Thursday

July 28, 2016
**Calculus**

Sketch the vector field F⃗ (r⃗ )=2r⃗ in the plane, where r⃗ =⟨x,y⟩. Select all that apply. A.All the vectors point away from the origin. B. The vectors increase in length as you move away from the origin. C. All the vectors point toward ...
*Saturday, October 10, 2015 by A*

**Calculus**

(x^2+y^2)^2=16y Find all values of x where the tangent line is vertical I found the derivative and looked for where it was undefined but it didn't work
*Saturday, October 10, 2015 by Henry*

**Math Calculus**

Postal regulations specify that a package sent by certain shipping methods may have a combined length and girth of no more than 99 inches. Find the dimensions of a CYLINDRICAL package with the greatest volume that may be sent by this shipping method. HINT* the length plus the ...
*Saturday, October 10, 2015 by Heather*

**Calculus**

what is the limit as h approaches 0 of ((x+h)^pi-x^pi)/h? Multiple choice answers: A: lnx B: lnx (x^pi) C: Pi lnx D: (pi^2) ln (x^2) E: (pi^x) lnx I know this is d/dx x^pi, or Pi x^(Pi-1)
*Saturday, October 10, 2015 by Henry*

**Calculus i need help**

Find dy/dx if x^2.y+sin(xy)+y^4.x^2+3xy=5???
*Saturday, October 10, 2015 by Collins*

**Pre-Calculus**

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of f is above or below ...
*Saturday, October 10, 2015 by Leizy*

**calculus**

Show that sinh (sinh^-1 x) = x
*Saturday, October 10, 2015 by ligas*

**calculus**

y = x^2 − 9x + 29/x − 5 relative maximum (x, y) = relative minimum (x, y) =
*Saturday, October 10, 2015 by akash*

**calculus**

Identify any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = x^3 + 3x^2 + 3x + 2 x-intercept (x, y) = y-intercept (x, y) = relative maximum (x, y) = relative minimum (x, y) = point of inflection (x, y) = ...
*Saturday, October 10, 2015 by akash*

**calculus**

Identify any intercepts, relative extrema, points of inflection, and asymptotes. y = 4x^2 − 24x + 34 X-intercept ? (x, y) (smaller x-value) (x, y) (larger x-value) relative minimum (x, y)
*Saturday, October 10, 2015 by akash*

**calculus**

using the two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by a fencing material 30 ft long?
*Friday, October 9, 2015 by ligas*

**Pre-calculus**

Hi i need to find x in 9^(2x-6)=6^(8x-5) So what i did was: 3^(4x-12)=6^(8x-5) log3(3)^(4x-12)=log3(6)^(8x-5) 4x-12=(8x-5)log3(6) now i'm stuck. and i actually feel that the whole thing is wrong. help, pls
*Friday, October 9, 2015 by Lid*

**Calculus**

lim x -> pi/2 (sin(x/2)-cos(x/3)) Evaluate Please help
*Friday, October 9, 2015 by Alz*

**Calculus 1**

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
*Friday, October 9, 2015 by TayB*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=sqrt(x), about y=1. I have to use either the disk or washer method and i believe i use washer. i set up the integral to be pi[(1-x^3)^2 -(1-sqrt(x))^2] from 0 to 1 for my limits. i worked it out ...
*Friday, October 9, 2015 by Jedidiah*

**Calculus**

Use the FTC 1 to find the area of the region under the graph of the function f(x)= 8x-x^2 on [0,8]. I got 244/3 but the answer key says 256/3.
*Thursday, October 8, 2015 by Anonymous*

**Pre-Calculus**

Find the difference quotient usingF(x)-f(1)/x-1 1. f(x)=-3x+2 Given F(x) =2x Find f(x+🔼x) -f(x)/🔼 x
*Thursday, October 8, 2015 by Please HELP*

**Calculus 1**

Related Rates: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one ...
*Thursday, October 8, 2015 by TayB*

**calculus**

Given the function f(x)=1/4 x^4 - 3/2 x^2 a. discuss the relative maxima, minima relative b. determine where f is increasing and where f is decreasing c. Find the points of inflection. d. Discuss the concavity
*Thursday, October 8, 2015 by zel*

**Calculus 1**

Related Rates: The minute hand on a watch is 9 mm long and the hour hand is 6 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)
*Thursday, October 8, 2015 by TayB*

**Calculus 1**

Related Rates: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?
*Thursday, October 8, 2015 by TayB*

**Calculus 1**

Water is leaking out of an inverted conical tank at a rate of 9,500 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the ...
*Thursday, October 8, 2015 by TayB*

**HELP HELP CALCULUS **

y=e^(5e^x) differentiate first and second derivative
*Wednesday, October 7, 2015 by Anonymous*

**Calculus**

I've done everything I can think of to solve this, but I have no idea. Find the derivative: y = sq rt{11x + sqrt[11x + sqrt(11x)]}
*Wednesday, October 7, 2015 by Kelly*

**Calculus 1**

Related Rates: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.
*Wednesday, October 7, 2015 by TayB*

**Calculus**

A man of height 1.7 meters walks away from a 5-meter lamppost at a speed of 1.6 m/s. Find the rate at which his shadow is increasing in length. (Round your answer to three decimal places.) This problem is absolutely killing me I see a lot of examples like this on here but I ...
*Wednesday, October 7, 2015 by Jake*

**Calculus 1**

Related Rates Problem: Two cars start moving from the same point. One travels south at 40 mi/h and the other travels west at 30 mi/h. At what rate is the distance between the cars increasing three hours later?
*Wednesday, October 7, 2015 by TayB*

**Calculus**

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is x(t) = 8 sin t, where t is in seconds and x is in centimeters. The first part of the question is to find the velocity and acceleration equations, which I got to be: v...
*Tuesday, October 6, 2015 by kelly*

**Calculus/Math**

lim ((1-2x)/(√1+x^2)-1) x→∞ Find the value.
*Tuesday, October 6, 2015 by Marc*

**Calculus 1**

The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a/(1 + be^−0.5t) where t is measured in hours. At time t = 0 the population is 10 cells and is increasing at a ...
*Monday, October 5, 2015 by TayB*

**calculus**

Find the resultant vector. 1) A force of 35 grams and 45 grams applied at right angles. 57.009 g at 52° with respect to the 35 kg force 2) Velocities of 400 mph due north and 500 mph due east. 640.31 mph at 51° with respect to the 400 mph force 3) Displacements of 90 ...
*Monday, October 5, 2015 by sasha*

**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 1.2 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?
*Monday, October 5, 2015 by Madison C.*

**calculus**

It is desired to design a ski jump ramp. The ramp will be represented by a polynomial whose graph is a side view of the ramp. The ramp must fulfill the following specifications: The ramp begins at a height of 100 feet and ends at a height of 10 feet above the ground. From ...
*Monday, October 5, 2015 by Jennifer*

**AP Calculus AB**

Hello! I'm having trouble with this related rates problem: A 5ft tall person is walking away from a 16ft tall lamppost at a rate of (2/x) ft/sec, where x is the distance from the person to the lamppost. Assume the scenario can be modeled with right triangles. At what rate ...
*Sunday, October 4, 2015 by Andy*

**Calculus **

Differentiate. g(x) = 5e^x√x
*Sunday, October 4, 2015 by Joey*

**Calculus**

Calculate the approximation. L4, f(x)=cos^2 x , [pi/6, pi/2]
*Sunday, October 4, 2015 by Anonymous*

**Pre-Calculus**

Not sure what to solve... I tried to solve it but i ended up proving that it worked. a. Find the equations of the tangents at C (-2,1) and D (1,2) on the circle x^2+y^2=5 b. Find the point of intersection of the tangents. ~What I did was find the slope and then B, within the ...
*Sunday, October 4, 2015 by Anonymous*

**Calculus**

Finding critical numbers g(theta) = 16(theta) - 4tan(theta) I can only get the derivative of g to be g'(theta) = 16 - 4sec^2(theta). Am I supposed to move on to get sec^2(theta) = 4, then sec(theta) = 2?
*Sunday, October 4, 2015 by Justin*

**Pre-Calculus**

Venus orbits the sun in an approximately circular path. Venus is about 67 million miles from the sun. A comet is located 80 million miles north and 73 million miles west of the sun. The comet follows a straight-line path and exits Venus's orbit at the east most edge. a. ...
*Sunday, October 4, 2015 by Anonymous*

**Pre-Calculus**

The cup on the 9th hole of a golf course is located dead center in the middle of a circular green that is 70 ft in diameter. You ball is located 50 feet south, and 40 feet west of the cup. The ball follows a straight line path and exits the green at the right most edge. Assume...
*Sunday, October 4, 2015 by Anonymous*

**Calculus**

We are finding critical numbers f(x)= 8x^3+x^2+8x f'(x)=24x^2+2x+8 -> 2(12x^2+x+4) I'm honestly stuck. All I can tell is that I need to set my f'(x)=0, but I am lost there too. Quadratic form. equates to (-1±i√191)/24 I believe. That is as far as I ...
*Sunday, October 4, 2015 by Justin*

**Calculus**

We are finding critical numbers f(x)= 8x^3+x^2+8x f'(x)=24x^2+2x+8 -> 2(12x^2+x+4) I'm honestly stuck. All I can tell is that I need to set my f'(x)=0, but I am lost there too. Quadratic form. equates to (-1±i√191)/24 I believe. That is as far as I ...
*Sunday, October 4, 2015 by Justin*

**Calculus**

We are finding critical numbers f(x)= 8x^3+x^2+8x f'(x)=24x^2+2x+8 -> 2(12x^2+x+4) I'm honestly stuck. All I can tell is that I need to set my f'(x)=0, but I am lost there too. Quadratic form. equates to (-1±i√191)/24 I believe. That is as far as I ...
*Sunday, October 4, 2015 by Justin*

**calculus**

If f(x) = 5ex cos x, find f '(x) and f ''(x).
*Sunday, October 4, 2015 by jam*

**calculus i need help also**

If y=2x^2-21x^2+60x+6 what is the value of x? dx^2/dy^2=0
*Saturday, October 3, 2015 by collins*

**calculus need help**

use the first principle to obtain the differencial coefficient y=1/(2x-1)
*Saturday, October 3, 2015 by collins*

**Calculus**

The revenue for a sale of x books at $70 each is given by R(x)=70x. The commission for a revenue of x dollars is given by C(x)=.20x. Express the commission as a function of the number of books sold.
*Saturday, October 3, 2015 by Suzanne*

**Calculus 1**

Find y' if y=ln(9x^2+7y^2).
*Friday, October 2, 2015 by TayB*

**Calculus 1**

Find the equation of the tangent line to the curve y = (9 ln x)/x at the points (1, 0) and (e, 9/e).
*Friday, October 2, 2015 by TayB*

**Pre-calculus**

Find the inverse function of f(x) = 4 - 8/x^2, where x>0 What I think is because there is a restriction to domain (x>0), the function is invertible since sqrt(x) will always result in +-x. Am I right?
*Thursday, October 1, 2015 by Lid*

**AP Calculus**

a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. find the dimensions of a norman window of maximum area if the total perimeter is 72 units. Base value is 21.
*Thursday, October 1, 2015 by Tom*

**Calculus**

Show that u(x, t) = f(x−ct)+g(x+ct), where c is a constant and f and g have continuous second derivatives, is a solution of the wave equation in one dimension, ie (∂t)^2 u = c^2 ∂x^2 u. Note that this solution to the wave equation consists of two functions ...
*Wednesday, September 30, 2015 by Margo*

**Multivariable calculus**

Find dy/dx x=te^t y=t+sint
*Wednesday, September 30, 2015 by Anonymous*

**math,(integral calculus)**

Integrate with respect to x:4x^2.dx
*Wednesday, September 30, 2015 by I-learn*

**Calculus**

The equation of motion of a particle is s = t3 − 12t, where s is in meters and t is in seconds. For the velocity function, I got v(t)=3t^2-12 and for acceleration, a(t)=6t. The final question is: Find the acceleration when the velocity is 0. How do I do that?
*Tuesday, September 29, 2015 by Kelly*

**Calculus 1**

The curve with the equation y^2=5x^4-x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (-1,2).
*Tuesday, September 29, 2015 by TayB*

**Calculus 1**

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2/3 +y^2/3 =4 (-3sqrt(3),1) (astroid)
*Tuesday, September 29, 2015 by TayB*

**Calculus 1**

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x^2+2xy-y^2+x=6 , (2,4) (hyperbola)
*Tuesday, September 29, 2015 by TayB*

**Calculus**

Find the antiderivatives. 1. f(x)= x sin (x^2) 2. f(x)= x sin x
*Tuesday, September 29, 2015 by Anonymous*

**calculus**

1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π? 2. what trig function never crosses the x-axis and has a value of 2 at π/6? are these correct? 3. what trig function has a period of π and is undefined for -π/...
*Monday, September 28, 2015 by anon*

**Calculus**

Find y" by implicit differentiation. x^3+y^3 = 1 (x^3)'+(y^3)' = (1)' 3x^2+3y^2(y') = 0 3y^2(y') = -3x^2 y' = -3x^2/3y^2 y' = -x^2/y^2 y" = [(y^2)(-x^2)'-(-x^2)(y^2)']/y^4 y" = [(y^2)(-2x)-(-x^2)(2y)]/y^4 y" = [(-2xy^2...
*Sunday, September 27, 2015 by Justin*

**Calculus**

Let u=f(r) and r=|x|=((x1)^2 +···|(xn)^2)^1/2. Show that ∑ (∂u/∂xj)^2 = (f′(r))^2 Please help! it's an assignment due tomorrow
*Sunday, September 27, 2015 by Sarah*

**Calculus**

Let u=f(r) and r=|x|=(x1^2 +···|xn^2)^1/2. Show that ∑ 1 to n (∂u/∂xj)^2 = (f′(r))^2
*Sunday, September 27, 2015 by Martha*

**Physics**

The figure below represents part of the performance data of a car owned by a proud physics student. (The horizontal axis is marked in increments of 1 s and the vertical axis is marked in increments of 10 m/s.) f (a) Calculate the total distance traveled by computing the area ...
*Sunday, September 27, 2015 by Kaleem*

**Calculus**

Consider the line through the points (3,2,5) and (1,1,1). Consider the plane A that is perpendicular to this line, and passing through the point (-1,0,2). Consider the plane B that passes through the points (1,-1,0), (0,2,0), and (0,5,2). Consider the intersection of plane A ...
*Sunday, September 27, 2015 by Alexa*

**Calculus**

limit (x^2+y^2)/(x+y)^2 as (x,y)->(0,0) I don't know how to prove it doesn't exist. Please help!
*Sunday, September 27, 2015 by Margo*

**calculus**

domain of -9/2+t^2 and 1-4t/2+t
*Saturday, September 26, 2015 by Anonymous*

**Calculus**

Let f(x)=1/x. Compute the difference quotient for f(x) at x=1 with h=0.3 I know that the formula for difference quotient is (f(x+h)-f(x))/h, but I am not sure how I am supposed to plug this in. I have tried a few ways but webworks says that the answer is wrong every time.
*Saturday, September 26, 2015 by :(*

**differential calculus**

differentiate g(t)=3/sqrt(t)
*Saturday, September 26, 2015 by Anonymous*

**Calculus**

You are expecting a tax refund of $4,000 in 4 weeks. A tax preparer offers you an "interest-free" loan of $4,000 for a fee of $50 to be repaid by your refund check when it arrives in 4 weeks. Thinking of the fee as interest, what simple interest rate would you be ...
*Saturday, September 26, 2015 by Anonymous*

**Calculus**

Just got through with derivatives, power rule, and chain rule. I am supposed to find the first and second derivatives of the function. y = 4x/√x+1 and y = cos^2(x) y' = [(x+1)^(1/2)(4)]-[(4x)(1/2(x+1)^(-1/2))(1)] y' = [4(x+1)^(1/2)-4x]/[2(x+1)^(1/2)(x+1)] ...
*Saturday, September 26, 2015 by Justin*

**Calculus**

The Norman window illustrated below has a semicircular section on top of a rectangle. The radius of the semicircle is x. The long side of the rectangle is three times the radius of the semicircle. a)Express the total area of the window, A, as a function of x. b) Express the ...
*Friday, September 25, 2015 by Ellie*

**Calculus**

We just learned derivatives and now on the Chain Rule. y = r/[(sqrt)(r(sqrd)+1)] y' = [[(sqrt)(r(sqrd)+1)(r)'] - [(r)(sqrt)(r(sqrd)+1)']] / [(sqrt)(r(sqrd)+1)](sqrd) y' = (sqrt)(r(sqrd)+1) - r[1/2(r(sqrd)+1)(raised to -1/2)](2r) My final answer is -3r/[2(sqrt)(...
*Friday, September 25, 2015 by Justin*

**calculus**

Find the point on the curve y = x^3 which is nearest the point (4, 0).
*Friday, September 25, 2015 by Anonymous*

**calculus**

Find the point on the curve y =2/3 〖√(18-x^2 )〗 (first quadrant) where a tangent line may be drawn so that the area of the triangle formed by the tangent line and the coordinate axes is a minimum.
*Friday, September 25, 2015 by Anonymous*

**calculus**

A rectangular field is to be fenced, one side of which is the edge of a straight river. It is given that the material for the two opposite side costs Php 3.00 per meter and the material for the side opposite the river costs Php 6.00 per meter. If an amount of Php 600.00 is ...
*Friday, September 25, 2015 by Anonymous*

**calculus**

A manufacturer of a certain brand of appliance estimates that he can sell 5000 units a year at Php 900.00 each and that he can sell 1500 units more per year for each Php 100.00 decrease in price? What price per unit will give the greatest returns?
*Friday, September 25, 2015 by Anonymous*

**Calculus 1**

The curve y = |x|/(sqrt(5- x^2)) is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (2, 2)
*Friday, September 25, 2015 by TayB*

**Pre Calculus**

The doubling period of a baterial population is 10 minutes. At time t=80 minutes, the baterial population was 50000 1What was the initial population at time t=0 2Find the size of the baterial population after 4 hours
*Thursday, September 24, 2015 by Marina*

**Calculus**

Find all solutions of the equation correct to three decimal places. (ex: 0.617 or -1.764) x^3=3x-3
*Thursday, September 24, 2015 by Alisha*

**Calculus**

Which of the following is not a solution to the following equation? x^3-5x^2+4 = 0 x = 0 x = 4.83 x = -0.83 x = 1
*Thursday, September 24, 2015 by Alisha*

**calculus**

with respect to x;4^2.dx
*Thursday, September 24, 2015 by loveth*

**Calculus **

Maclaurian' series example "f(x)=tanx" give me answer
*Thursday, September 24, 2015 by Swapnil *

**Calculus 1**

Find the derivative of the function. y=(e^3u -e^-3u)/(e^3u+e^-3u)
*Thursday, September 24, 2015 by TayB*

**pre-calculus**

Almonds cost fiver per pound and cashews cost nine per pound. How many pounds of almonds should be mixed with the cashews to make 10 pounds of a mix that sells for eight dollars per pound?
*Wednesday, September 23, 2015 by mary*

**calculus **

simplify the given expression using factors 1. 5(x^2+4)^4(2x)(x-2)^4+(x^2+4)^5(4)(x-2)^3 2. (x^2+3)^(-1/3)-2/3x^2(x^2+3)^(-4/3) 3. 2x(x+6)^4-x^2(4)(x+6)^3/(x+6)^8 4. (7-3x)^1/2+3/2x(7-3x)^(-1/2)/7-3x
*Wednesday, September 23, 2015 by Anonymous*

**calculus **

dont get it write intervals for the function sin(x)/1-cos (x) is continuous on.
*Wednesday, September 23, 2015 by Anonymous*

**Calculus**

How do you simplify vectors? 1)AB + BC + CD 2) BC - FE - BA + DE - DC Calculus - Steve, Tuesday, September 22, 2015 at 11:39pm AB+BC = AC so, AB+BC+CD = AD BC-DC = BC+CD = BD See if you can use that idea to rearrange +/- terms so the ends line up in order Calculus - Anonymous...
*Tuesday, September 22, 2015 by Anonymous*

**Calculus**

How do you simplify vectors? 1)AB + BC + CD 2) BC - FE - BA + DE - DC
*Tuesday, September 22, 2015 by Anonymous*

**Calculus**

Can you please explain to me what are the qualifications for a function to be continuous? Please explain your response in easy to understand wording. thank you in advanced!
*Tuesday, September 22, 2015 by Catera *

**Calculus **

What does it mean when the limit of f(c) doesn't exist?
*Tuesday, September 22, 2015 by Catera *

**Calculus 3! ASAP please**

1.A given line is described by the system of equations x=2t+7; y=-3t+4; z=5-t; find the equation of a line parallel to the given line and which contains the point (1,1,0). 2.Let a=<0,6,2> and b=<0,2,4>, then the component of a parallel to b is given by? - the ...
*Tuesday, September 22, 2015 by Sally*

**Calculus 3 **

1. An object moves along a straight track from the point (1,−2,1) to the point (0,−7,5). The only force acting on it is a constant F=2i−3j−5k newtons. Find the work done if the distance is measured in meters. 2. A wrench 0.5 meters long lies along the ...
*Tuesday, September 22, 2015 by jagga*

**Calculus 1**

Differentiate. f(x)=5sqrt(x)sinx
*Tuesday, September 22, 2015 by TayB*

**Calculus**

Differentiate each function with respect to x: F(x)=x/(x+1)^1/2
*Monday, September 21, 2015 by Sm*

**Pre-Calculus**

how to make a xy table for the following greatest integer equation when using -1,-2,0,1,2 to plug into x f(x)=2[x], g(x)=[2x], f(x)=-[[x]], and g(x)=[[-x]]
*Monday, September 21, 2015 by s*

**Pre-Calculus**

Why does sin 30° = 150° (or sin π/6 = sin 5π/6)? Refer to both the unit circle and the graph of the sine curve.
*Monday, September 21, 2015 by A*

**calculus**

10. A military jet flies horizontally with a velocity of 450 m/s and 20,000 m above the ground. When the jet is straight above an artillery gun a shell is fired. Assuming the shell hits the jet. a. Calculate the horizontal component of the initial velocity of the shell. b. ...
*Sunday, September 20, 2015 by Sue*

**calculus**

Please answer. An airplane at an altitude of 3000m, flying horizontally at 300km/hr, passes directly over an observer. Find the rate at which it is approaching the observer when it is 5000m away.
*Sunday, September 20, 2015 by joecel*

**Pre-Calculus**

how do i find the vertical asymptote of x−1 / x(x-2) so far i got x-1 / x^2-2x
*Sunday, September 20, 2015 by Devin *