Wednesday

December 17, 2014

December 17, 2014

Number of results: 97,887

**calculus**

Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1. a) f(x) = 1/ sqrt of x b) f(x) = 60 - 5t^2
*February 14, 2010 by Anonymous*

**calculus**

Consider the following. y = (2x2 + 5)(x3 − 25x) at (5, 0) (a) At the indicated point, find the slope of the tangent line. (b) Find the instantaneous rate of change of the function.
*March 10, 2011 by Adam Janky *

**Math - point on the graph**

Determine the coordinates of the point on the graph of f(x)=sqrt(2x+1) where the tangent line is perpendicular to the line 3x+y+4=0
*October 21, 2010 by Anonymous*

**Geometry**

Write an equation for the line perpendicular to line XY that contains point Z. line XY: 3x + 2y = -6, Z(3,2) I realize that the slope of a perpendicular line is the opposite reciprocal of the first line. But, how do I use point Z in this problem? Thank you.
*November 9, 2009 by Heather*

**alegbra**

Find an equation of the line having slope and containing the given point. M=4/5, (3, -7) The equation of the line is Y= I have tried to work this problem and could not get the answer. Please help me.
*March 19, 2009 by Johnnie*

**algebra**

find the equation for the line that passes through the point (-5,-1) and that os parallel to the line with the equation -x+2y=5
*July 7, 2010 by cm*

**calculus**

Given the function: y = 2 - x - x^3 use limits to find the slope (and then the equation) of the tangent line at x =2.
*September 25, 2008 by Alex*

**calculus**

Given the function y = 2 - x - x^3 Use limits to find the slope (and then the equation) of the tangent line at x = 2
*September 30, 2008 by Erika*

**math calc**

The equation of the tangent line to f(x) =sqrt{x} at x = 25 can be written in the form y = mx+b where m =.1 b =? i don't know how to find the value of b
*March 27, 2009 by Manny*

**Calc**

Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 5 is y= 75x - 250. Using this, we find our approximation for 4.6 ^3 is ?
*August 5, 2013 by Anonymous*

**math**

Find the equation of the tangent line to the graph of f(x) = (4x − 8)/(x + 1) at x = 0. (Use y for your dependent variable.)
*October 9, 2014 by Michael*

**Calculus**

Find an equation of the tangent line to the graph of f(x)=xsinx when x=0. A. y=0 B. f'(x)=0 C. y=xcosx+sinx D. y=x E. None of these
*November 30, 2014 by Anonymous*

**Precalc**

At the point were a line intersects a plane [with the equation (24x+32y+40z=480) and three points of A(5, 10, 1), B(6, 3, 6), and C(12, 1, 4)], the vector i-, vector j-, and vector k-coefficients of the line equal the corresponding values of x, y, and z for the plane. By ...
*January 7, 2012 by Grace*

**maths**

find the equation to the straight line which passes through the point of intersection of the line 3x+4y-1=0 and 5x+8y-3=0 and is perpendicular to the line 4x-2y+3=0
*January 10, 2013 by Anonymous*

**math**

can somebody show me how to do this? at what point on the graph of y= 3^x +1 is the tangent line parallel to the line y= 5x -1 ?
*October 29, 2009 by carolina*

**calculus**

Determine the coordinates of the point on the graph of f(x)= (2x+1)^(1/2) where the tangent line is perpendicular to the line 3x+y+4=0
*February 28, 2013 by Anonymous*

**advanced algebra 2**

Find an equation for the line with the given properties: 1) Containing the points (1, 3) and (-1, 2) 2) Slope = -2/3; containing the point (1, -1) 3) X-intercept = 2; y-intercept = -1 4) Parallel to the line 2x – y = -2; containing the point (-1, 2) 5) Perpendicular to the ...
*August 10, 2012 by kerry*

**maths**

if y=e^(3x) sin 4x. Show that (d^2y/dx^2)-(6dy/dx)+25y=0 (b) for the curve with equation y=(x^2+1)/(x^2-4), find (i) the cordinates of the turning point(s). (ii) the equation of the asymptotes
*October 3, 2013 by masuzyo*

**calculus please help**

Use the four step process to find the slope of the tangent line to the graph at any point: f(x) = -1/2(x^2)
*February 11, 2011 by Anonymous*

**Calculus**

Of the infinitely many lines that are tangent to the curve y = −7 sin x and pass through the origin, there is one that has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places.
*November 20, 2014 by Laura*

**calculus**

Find the equation of the line tangent to at x=1. Give your answer in y=mx+b form as an equation. If b=0, make sure you put +0 after mx. For example, even if your answer is y=3x, type in y=3x+0.
*October 2, 2011 by brandy*

**algebra 1**

Thelma wants to find the equation of a line that passes through the point (2, 2) and is perpendicular to the line Which equation best represents Thelma's equation?
*April 29, 2013 by shay*

**calculus **

determine the slope of the tangent for the following function. Then determine the equation of the tangent line at x=1 F(x) = x F(x) = x^4
*February 13, 2010 by Anonymous*

**cal**

Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1. a) f(x) = x b) f(x) = x^4
*February 14, 2010 by Anonymous*

**calculus**

Determine the slope of the tangent m, for each of the following functions. Then determine the equation of the tangent line at x=1. For f(x) = 1/x^3
*February 14, 2010 by Anonymous*

**Calculus II**

Here's the problem: Find the area of a plane region bounded by y=x^3 and its tangent line through (1,1). So far I have the graph on my graphing calc, so I have an idea at what I'm looking at. I found the tangent line to y=x^3 to be y=3x-2. Now I am stuck. I am trying to find ...
*May 29, 2007 by Ace*

**Maths**

Find the equation of the normal to the curve y = 3x^2 - 5x that is perpendicular to the line y = x + 4.
*October 23, 2009 by Annie*

**maths**

Find the equation of the normal to the curve y=2x^2+3x+4 which is perpendicular to the line y=7x-5
*October 23, 2010 by Adam*

**Math**

Find the equation of normal to the curve 3x^2 - y^2 =8 which is parallel to the line x + 3y =4.
*June 22, 2013 by Chockalingam*

**Math**

At what point on the graph of y=(1/2)x^2-(3/2) is the tangent line parallel to the line 4x-8y=5? A. (1/2,-3/8) B. (1/2,-11/8) C. (2,3/8) D. (2,1/2) E. (-1/2,-11/8)
*December 1, 2013 by Millie*

**CALC AB **

if p(x)=(x-1)(x+k) and if the line tangent to the graph of p at the point (4,p(4)) is parallel to the line 5x-y+6=0, then k=? a. -1 b. -2 c. 1 d. 0 e. 2
*October 3, 2014 by Jacke *

**college algebra**

1. find the equation of the line with the given properties. Express the equation in general form or slope-intercept form. perpendicular to the line -3x_y= -27; contains the point (9, -1) the equation of the line is ? 2. solve the polynomial inequality and then graph the ...
*December 1, 2012 by confused--two questions please help*

**math**

Find the slope of the secant to the curve f(x) = -2logx + 3 between: (1 each) i) x = 1 and x = 2 ii) x = 1 and x = 1.5 iii) x = 1 and x = 1.1 vi) x = 1 and x = 1.01 b) Extend the result from part a to determine the slope of the tangent to the curve at x = 1 accurate to 3 ...
*March 19, 2012 by mark*

**calculus**

The slope of a curve is at the point (x,y) is 4x-3. Find the curve if it is required to pass through the point (1,1). Work... 4(1)-3=1 y-1=1(x-1) y=x
*November 18, 2007 by Anonymous*

**math**

the straight L has gradient 3 and passes through the point A(-6,4). a) find an equation for L in the form y=mx+c b) straight line R has the equation in the form of -7y+x+14=0. Given that R crosses the y-axis at the point B and intersects L at the point C, find the coordinates ...
*February 24, 2012 by aminath*

**math**

(a)Given the points P(3,5),Q(8,10)and R(8,0),find the equation of a line which is perpendicular to QR and passes through the mid point of QR. (b)The line 2x+3y=2 and 7x-3y=10 intersect at A . Find the equation of the line which passes through A and is perpendicular to the line...
*June 5, 2013 by JOJO*

**Calculus**

find the equation of a line tangent to the graph of y = x / (square root of 5x^s +4), at x = 1. am i suppose to take the derivative? if so, then what else?
*November 13, 2007 by dave*

**math**

how do i solve this problem? find an equation for a line that is tangent to the graph of y=e^x and goes through the origin.
*October 29, 2009 by jayla*

**calculus**

Find the equation, in slope intercept form , of the line tangent to the graph of the square root of (x^3+7x+1), when x=3
*December 8, 2011 by Patty*

**Calc**

Find the equation of the tangent line to f(x)=sqrtx^2+6x at x=2, give your answer in slope-intercept form
*July 20, 2012 by Ashley*

**Calculus**

Find the equation of the tangent line to the graph of the function f(x)= 2x^3−3x^2+4x+2 at x=2 I got y=16x-12 but I know it is wrong.
*October 15, 2012 by Anonymous*

**Analytic Geometry**

Find the equation of a circle passing through (3,7) and tangent to the line x-3y+8=0. Please, How do I solve this? Help me
*January 26, 2013 by Lea*

**Analytic Geometry**

Find the equation of a circle passing through (3,7) and tangent to the line x-3y+8=0. Please, How do I solve this? Help me
*January 26, 2013 by Lea*

**Calculus**

Find the slope and equation of the tangent line to the graph of the function at the given value of x. f(x)=x^4-20x^2+64;x=-1
*October 31, 2014 by Duane*

**Maths**

A circle C passes through the point (-12,9) and is given by the equation (x-a)^2 + (y-b)^2 = r^2. If the equation of the tangent to the given circle at the point (-4,1) is given by x-y+5=0, find the values of a,b and r. The answers have to be a=-8, b=5 r=5.657
*March 17, 2008 by Claire*

**Calculus**

Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (t)i + (2/3)t^(3/2)k, 0 less than or equal to t less than or equal to 8
*September 25, 2012 by Beau*

**Calculus-derivatives**

What is the slope of the tangent of each curve at given point y=√(16x^3), (4,32) If I find the derivative of y=√(16x^3) Will it be 16/-x^3
*February 15, 2012 by Jake*

**Calculus**

The line y=2x+b is tangent to the graph of y=x^1/2 at the point P=(a, a^1/2). Find P and determine b. I don't know what to do because they don't give you the x coordinate or anything to plug into the derivative. Help?
*September 20, 2012 by Macy*

**math, algebra**

the problem reads: Write the equation of the line which passes through the point (2,1) and is parallel to another line with equation y = (5)/(2) x + 6 the answer i get is the following is this correct though y = (5)/(2) x - 4 Since your new line is parallel to y=(5/2)x + 6 it ...
*March 31, 2007 by jasmine20*

**math**

I need help with "write in equation in slope-intercept form for the line that is parallel to to the given line line and and that passes through the given point. y=1/2x=5;(4,-3) How do you find a line that is perpendicular. Please and thank you! :)
*February 8, 2014 by Kerri*

**Calculus **

I am so lost, I have no idea what to do next. Find the equation of the tangent line to the graph at the indicated point f(x) =x^2 +x ; a=-1 I started out using f(-1)= (-1+h)-(-1)/h but i am so lost on what to do next. I have tried to look at examples in the book, but i do not ...
*September 25, 2014 by Erin*

**Math**

Write your answer in standard form. Show all your work if you want to be eligible for partial credit. Write the equation of a line perpendicular to the line y = (2/3)x - 7 and passing through the point (4,-2). The slope of the line y = (2/3)x - 7 is 2/3. The slope of a line ...
*November 7, 2006 by Lina*

**calculus**

Two lines through the point(1,-3) are tangent to the curve y=x2. Find the equations of these two lines and make a sketch to verify your results. Thank you
*September 27, 2011 by Akanimo*

**Calculus**

The point P(4,2) lies on the curve y=x^1/2 If Q is the point (x,x^1/2) use your calculator to find the slope of the secant line PQ for the following values of X: 1)3.5 2)3.9 3)3.99 4)3.999 5)4.5 6)4.1 7)4.01 8)4.001 i plugged these points into the intial equation and got that ...
*September 25, 2007 by Judy*

**algebra 1,urgent**

the expression (4x^2-3x+1)-(x^3+2x+7) what is the coefficient of the x term in the simplified expression? what is an equation of a line parallel to the line with equation 2 y=14-6x a.y=-6x+18 b.y=-3x-9 c.y=6x+3 d.y=3x+8 Solve linear system, which substitution of unkowns is ...
*April 23, 2013 by Sven*

**AP Calc-easy ?**

Given: f(x)= x^3 + x^2 - 2x over the closed interval [0,2] Write the equation of the tangent line to f(x) passing through point A(-1,-2). *At first glance I knew how to do it, but f(-1) does not equal -2...so do I add a constant onto f(x) to make f(-1) = -2 or what? thanks
*March 7, 2007 by blondie07*

**algebra 3**

what is the equation of the line with {3,3} and is perpendicular to the line y= negative 2x plus 3 The slope of the line is -2. The slope of a line perpendicular to this one must be its negative reciprocal, or 1/2. Use the point-slope form to find the other line: y - y1 = m(x...
*January 11, 2007 by Darius Graham*

**Pre-Calculus**

Determine the equation of a line that passes through (2,2) and is parallel to the line tangent to y=3x^3-2x at (-1,5)?
*February 12, 2013 by Sarah*

**calculus**

find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)
*April 10, 2012 by mabel*

**Derivatives?**

Given that f(-0.5)=2 and f'(-0.5)=4, use a tangent line approximation to estimate f(0). The lesson is not very clear on what a tangent line approximaton is.
*June 5, 2012 by JULIA*

**calculus**

Find an equation of the tangent line at x = 0 for the given function. f(x) = 5x2 + cos(x) I really need help on this one.
*June 20, 2010 by Irene*

**Calculus**

Find the equation of the tangent line to f(x)=x sec x at ((pi/4),(pi•sqrt 2)/4). Please check my derivative .. Is it (sin^2(x)+ 1)/cos^3 (x)?
*November 12, 2014 by Anonymous*

**calculus**

Let f be the function given by f(x)= x^2+4x-8. The tangent line to the graph at x=2 is used to approximate values of f. For what value(s) of x is the tangent line approximation twice that of f?
*December 11, 2011 by Jane*

**Calculus**

Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)
*March 4, 2010 by Salman*

**Calculus**

Find an equation of the tangent plane (in the variables x, y and z) to the parametric surface r(u,v) =(2u, 3u^2+5v, -4v^2) at the point (0,-10,-16)
*March 4, 2010 by Salman*

**Calculus 12th grade (double check my work please)**

2- given the curve is described by the equation r=3cos ¥è, find the angle that the tangent line makes with the radius vector when ¥è=120¨¬. A. 30¨¬ B. 45¨¬ C. 60¨¬ D. 90¨¬ not sure A or D 2.) which of the following represents dy/dx when y=e^-2x Sec(3x)? A.3e^-2x sec(3x) tan (...
*March 6, 2011 by anon*

**Calc, Implicit Differentiation**

Regard y as independent variable and x as dependant variable and find the slope of the tangent line to the curve (4x^2 + 2y2)^2 - x^2y = 4588 at point (3,4). Correct answer is -0.668827160493827 Here's what I did: 2(8x(dy/dx) + 4y) -2x(dx/dy)y + x^2 = 0 16x(dx/dy) + 8y - 2x(dx...
*October 21, 2006 by Michael*

**Math**

This question makes reference to an orthonormal basis (i,j), and an origin O. 1. Consider the triangle ABC, with vertices A(0,-2), B(9,1), C(-1,11). Find: a) a cartesian equation of the altitude from C; b) a cartesian equation of the circle which has BC as a diameter; c) a ...
*February 27, 2008 by Anonymous*

**Calculus**

A curve is defined by the parametric equations: x = t2 – t and y = t3 – 3t Find the coordinates of the point(s) on the curve for which the normal to the curve is parallel to the y-axis. You must use calculus and clearly show your working, including any derivatives you need to ...
*July 18, 2014 by Daksh*

**Calculus**

Use linear approximation, i.e. the tangent line, to approximate (the 3 is inside the v part if you know what I mean, it's not 3 times sqrt) 3√125.2 as follows: Let f(x) = 3√x. The equation of the tangent line to f(x) at x=125 can be written in the form y=mx+b where...
*September 28, 2009 by Z32*

**Math**

For the given point and line, find by projection the point on the line that is closest to the given point and use perp to find the distance from the point to the line. P (3,-5) line: x = (2,-4)+t(3,-4)
*September 25, 2014 by Wes*

**CAL**

The slope of the tangent line to the graph y= x^3/3-x at the point (1, -2/3) So I plugged this into y= and I found the (1,-2/3) point but I don't know what to do next, can you help?
*November 18, 2014 by Arnold*

**Calculus Help Please**

Consider the implicit function ln(xy)-cos^-1(x-1)=x a. Find dy/dx. b. Find y when x = 1. c. Find the equation of the tangent line in slope-intercept form when x = 1. Show steps please! Thanks!
*April 8, 2014 by Tenshi*

**Math**

In the diagram below of triangle ACD, E is a point on line AD and B is a point on line AC, such that line EB is parallel to line DC. If AE = 3, ED = 6, and DC = 15, find the length of line EB.
*February 9, 2010 by John*

**cal**

Write the equation of the tangent at (2,2) to the curve x^2-2xy+y^2+2x+y-6=0 Can anyone please give me some ideas to do it?Thanks!
*January 4, 2009 by Ivy*

**Algebra**

Is it possible to find the slope of a line if the equation has two ys? Find slope of the line whose equation is 8y = 7 - 2y Solve for y and you'll have a horizontal line. Combine the y terms. 8y+2y=7 10y=7 y=7/10 The general equation for a straight line is y = mx + b m is the ...
*November 3, 2006 by Samantha*

**Geometry**

Point A is 5 feet from the center of the circle and 11 feet from point B. Line AB is tangent to circle O at A. Find OB to the nearest tenth.
*April 15, 2012 by Joe*

**calc so confused**

Point (5,3) lies on curve y=sqrt(x+4). If Q is the point (x,sqrt(x+4)), use your calculator to find the slope of the secant line PQ for the following values of x. a)x=4.5 I just want help on this one. What do I do? I don't even understand the question.
*September 18, 2007 by apoorva*

**Calculus PLEASE check my work ,**

1.) which of the following represents dy/dx when y=e^-2x Sec(3x)? A.3e^-2x sec(3x) tan (3x)-2e^-2x Sec(3x)<<<< my choice B.)3e^-2x sec(3x)tan (3x)-2xe^-2x sec(3x) C.)3e^-2x sec(3x)tan (x)-2e^-2x Sec(3x) D.)3e^-2x sec(3x)tan (x)-2xe^-2x sec(3x) 2.)calculate dy/dx if...
*March 12, 2011 by anon*

**math**

Find an equation of the line that has a positive slope and is tangent to the circle (x-1)^2 +(y-1)^2=4 at one of its y-intercepts . Write your answer in the form of y=mx+b.
*March 2, 2008 by jen*

**calculus**

Consider the function. f (x) = 5x3 + 3x (a) Compute the derivative at x = 3 using the limit definition. f '(3) = (b) Find an equation of the tangent line. 2
*June 14, 2010 by Irene*

**Calculus**

Find the slope-predictor formula and write an equation for the line tangent to (a, f(a)) for f(x) = x2 - 6x + 4. Make sure you detail the process.
*December 16, 2010 by Brian Meredith*

**finitemath**

Find an equation of the line containing the given pair of points (3,5)& (9,8) Ok, if we know 2 points we can determine the slope as the difference of the y-values over the difference of the x-values. Thus if P=(3,5)& Q=(9,8) m =(8-5)/(9-3) Now if you know the slope and a point...
*August 28, 2006 by LaTannyia*

**Calculus**

find the equation of both the tangent lines to the ellipse x^2+9y^2=81 that pass through the point (27,3)
*October 2, 2008 by kelly*

**mathematics**

Find the equation of the smaller circle tangent to both axes and passing the point (-3,6)
*August 3, 2011 by ceasar1*

**Calculus**

A differentiable function f(x,y) has the property that f(2,2)=2 and fx(2,2)=1 and fy(2,2)=2. Find the equation of the tangent plane at the point on the surface z=f(x,y) where x=2, y=2.
*October 17, 2012 by Caroline*

**calculus**

At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous rate of change of the function.
*March 10, 2011 by Adam Janky *

**Calculus**

I was wondering if you would be able to check if my answers are correct: 1. An oil tank is being drained for cleaning. After t minutes there are v litres of oil left in the tank, where v(t)=40(20-t)^2, 0<=t<=20. Determine the rate of change at the time t=10. For this ...
*April 10, 2014 by Sarah*

**Calculus Assignment**

Hey there. Okay well I just started first year university and we got an assignment to sorta brush up our rememberance of everything and well...I'm not remebering to well. If anyone can help me with this question that would be great. Thanks. The secant method of finding a root ...
*September 12, 2006 by Tracy*

**Math**

From an exterior point P that is h units from a circle of radius r, a tangent line is drawn to the circle. Let y denote the distance from the point P to the point of tangency T. Express y as a fuction of h.
*January 29, 2012 by Jennifer*

**geometry**

The equation of a circle is(x-3)squared plus (y+2)squared.The point (8,-2)is on the circle.What is the equation of the line that is tangent to the circle at (8,-2)? y=8 x=8 x=3 y=3
*January 18, 2012 by Dana*

**Math, 11**

okay so i am trying to model a cubic equation to fit my curve my base curve is specifications: x value-0 to 6.19 amplitude-0.77 amplitude coordinates-3.73,0.77 x intercepts-0,0 and 6.19 , 0 this is my curve and i have to make a equation and include transformations to make this...
*April 24, 2010 by Functions*

**12th grade calculus**

find points on the curve x^2+xy+y^2=7 (a) where the tangen is parallel to the x-axis adn (b) wehre the tangent is parallel to athe y-axis. (in this case, dy/dx is not defined, but dx/dy is. what value does dx/dy have at these point?)
*October 19, 2008 by -*

**Algebra**

Need help with two questions. I've been stuck on them for a while now. 1) Find a general form of an equation of the line through the point A that satisfies the given condition. A(−2, 5) slope 3/4 2)Find a general form of an equation of the line through the point A that ...
*February 25, 2013 by Jim*

**Geometry**

Prove that the tangents to a circle at the endpoints of a diameter are parallel. State what is given, what is to be proved, and your plan of proof. Then write a two-column proof. Hint draw a DIAGRAM with the points labeled. Can some one please check for me Given : ...
*July 5, 2007 by DANIELLE*

**Calculus 12th grade (double check my work please) **

1.) which of the following represents dy/dx when y=e^-2x Sec(3x)? A.3e^-2x sec(3x) tan (3x)-2e^-2x Sec(3x)<<<< my choice B.)3e^-2x sec(3x)tan (3x)-2xe^-2x sec(3x) C.)3e^-2x sec(3x)tan (x)-2e^-2x Sec(3x) D.)3e^-2x sec(3x)tan (x)-2xe^-2x sec(3x) 2.)calculate dy/dx if...
*March 7, 2011 by anon*

**college alg**

find the equation of a line that is parallel to the line x=6 and contains the point (-8,9) please show work, it also wants me to show the answer in an equation
*September 4, 2012 by alli*

**Calculus**

the slope of the line tangent to the curve y=(tanx/cosx) at x=(pi/3) is? a)-8 b)2√3 c)3√2 d)8 e)14
*December 5, 2012 by Rudy*

**calculus**

I am trying to find equation of the tangent line to the curve 2/(1-3x) at x=0 using the definition. I applied it into the formula lim h->0 [f(a+h) - f(a)]/h which gave me [2/(1-3x+h) - 2/(1-3x)]/h I took the conjugate and came with [4/(1-3x+h)^2 - 4/(1-3x)^2] / h(2/(1-3x+h...
*October 1, 2011 by Daniel*

**Chemistry**

okay so I have this question; Co3^2- is a component of soil and can neutralize acid deposition. Sketch the pH curve for soil containing carbonate ions that undergoes continual addition of hydronium ions from acid deposition. Include relevant chemical equations and information ...
*June 14, 2010 by Jessica*

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