my answer!
posted on February 29, 2012 
math
x = 2 5/6 or 17/6 ((5 13/21)  (2 11/14))
posted on 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!
posted on 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?
posted on 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
posted on February 29, 2012 
Calculus (Antiderivatives)
Thank you for the apology, no hard feelings!
posted on 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 nonserious answers, thank you.
posted on February 11, 2012 
business math
I don't think your entire question was posted.
posted on February 8, 2012 
7th grade Lang. Art
Tamper Both meddling and tampering concern getting involved where you are not supposed to.
posted on 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,
posted on 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!!!
posted on January 18, 2012 
Calculus (Tangent Line Approximation)
Just wanted to make one more clarification, the equation is supposed to be (1 + x)^n.
posted on 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
posted on 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
posted on 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
posted on 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?
posted on 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?
posted on December 17, 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!
posted on 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.
posted on December 16, 2011 
Calculus (Optimization)
Now I'm lost, I don't get why you changed the signs.
posted on December 16, 2011 
Calculus (Optimization)
I rechecked and found that 3x^222x+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).
posted on 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
posted on December 16, 2011 
Calculus (Optimization)
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,
posted on 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)
posted on 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!
posted on December 16, 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
posted on November 19, 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
posted on 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.
posted on 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
posted on November 12, 2011 
Find the Zeros
Thank you Damon. The first time I posted this question, someone gave me the answer 3.1216 for the positive zero. But when I doublechecked the answer, it didn't work correctly. I figured something was up and wanted to clarify the answer. 3.161593987 works
posted on 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.
posted on November 11, 2011 
Calculus
Thank you, this helps tremendously!
posted on November 11, 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?
posted on November 1, 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.
posted on October 27, 2011 
English Language
Sorry, according to my lesson, my antecedent deduction was correct and your verb tense argument was wrong.
posted on 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.
posted on 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?
posted on October 27, 2011