Friday
December 19, 2014

# Homework Help: Math: Calculus

Calculus
400 feet of fencing is to be used to enclose four adjacent pieces of land. What dimensions will produce the largest area?
Saturday, October 25, 2014 at 7:46pm

Calculus/pre-trig
Write the formula for the discriminant. State the types of roots for a quadratic equation, explaining how the discriminant helps you determine the type.
Saturday, October 25, 2014 at 7:25pm

Calculus (math)
A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12 feet deep?
Saturday, October 25, 2014 at 6:31pm

calculus
A spherical snowball is placed in the sun. The snowball melts so that it's surface area decreases at a rate of 2 cm2 /min. Find the rate at which the diameter decreases when the diameter is 8 cm
Friday, October 24, 2014 at 9:26pm

Calculus
Given x^2+y^2=4, find the equation of the tangent line at the point (-1,sq.rt.3). Then, at what point is the slope 0? What point is the slope -1? I have no clue what to do!
Friday, October 24, 2014 at 12:13am

The power, P, dissipated when a 6-volt battery is put across a resistance of R ohms is given by P=36R. What is the rate of change of power with respect to resistance?
Thursday, October 23, 2014 at 10:33pm

Calculus
I need help determining the intervals of increase, decrease and the intervals of upward and downward concavity given f prime. f'(x)=(64x^4 - 125x) ^(-2/3). Im not sure how to solve this. I know that the function has no intervals of decrease, its the rest im having trouble ...
Thursday, October 23, 2014 at 1:17pm

Calculus
Let f be a function such that f(−6)=−6, f(6)=6, f is differentiable for all real values of x and −1≤f'x≤1 for all real values of x. Prove that f(x)=x for all −6≤x≤6 I tried applying the mean value theorem here but I'm not...
Thursday, October 23, 2014 at 4:58am

calculus
Let \lambda be a positive real number. Evaluate \sin^{-1}(\lambdai)
Tuesday, October 21, 2014 at 11:43pm

Calculus
Find f'(a). f(x)=(x^2+1)/(x-2) Is it (x^2-5x+2)/(x-2)^2 ?
Tuesday, October 21, 2014 at 9:42pm

Calculus
Use linear approximation, i.e. the tangent line, to approximate \sqrt[3] { 7.9 } as follows: The equation of the tangent line to f(x) at x = 8 can be written in the form y = Using this, we find our approximation for \sqrt[3] {7.9} is
Tuesday, October 21, 2014 at 9:27am

calculus
find the absolute maximum and minimum of the function y=2cos(t)+sin(2t) on the interval of [0, pi/2] I have taken the derivative but I have no clue how to solve it for 0
Monday, October 20, 2014 at 8:40pm

calculus
Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)
Monday, October 20, 2014 at 6:49pm

Calculus
Find the critical numbers of the function f(x)=x^1/6−x^−5/6.
Monday, October 20, 2014 at 3:46pm

Calculus
Consider the function f(x)=ln(x)/x^6. For this function there are two important intervals: (A,B] and [B,∞) where A and B are critical numbers or numbers where the function is undefined. Find A Find B For each of the following intervals, tell whether f(x) is increasing or...
Monday, October 20, 2014 at 3:45pm

calculus
9) Find all critical numbers of the function f(t)=9t^2/3+t^5/3
Monday, October 20, 2014 at 3:44pm

Calculus
7) Consider the function f(x)=x2e4x. For this function there are three important intervals: (−∞,A], [A,B], and [B,∞) where A and B are the critical numbers. Find A and B For each of the following intervals, tell whether f(x) is increasing (type in INC) or ...
Monday, October 20, 2014 at 3:43pm

Calculus
f(x)=4x3−18x2−480x−2 is decreasing on what interval? It is increasing on what interval(s) ? The function has a local maximum at ?
Monday, October 20, 2014 at 3:42pm

Calculus
18) Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. f(x)=2x/6x+12,[1,4]
Monday, October 20, 2014 at 3:40pm

Calculus
A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.4 centimeters per second. What ...
Monday, October 20, 2014 at 3:21pm

Calculus
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 3 cubic feet per minute. If the pool has radius 6 feet and height 10 feet, what is the rate of change of the height of the water in the pool when the depth of the...
Monday, October 20, 2014 at 3:20pm

Calculus
Consider the closed curve in the day plane: 2x^2-2xy+y^3=14 a) show that dy/dx=2y-4x/3y^2-2x (I got this part) b) find equation lines to the curve when y=2 c) if the point (2.5, k) is on the curve, use part b to find the best approximation of the value of k
Monday, October 20, 2014 at 9:04am

calculus
A lamp post 3m high is 6m from a wall. A 2m man tall is walking directly from the post toward at 2.5m/s. How fast is his 1.5 from the wall
Monday, October 20, 2014 at 7:51am

Calculus
An inverted conical tank is being filled with water, but it is discovered that it is also leaking water at the same time. The tank is 6 meters high and its diameter at the top is 4 meters. The water is being added to the tank at a constant rate. Some of this water is found to ...
Sunday, October 19, 2014 at 8:27pm

Calculus
A bright light on the ground illuminates a wall 12 meters away. A man walks from the light straight toward the building at a speed of 2.3 m/s. The man is 2 meters tall. When the man is 4 meters from the building, how fast is the length of his shadow on the building decreasing?
Sunday, October 19, 2014 at 8:27pm

Calculus
A pulley system on a pier is used to pull boats towards the pier for docking. Suppose that a boat is being docked and has a rope attaching the boat's bow on one end and feeding through the pier's pulley system on the other end. The pulley system is 1 meter higher than ...
Sunday, October 19, 2014 at 8:26pm

Calculus
Find the value of a so that the tangent line to y = ln(x) at x = a is a line through the origin. I am unsure how to go about this.
Sunday, October 19, 2014 at 7:18pm

Calculus
find y' of 4(cos(x^3))^2 when x = 1. I got -24(1)(cos(1)(sin(1) = -0.4187 but the answer is -10.9.
Sunday, October 19, 2014 at 5:59pm

Calculus
Find an equation of the tangent line to the curve f(x) = (sins)^2 + 2tanx at x= pi/4. I worked through it and got y = 5x + 5/2 for my answer, but the answer key says that it is y - 5/2 = 5(x - pi/4). Why is the pi/4 in the answer? Thanks for any help!
Sunday, October 19, 2014 at 3:53pm

calculus
find the x-coordinate of all points on the curve y=12Xcos(5X)-(30*sqrt3*X^2) + 16, pi/5<X<2pi/5 where the tangent line passes through the point (0,16), (not on the curve) I have absolutely no idea how to solve this one
Sunday, October 19, 2014 at 1:34pm

Calculus
Find f''(1/2) using f(x) = ln(1-x). f'(x) = 1/(1-x) * -1 = -1/(1-x) so then using quotient rule: f''(x) = ((-1*-1) - ((1-x)(0))) / (1-x)^2 f''(1/2) = 1/(1-(1/2))^(2) = 4 Is this correct?
Sunday, October 19, 2014 at 2:12am

Calculus
What is the derivative of (ln(x))^x ? I have: f(x) = ln(x)^x f(x) = xlnx f'(x) = x/x + 1 * ln(x) f'(x) = 1 + ln(x) Is this correct?
Sunday, October 19, 2014 at 1:50am

calculus
can anyone help me with that question what is the domain of log(log(x)the base is 0.2)
Saturday, October 18, 2014 at 10:57pm

calculus
Use polar coordinates to find the volume of the given solid. Inside the sphere x^2+y^2+z^2=25 and outside the cylinder x^2+y^2=1
Saturday, October 18, 2014 at 10:27pm

calculus
Find the points of the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface coincides with the line joining the origin to the point. What is the acute angle betwwen the normal and the z-axis at these points?
Saturday, October 18, 2014 at 10:26pm

calculus
A cable runs along the wall from C to P at a cost of $3 per meter, and straight from P to M at a cost of$5 per meter. If M is 16 meters from the nearest point A on the wall where P lies, and A is 50 mters from C, find the distance from C to P such that the cost of installing ...
Saturday, October 18, 2014 at 10:25pm

calculus
Find the points of the paraboloid z=x^{2}+y^{2}-1 at which the normal line to the surface coincides with the line joining the origin to the point. What is the acute angle betwwen the normal and the z-axis at these point
Saturday, October 18, 2014 at 10:23pm

calculus
use differentials to determine by approximately how many centimeters does the diagonal of a square table increase if its area is increased from 50 square centimeters to 54.45 square centimeters? Area= s^2 Diagonal= sqrt(2s^2) so, D= sqrt(2A) dD=A^(-1/2) dA dD= 50^(-1/2)* 4.45 ...
Saturday, October 18, 2014 at 9:07pm

Calculus
If G(x)=(x)/(1+2x), find G'(a) and use it to find an equation of the tangent line to the curve y=(x)/(1+2x) at the point (-1/4,-1/2). My answer: G'(a)=1/(1+2x)^2 Equation of tangent line: y= 4x+0.5
Saturday, October 18, 2014 at 3:55pm

Calculus
A pebble is dropped from an open window 100 meters above the ground. a) What is the velocity of the pebble after 2 seconds? b) What is the velocity of the pebble when it hits the ground?
Saturday, October 18, 2014 at 3:07pm

Calculus
Find the slope of the curve f(x)=1/(x^2+3). My answer: (-2x)/(x^2+3)^2
Saturday, October 18, 2014 at 2:46pm

Calculus
The number of bacteria after t hours in a controlled laboratory experiment is n=f(t). Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f'(5) or f'(10)? If the supply of nutrients is limited,would that affect ...
Saturday, October 18, 2014 at 2:44pm

calculus
2 given s(t)=3t +5t+3, find the instantaneous velocity when t i= 5.
Saturday, October 18, 2014 at 12:17pm

calculus
how would you represent the area outside given y= 4cos(2theta) but outside y=4 ?
Saturday, October 18, 2014 at 11:11am

Calculus
A rectangular field is to be enclosed by a fence and divided into three lots by fences parallel to one of the sides. Find the dimensions of the largest field that can be enclosed with 800 feet of fencing. Help me please!!!!!!!!!!! THANK YOU
Saturday, October 18, 2014 at 11:05am

Calculus
The cost of producing x ounces of gold from a new gold mine is C=f(x) dollars. Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain.
Saturday, October 18, 2014 at 11:02am

DIFF CALCULUS
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at ¼ cubic meter per minute, and there is 1 meter of water at the deep end. a. What percent of the pool is filled? ...
Saturday, October 18, 2014 at 10:03am

calculus
a ladder 6 feet long leans against a vertical building. the bottom of the ladder slides away from the building horizontally at rate of 1/2 ft/sec. A) at what rate is the top of the ladder sliding down the wall when the bottom of the ladder is 3 feet from the wall? b)at what ...
Saturday, October 18, 2014 at 12:58am

Calculus
The number of bacteria after t hours in a controlled laboratory experiment is n=f(t). Suppose there is an unlimited amount of space and nutrients for the bacteria. Which do you think is larger, f'(5) or f'(10)? If the supply of nutrients is limited,would that affect ...
Friday, October 17, 2014 at 10:50pm

Calculus
The cost of producing x ounces of gold from a new gold mine is C=f(x) dollars. Do you think the values of f'(x) will increase or decrease in the short term? What about the long term? Explain.
Friday, October 17, 2014 at 10:44pm

calculus
ind the point(s) on the cone z^2 = x^{2}+3y^{2} that are closest to the point (-1,-7,0)
Friday, October 17, 2014 at 10:09pm

Calculus
what is the limit of arcsinx as x approaches 1 from the left
Friday, October 17, 2014 at 10:01pm

Calculus
1. If the tangent line to y=f(x) at (4,3) passed through the point (0,2), find f(4) and f'(4). My answer: f(4)=3 f'(4)=1/4
Friday, October 17, 2014 at 9:26pm

calculus
A sample poll of 100 voters revealed the following information concerning three candidates A, B, and C who were running for three offices. 10 voted in favor of both A and B, 35 voted in favor of A or B but not C, 25 voted in favor of B but not A or C, 65 voted in favor of B or...
Friday, October 17, 2014 at 8:59pm

Calculus
Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid x^2/81+y^2/25+z^2/49=1
Friday, October 17, 2014 at 8:39pm

calculus
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x^2y+3y^2-y subject to the constraintx^2+y^2less than or equal to 10
Friday, October 17, 2014 at 8:36pm

calculus
Given g(x) = (x + cosx)/(e^x - 2x^3 + 5). Find g'(x). Do not need to simplify.
Friday, October 17, 2014 at 12:11pm

calculus
Find the point on the surface z = 2x2+xy+3y2 where the tangent plane is parallel to the plane 8x-8y-z=5.
Friday, October 17, 2014 at 12:09pm

CALCULUS
Hi guys can you help me! Please teach me step by step.. I really need it. pls! Thank you......... A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at ¼ cubic meter ...
Friday, October 17, 2014 at 11:35am

A theatre company allows a group of 10 people to buy theatre tickets at a price of $28 per person. For each person in excess of 10, the price is decreased by$2 per person for everyone down to a minimum of $10 per person. What number of people will produce the maximum revenue ... Friday, October 17, 2014 at 10:35am Calculus 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^94.86753-t)+70 , 0 ≤ t, where t is time (in hours) after taking ... Friday, October 17, 2014 at 10:34am calculus 6) The function f(x)=4x3−18x2−480x−2 is decreasing on the interval ? Enter your answer using the interval notation for open intervals. It is increasing on the interval(s) ? The function has a local maximum at ? Friday, October 17, 2014 at 10:27am calculus A bright light on the ground illuminates a wall 12 meters away. A man walks from the light straight toward the building at a speed of 1.1 m/s. The man is 2 meters tall. When the man is 4 meters from the building, how fast is the length of his shadow on the building decreasing... Friday, October 17, 2014 at 10:21am calculus 2) Let g(s)= t(4−t)^1/2 on the interval [0,2]. Find the absolute maximum and absolute minimum of g(t) on this interval. Enter DNE if the absolute maximum or minimum does not exist. The absolute max occurs at t= . The absolute min occurs at t= Friday, October 17, 2014 at 10:21am calculus f(x)=x2(x−24). So f is decreasing (and f′ is negative) on the interval (0,a) for a= ? Friday, October 17, 2014 at 10:20am CALCULUS 1. A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.) Friday, October 17, 2014 at 10:05am Calculus Suppose a ball is thrown straight up into the air, and the height of the ball above the ground is given by the function h(t) = 6 + 37t – 16t2, where h is in feet and t is in seconds. At what time t does the ball stop going up and start returning to earth? Friday, October 17, 2014 at 9:53am diff calculus 1.) triangular corner lot has perpendicular sides of lengths 120 feet and 160 feet. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets. Friday, October 17, 2014 at 7:26am calculus f(x)= 3+4xe^{-5x}complete the sentences concerning the function a) the function f is decresing on the iterval...... b) the function f is increacing on the interval c) the function f is concave down on the interval d) the function f is concave up on the interva Friday, October 17, 2014 at 1:07am calculus can you find a sequence{an} such that {an} diverges, and the series of an converges? justify Friday, October 17, 2014 at 1:06am calculus If f(x) = 3 cos^2(x) − 6 sin(x) 0 ≤ x ≤ 2π Find the intervals of increase and decrease, the intervals of concave up and concave down, local maximum values, local minimum values, and inflection point Friday, October 17, 2014 at 1:04am Calculus The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 ,for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical into the colony's environment. At ... Thursday, October 16, 2014 at 11:54pm Calculus The population of a colony of bacteria is modeled by the function p(x)=50(e^-x - e^-x^2)+10 , for 0 ≤ x, where population P is in thousands, x is in hours, and x = 0 corresponds to the moment of introduction of a certain chemical into the colony's environment. At ... Thursday, October 16, 2014 at 11:52pm Calculus.. Two particles are moving in straight lines. The displacement (meters) of particle 1 is given by the function s(t)= cos(4x), where t is in seconds. The displacement (meters) of particle 2 is given by the function s(t)= t^3/3-t^2/2 +2(t) , where t is in seconds. Find the first ... Thursday, October 16, 2014 at 11:28pm AP Calculus In the answer space below, provide the larger of the two positive integers that add up to 60 and have the largest possible product. Thursday, October 16, 2014 at 10:37pm AP Calculus If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000. Thursday, October 16, 2014 at 10:36pm calculus Find the point on the plane z = 6x + 9y + 1 closest to the point P = (1, 0, 0). Hint: Minimize the square of the distance. (x, y, z) = Thursday, October 16, 2014 at 9:41pm calculus find the coordinates of the centroid bounded by y=25x^2 and y=4. the region is covered by a thin flat plate Thursday, October 16, 2014 at 9:36pm Calculus Derivative of the implicit Function: arctan(x^5y)=xy^5 Here is where I am at. I am pretty frustrated: arctan(x^5y)-xy^5=0 1/1+(x^5y)^2 * (d/dx(x^5)*y+x^5*d/dx(y))-(d/dx(x)*y^5+x​*d/dx(y^5))=0 1/(1+x^5y)^2 * (5x^4y+x^5dy/dx) - (y^5+x^5y^4dy/dx) (5x^4y)/[(1+x^5y)^2] + (x^... Thursday, October 16, 2014 at 2:52pm Calculus A 13 foot ladder is leaning against the house when it's base starts to slide away. By the time is 12 feet from the house the base is moving at the rate of 5 ft/sec. 1.How fast is the top of the ladder sliding down the wall at that moment? 2. At what rate is the angle theta... Thursday, October 16, 2014 at 8:26am calculus Find the maximum and minimum values of f(x, y) = xy on the ellipse 8\!x^{2} + y^{2} = 9. Thursday, October 16, 2014 at 12:36am calculus Find the center of mass in the 1st quadrant of the circle x^2+y^2=4 where rho(x,y)=k(x^2+y^2) Thanks. Wednesday, October 15, 2014 at 8:14pm REALLY HARD CALCULUS PROBLEMMMM PLEASE HELP ME??? A circular swimming pool has a diameter of 16 m, the sides are 3 m high, and the depth of the water is 2.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s 2 and the density of water is 1000 kg/m 3 .) ... Wednesday, October 15, 2014 at 4:31pm Integral Calculus A force of 4 pounds is required to hold a spring stretched 0.1 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length? Wednesday, October 15, 2014 at 4:28pm calculus Use iterated integral to find the area enclosed by r=2sin2(theta). How do i graph this? Wednesday, October 15, 2014 at 12:15pm Calculus problem (PLEASE HELP!!) The diameter of a human pupil in millimetres is given by D= (2 + 4x^-0.3) / (1 + x^-0.3) where x is the luminance measured in candelas per square metre. Using this function,what is the diameter of the pupil when there is no light? What happens to the diameter of the pupil as ... Wednesday, October 15, 2014 at 9:02am Calculus (Need help) Not sure how do do this. Please help? Find all values of a and b so that the function is continuous for all x E R. f(x)= −3a + 4(x^5)b x ≤ −1 { ax − 2b −1 < x < 1 3x^2 − bx + a x ≥ 1 Wednesday, October 15, 2014 at 7:21am Calculus I lim x→ ∞ of e^(−x) sin√x A little lost. Help would be appreciated. Wednesday, October 15, 2014 at 5:49am pre-calculus You are given a pair of equations, one representing a supply curve and the other representing a demand curve, where p is the unit price for x items. -45 x^2 - 74.5199999999995 x + 15921.36 - 1224.72 p = 0 and 54 x^2 + 1743.12 x + 13880.16 - 6940.08 p = 0 a. Identify which is ... Tuesday, October 14, 2014 at 10:01pm pre-calculus It has been found that the supply of lamps varies linearly with its price. When the price per item was$ 94.67 ,64 items are supplied; When the price was $134.67 , 124 items are supplied. How many lamps are supplied when the price per item is$ 118.00 ? What is the lowest ...
Tuesday, October 14, 2014 at 9:58pm

Calculus
Find all values of a and b so that the following function is continuous for all x ∈ R. f(x) = −3a + 4x^5(b) x ≤ −1 ax − 2b −1 < x < 1 3x^2 − bx + a x ≥ 1
Tuesday, October 14, 2014 at 6:32pm

calculus
The half-life of Radium-223 is 11.43 days. If a sample has a mass of 400 mg, find the mass (in mg) that remains after 6 days
Tuesday, October 14, 2014 at 4:04pm

Foundations and Pre-Calculus Math 10
Find the radius of a cone with a height of 3m and a volume of 30m cubed. So far I have 90m cubed / 3m = pi(r^)3m/3m. Then I get stuck. Help! I'm really bad at math. ):
Tuesday, October 14, 2014 at 1:30pm

pre-calculus
The Hotel Florence has 550 rooms. Currently the hotel is filled . The daily rental is $700 per room. For every$ 14 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of \$ 14 increases that can be made. What should x be so as to maximize the ...
Monday, October 13, 2014 at 10:51pm

calculus
Use diferenciales para estimar la cantidad de estaño en una lata cerrada de este metal con diámetro de 8 cm y altura de 12 cm, si el estaño tiene 0.004 cm de grosor.
Monday, October 13, 2014 at 7:12pm

Pre-calculus
You are given a pair of equations, one representing a supply curve and the other representing a demand curve, where p is the unit price for x items. 80 p + x - 380 = 0 and 84 p - x - 40 = 0 Identify which is the supply curve and demand curve and the appropriate domain. Put the...
Monday, October 13, 2014 at 6:23pm

calculus
Find the dimensions of the rectangular box having the largest volume and surface area 60 square units
Sunday, October 12, 2014 at 6:49pm

Calculus
Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high? (Round your ...
Sunday, October 12, 2014 at 6:25pm

calculus
The volume of a cube is increased from 729 cubic centimetres to 849.285 cubic centimetres. Use differentials to determine: a) by approximately how many centimetres the side length of the cube increases ? B) by approximately how many square centimetres does the surface area of ...
Sunday, October 12, 2014 at 3:18pm

Calculus
A water trough is 9 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 80 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when ...
Sunday, October 12, 2014 at 2:21pm

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