







Solve sinX=0.703X for X 
20180313 

From PARAM: sinX=0.703X Answered by Penny Nom. 





A cubic equation 
20160725 

From Chinmay: x³2x²7x+5 Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





The positive root of sin(x) = x^2 
20151213 

From Kemboi: Find the positive root of the equation sin(x) = x^2 Answered by Penny Nom. 





The method of elimination 
20150501 

From oreanna:
Question from oreanna, a student:
How do u solve 2x+9y=3
7x4y=25 in elimination Answered by Penny Nom. 





1/6k=11 
20141113 

From Marty: Using the balance method, what is the answer to 1/6k=11, trying to find what k equals. Thanks Answered by Penny Nom. 





The method of elimination 
20140705 

From leo: please explain how can i solve this problem
3x6y=38
6x9y=44
using elimination and simultaneous method thank you :) Answered by Penny Nom. 





x  2 Sin[x] = 0 
20140508 

From chanmy: please help me to sole this equation x  2 Sin[x] = 0,thank you Answered by Penny Nom. 





n log n = 36 * 10 ^ 12 
20131112 

From shihab: How to find value of n in this equation :
n log n = 36 * 10 ^ 12 Answered by Penny Nom. 





Four equations 
20130808 

From may: HI how to solve this 4 equations?
A+C = 0
4A+B8C+D=1
3A+16C8D=29
12A+3B+16D=5 Answered by Robert Dawson. 





Solve sin 3x = 0.1254 with x between o and 360 degrees 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Solve sin 3x = 0.1254 with 0 
20130221 

From David: sin 3x = 0.1254 0 Answered by Harley Weston. 





Sinx=logx+x^2 
20121128 

From yasmin: Sinx=logx+x^2 Answered by Harley Weston. 





A volume of revolution 
20120715 

From Tewodros: Let f(x) = e^x and g(x) = x^1/2 both be defined on [0,1]. Consider the region bounded by f(x), g(x), x = 0, x = 1. Rotate this region about the yaxis and determine the volume using the shell method. Answered by Harley Weston. 





Using Newton's Method to find a root 
20120409 

From Nancy: Use Newton's method to find the real root function, accurate to five decimal places
f(x) = x^5+2x^2+3 Answered by Penny Nom. 





Four apples and two oranges cost Rs. 30... 
20120113 

From nasr: Four apples and two oranges cost Rs. 30, and one apple and 3 oranges costs Rs.15.How much does each apple and each oranges cost? Answered by Harley Weston. 





A volume of revolution 
20120111 

From john: find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the xaxis about the line y=8. The answer in the back of the book is 704 pi divided by5 Answered by Penny Nom. 





Eliminate y 
20110407 

From Lynn: 2x + y = 8
y + 3z =5
z + 2w =1
5w + 3x = 9
Form three equations with y eliminated Answered by Penny Nom. 





The percentday method 
20101204 

From Kenneth: I read about this method in an old business mathematics book and was curious about how it works to produce the correct answer.
“Percentday method is based on 360 days’ time and 1% interest. Any interest rate multiplied by any number of days is equal to so many %days.”
Example: 82 days at 5% equals 410%days. Answered by Penny Nom. 





Elimination and substitution 
20100918 

From Lauren: Solve one using the method of substitution and the other with the method of elimination.
v
a. y=5x+4
x=2y+1
b. 4x+3y=7
6x3y=13 Answered by Penny Nom. 





A logarithmic equation 
20100908 

From Rohit: x^2 + k*ln(x)  c  k = 0
Where k and c are constants. Answered by Penny Nom. 





x/a +y /b =a+b : x/a^2+ y/b^2 =2 
20100530 

From smithu: x/a +y /b =a+b : x/a2+ y/b2 =2 solve by using elimination method ,
cross multiplication, substitution method Answered by Penny Nom. 





Arc length and Chord length 
20100313 

From Darryl: Is there a formula to determine the chord length of an arc knowing only the arc length and the arc depth (sagitta)? I know you can't find the radius with only these two inputs, but can you find the chord length? Answered by Harley Weston. 





Substitution method 
20100217 

From Melodie: 7x  4y = 10
4y= x2 Answered by Tyler Wood. 





Linear programming using the Simplex Method 
20091228 

From William: A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running,
at least three tons of ore must be processed each day. Ore from source A costs $20 per ton to
process, and ore from source B costs $10 per ton to process. Costs must be kept to less than $80 per day.
Moreover, Federal Regulations require that the amount of ore from source B cannot exceed twice the
amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B
yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to
maximize the amount of gold extracted subject to the above constraints?
I need a linear programming solution or algorithm of the simplex method solution.
Not a graphical solution. Thanks. Answered by Janice Cotcher. 





A linear system 
20091020 

From marissa: Solve this linear system
2xy=5
3x+y=9 Answered by Penny Nom. 





541.39(1 + i)^15 = 784.09 
20091014 

From Fitore: Hi, I noticed that this question was already posted up, however I was hoping I could solve it without having to use logs. Can you please help me? The equation is:
541.39(1 + i)^15 = 784.09 Answered by Penny Nom. 





Elimination method 
20091008 

From Kenty: How do I solve this problem using the elimination method?
3x7y=0
6x+4y=0
I am not sure how so if someone can show me a similar problem (instead of
solving this one for me) that would be fantastic. Answered by Penny Nom. 





Two equations in two unknowns 
20090918 

From Citizen: x+3y=7
x+4y=7 Answered by Penny Nom. 





The method of substitution 
20090917 

From laura: ok! i really need help with this question plz help!!
x=  4y +5
x+2y = 7 Answered by Penny Nom. 





Find the central angle 
20090818 

From Larissa: In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem. Answered by Harley Weston. 





Linear systems 
20090220 

From Rose: I have been having trouble trying to figure out these three math problems , I need help breaking them down so I could understand them better please help.
1. x = 7  x
2 x  y + 8
2. 8 x + 5 y = 1 8 4
x  y = 3
3. y + 2 x = 3
y + 2 x = 4
I can't figure out how to break them down in the right order. Answered by Penny Nom. 





The substitution method 
20090218 

From Nicolette: I am working on linear programming problems that I need to solve pairs of linear equations for. I am confused and am not sure how to solve these problems!
5x+3y=7 y=x3 How can i solve this using the substitution method? Answered by Penny Nom. 





The substitution method 
20090206 

From amber: Pleasse help me with this problem
x+y=2
y2x=1 Answered by Penny Nom. 





System of equations  comparison method 
20090102 

From nick: Hi, I am doing a project on system of equations by using comparison method,
but for some reason or another, i can't seem to find any information on the
comparison method at all. So, please would you help me by giving me a website
that you know of that has some information on my method. And, if you know the
answer, can you please tell me why or when do we use system of equations by
using comparison method?
Thank You Answered by Robert Dawson. 





The substitution method 
20080726 

From Enid: Solve by substitution method
3x + 7y = 25
7x + y = 63 Answered by Penny Nom. 





x^36x^2+3x+5=0 
20080522 

From faiz: x36x2+3x+5=0 Answered by Janice Cotcher and Harley Weston. 





Integrate 2x(x^21)^5 dx 
20080417 

From joey: pls help me to integrate
2x(x^21)^5 dx using the substitution u=x^21 Answered by Harley Weston. 





Estimate the cube root of 270 
20080311 

From Tom: (a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the NewtonRaphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results. Answered by Harley Weston. 





How would one find the radius? 
20071229 

From Ned: Given an arc with length of 192 inches (don't know chord length),
and arc height of 6 inches, how would one find the radius? Answered by Stephen La Rocque and Harley Weston. 





Solve sin(x)=x^2x 
20071211 

From ming: is there anyway you can solve
sin(x)=x^2x without a calculator? Answered by Stephen La Rocque. 





Chicken and goat feet 
20071205 

From Kim: Old McDonald raises goats and chickens. The animals have a total of
100 heads adn 360 feet. How many goats and how many chickens does Mr.
McDonald have? Answered by Stephen La Rocque and Penny Nom. 





Substitution method 
20071011 

From Kevin: 3xx+2y=36y=11 Answered by Stephen La Rocque. 





Two equations in two unknowns 
20070922 

From Mary: Having problems doing this problem, looking for a solution with the work. I would like to see how you got your answer, to see what I was doing wrong.
solve using the substitution method, is there "no solution" or "infinitely many solutions"
4x+y=4
2x+8y=0 Answered by Stephen La Rocque and Leeanne Boehm. 





The substitution method 
20070623 

From mary: solve the system by the method of substitution:
5x+2y=15
4xy=9 Answered by Stephen La Rocque. 





Simultaneous equations : the Elimination method 
20070621 

From Patricia: I need to find the value of X and Y using the Elimination method.
5/x + 3/y=4
25/x2/y=3 Answered by Stephen La Rocque. 





The substitution method 
20070508 

From A student: I need help on these two problems( substitution method)
2x+7y=10
x3y= 3
and
6x8y= 12 3x+4y=9 Answered by Penny Nom. 





A volume of revolution 
20070408 

From christina: find the volume of the solid formed when region bounded by y=x/3, y=2
and the yaxis. it is revolved about the xaxis.
the assignment was to use both the washer method and the shell method
but when i solved for the volume, i got different answers.
i think my shell method is wrong because i know i'm having difficulties
with using "dy" instead of "dx"
here's my work so far: Answered by Penny Nom. 





Factoring a trinomial 
20070327 

From Kim: Hi, could you please help me solve this.
3x(squared) +20x  7 Answered by Leeanne Boehm. 





The substitution method 
20070131 

From Victoria: how do i solve this problem using the substitution method? 2x5= 14 7x+14y= 5 Answered by Stephen La Rocque. 





The elimination method 
20070131 

From Addrianna: x2y=2 3x5y=7 Answered by Stephen La Rocque. 





A linear system 
20070104 

From Harold: System A (4, 2/3) 2x3y=6 and x3y=2
I approached this problem using the addition method.
Could i have found the answer using the graphing method? Answered by Penny Nom. 





Linear systems 
20060921 

From Alexander: Hello, i have a math assignment due tonight at midnight and i need some help please
It is using the addition method to solve linear systems Answered by Penny. 





The area of a sector and a triangle 
20060623 

From Howard: I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord. Answered by Stephen La Rocque and Penny Nom. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





The substitution method 
20041128 

From A student: I Was working and i ran into this problem can you help me solve it using the substitution method?
3x2y=10
x+5y=27 Answered by Penny Nom. 





Square roots and inequalities 
20041025 

From Waheed: Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)
Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides? Answered by Claude Tardif and Penny Nom. 





The method of substitution 
20040920 

From Kayla: y=x1
y=2x3 Answered by Harley Weston. 





The substitution method 
20040214 

From Keisha: I need to solve this problem by using the substitution method.
3x+y=1
x=2y+5
Please help me understand the method to solve. Answered by Penny Nom. 





Systems of equations 
20031119 

From Scott: I hope that u can help me....I
am a college student taking a class in Pre Calculus.....I have homework
due this Friday and it counts a BIG Percentage on my FINAL grade.....I
am getting mixed up and can not figure out a few problems.....Please help
me.....
Method Of Subsitution
Problem 1. y 8x = 5
x(squared) + y(squared) = 25
Problem 2. y = x(squared)  2x  6
Y = x(squared)  4
Answered by Penny Nom. 





Substitution method 
20030914 

From John:
Hello, my name is john and while I was finishing up my work I stumbled into these problems. a/4b=1 a+b=11 and 6ab=5 4a3b=8 Thanks a lot. I really need some help :) John Answered by Penny Nom. 





The substitution method 
20020224 

From Joe: whats the answer to this question? 3x+y=11 x+2y=3 its substitution method i am having alot of trouble figuring it out. send the answer as soon as possible. thank you Answered by Penny Nom. 





Solving x  sin(x) = constant 
20001229 

From Keith Roble: If x is in radians, how do you solve for x, where: xsin(x) = constant? Answered by Harley Weston. 





Question about 3rd degree polynomials 
19990423 

From Patrick Bryan: What is the general solution to the equation with the form: a*x^3 + b*x^2 + c*x + d = 0 I have once seen a solution to this a few years ago, but I do not recall if it was a general solution. What I do know, is that you could simplify this equation to: a*x'^3 + p*x' + q = 0... Answered by Doug Farenick. 





Duplation method of multiplication 
19981126 

From Sara Whitford: I am wondering why 16 and multiples of 16 do not work in the ancient duplation method of multiplication used by the Egyptians. I discovered the method in the Journeys math text gr 7 level. Just curious. Am I doing something wrong?? Answered by Jack LeSage and Harley Weston. 





Linear systems of equations 
19981116 

From Crystal Girvan: My name is Crystal Girvan.Im in grade 11. I have a question.We are solving linear systems of equations: comparison method. My questions is. it says a)use the method of comparison to solve this system a=b1, 3a+ b=3 b) verify your solutin in a I dont understand it. please help Answered by Jack LeSage. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 





Volumes 
19980829 

From Lorraine Wall: Consider the region in the first quadrant bounded by the x and y axes, the vertical line x=3 and the curve y = 1 / (x squared + 3). Determine the volume of the solid by rotating this region about the xaxis. Now that is the first part. I then have to find the coordinates of the centroid of the solid by rotating this region about the xaxis. Thanks. Lorraine Answered by Harley Weston. 





Volumes of Revolution 
19980724 

From Lorraine Wall: I'm on the section fpr The Computation of Volumes of Solids of Revolution and the following question is giving me problems: Consider the region in the first quadrant bounded by the xand yaxes, the vertical line x=3, and the curve y=1/(xsquared + 3) I can determine the volume of the solid by rotating the region about the yaxis using the shell method but I can't seem to be able to get started with the volume when rotated about the xaxis. Answered by Harley Weston. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? Answered by Harley Weston. 

