







Algebra 
20191106 

From Krizhia: How is y= 1/2 * (x1)² be x= √2y + 1. Please show me the steps Answered by Penny Nom. 





Solve for x in Y=1.5x + log (1+x) 
20181223 

From Asadollah: Please restate below expression in terms of y
Y=1.5x + log (1+x)
Thanks Answered by Penny Nom. 





The inverse square law 
20180605 

From Amy:
Question about inverse square law ;
Hi, I'm trying to understand some nuances about this law and
have been reading about it a lot online and trying out some homework
for personal interest (hobby )  not school related.
I understand that the simple formula is ; 1/d^2
I was wondering about what appears to be an oddity to me, that
I came across when I was working with a test example I found at this
link ;
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
The problem that caught my interest was this one on that page ;
"1) If a bright flashlight has a light intensity of 15.0 candela at a distance 1.00 m from the lens, what is the intensity of the flashlight 100.0 m from the lens?"
So I have a few different questions about this, but the most important
one is, what does it mean if we replace the "1" in ; 1/d^2 with a different value such as a ratio in the form of a decimal value, so instead we have something like this ;
0.75/d^2
???
Does this ratio represent a curve then?
I am thinking that the "1" in the normal formula represents a straight line
Some of the links I was researching ;
http://wisptools.net/book.php?c=3&s=2
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
https://www.ndeed.org/GeneralResources/Formula/RTFormula/InverseSquare/InverseSquareLaw.htm Answered by Penny Nom. 





The inverse of y=x^2+x+c 
20161221 

From Sam: What is the inverse of y=x^2+x+c for x? Answered by Penny Nom. 





The inverse of y = x(x  2) 
20161221 

From Sasha: Hello, I recently stumbled upon this question and I haven't been able to figure it out.
Why is the inverse of y=x(x2) not a function?
Suggest a domain restriction which would ensure that the inverse is a function.
Thank You :) Answered by Penny Nom. 





The derivative of the inverse of a function 
20161028 

From Kate: Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^1(4) if f(3)=4 and f'(3)=1/7 Answered by Penny Nom. 





The inverse function for f(x)=2x^2+5x 
20160423 

From Ashini: The inverse function for f(x)=2x^2+5x Answered by Penny Nom. 





The inverse of a function 
20160320 

From Billy: f(x) = Square root(x^2 + 2x)
What is the inverse? Answered by Penny Nom. 





tan inverse 1/4 
20160314 

From nazz: prove; tan inverse 1/4=1/3 cot inverse 52/47 Answered by Chris Fisher. 





Solve x=r(tsin(t)) for t 
20150228 

From David: I don't know how to write the function of t(x) by x=r(tsin(t)).
Can you teach me that? Answered by Harley Weston. 





The inverse of f(x) = x^2  x 
20140822 

From Tyler: Find the Inverse function of:
f(x) = x^2  x Answered by Robert Dawson. 





The inverse of y = 5^x 
20140307 

From Melody: how do you find the inverse of y = 5^x Answered by Penny Nom. 





Inverse trig functions 
20130519 

From ky: hello, so iv'e been asked to draw a triangle with sides of 3, 4, and 5.
And find the measure of all three angle using sin1, cos1, tan1.
I got really confuse, I'm taking the SAT pretty soon and it would be great
to get this... THANX Answered by Penny Nom. 





How do i write log_8(P) =7 in exponential form? 
20130414 

From nancy: How do i write this in exponential form log8P =7 Answered by Penny Nom. 





If 4 cooks can bake 8 pies in 6 hours????? 
20130318 

From Kenneth: Hello:
I want to determine which quantities are directly and inversely proportional in order to determine the answer for the following:.
If 4 cooks can bake 8 pies in 6 hours, 2 cooks can bake how many pies in 4 hours?
Answer: 2 2/3 pies
Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above?
I thank you for your reply. Answered by Robert Dawson. 





The inverse of y = x^2  2x 
20120420 

From Shona: How do I Find the inverse of the function y= x^2  2x ? Answered by Penny Nom. 





The length is inversely proportional to the width 
20120318 

From David: For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is12 and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9 Answered by Penny Nom. 





If x ix directly proportional to y then ... 
20120219 

From Crystal: I understand that we say x and y are proportional, then y = kx.
Generally when we say x is proportional to y, we think that when x increases y increases.
Now I am questioning whether that is actually true.
If k is negative, then when x increases, y DECREASES.
My question is does this mean this statement is incorrect:
If x is proportional to y, when x increases, y increases proportionally.
Is it more correct to say:
If x is proportional to y, when x increases, y either increases proportionally or decreases proportionally.
Along the same line of reasoning, when x is inversely proportional to y,
we think that when x increases y decreases, but that is true only if k is positive.
Is that correct? Answered by Harley Weston. 





Properties of real numbers applied to subsets 
20120201 

From Mark: Hello 
The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson. 





sin x = 0.25 
20110329 

From Wayne: How do you solve for x in the equation sin x = 0.25
the answer is 3.394 and 6.030 but I don't know the steps they used to calculate this Answered by Penny Nom. 





tanθ=1.192 
20110115 

From Adori: Use a calculator to approximate two values of the θ (0 ≤θ≤2π) that satisfy the equation.
a) tanθ=1.192
I do not understand how to find the second value of θ. Answered by Harley Weston. 





Angle of incline 
20100120 

From Alan: how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You Answered by Penny Nom. 





The domain, range and inverse of a relation 
20100108 

From Nazrul: Given that A={2,1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details.
Thank you. Answered by Penny Nom. 





The inverse of f(x)=1/x^2 
20091022 

From Jasmine: how to solve f(x)=1/x^2 > find f1[x], than state if its a function Answered by Harley Weston. 





The inverse of F(x)=x^26x+13, for x>3 
20090726 

From Juan: The function F is given by F(x)=x^26x+13, for x>3.
A. Write F(x) in the form (xa)^2+b
B.Find the inverse function F^1
C.State the domain of F^1 Answered by Penny Nom. 





Direct and inverse relationships 
20090406 

From allison: A piece of string is cut into n pieces of equal lengths L
(1) does n vary directly or inversely with L Answered by Penny Nom. 





Direct, inverse and indirect proportionality 
20090304 

From Brian: My 14 year old is confused about indirectly proportional and inversely proportional. On searching on the internet we were directed to:
http://mathcentral.uregina.ca/QQ/database/QQ.09.00/ellis1.html
Here leanne starts explaining indirectly proportional and ends up describing inversely proportional. Has Leanne got it wrong ?
What is indirectly proportional.
Thanks
Brian Answered by Chris Fisher. 





y varies jointly as x and the square of z and... 
20090105 

From peter: I don't really get the terms in this problem. Could you explain it: If y varies jointly as x and the square of z and inversely as the cube of w, by what factor is y increased when z is doubled and w is divided by 3 and x remains the same? Answered by Harley Weston. 





What is f^1(3) when f(x)=2x1? 
20090103 

From Peter: how do you do functions like f^1(3) when f(x)=2x1? Answered by Penny Nom. 





The inverse function for F(x)=x^3+x 
20081218 

From alireza: I want inverse function for F(x)=x^3+x Answered by Robert Dawson. 





Inverse variation 
20080522 

From leria: In Boyle's law, the pressure of gas varies inversely with the volume of the gas. A volume of 11.2 liters of air exerts a pressure of 2.0 atmospheres.
determine the constant of variation and write an equation the models the relationship between the pressure of the gas P and its volume, V. Use the equation to predict the volume of air necessary to exert a presure of 0.25 atmospheres. Answered by Janice Cotcher. 





The inverse of a function 
20080503 

From keith: please help me find the inverse of this function:
h(t) = 2 + 4 ln(15t) Answered by Stephen La Rocque. 





Two function problems 
20080410 

From keith: find the domain: F(x)= 1/ {ln (x+5)  ln (7x)}
find the inverse: g(t)= sqrt {23 ln (1t)} Answered by Penny Nom. 





cosec [arccos (1/y)] 
20080409 

From Tom: I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is? Answered by Penny Nom. 





Inverses of functions 
20080313 

From jess: if g(x)=2x+3 find g^1(g(4))
how do I sovle I cant's figure out what to do with the 4 Answered by Stephen La Rocque. 





Direct and inverse variations 
20071127 

From Julie: Please Help I do not understand this question. X varies directly as the square of S and inversely as T. How does X change when S is doubled ? When both S and T are doubled ? I appreciate your help with this problem. Answered by Stephen La Rocque. 





A matrix equation 
20071116 

From stephanie: Im supposed to solve
( 1 tan =E8/2) ( 1 tan =E8/2)^(1)
(tan =E8/2 1 ) (tan =E8/2 1 )
Matrix AA<(1)=I Answered by Penny Nom. 





Variation 
20071029 

From deeqa: 1. A car traveled 175mi at a certain speed. If the speed had been 20mph faster,
the trip could have been made in 1hr less time. Find the speed
2. The average weekly allowance A of children varies directly as their grade level, G.
If the average allowance of an 8thgrade student is $8.56 per week, what is the average
weekly allowance of a 5thgrade
The time T required to do a job varies inversely as the number of people P working. It takes 2hr for 4
working. It takes 2 hrs for 4 volunteers to distribute flyers to a neighborhood. How long would it take 12
volunteers to complete the job? Answered by Penny Nom. 





Inverses of Quadratic Functions 
20071011 

From Elliot: I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated. Answered by Steve La Rocque and Harley Weston. 





What is the inverse function of y=x^3 +x? 
20070919 

From saman: what is the inverse function of y=x^3 +x Answered by Harley Weston. 





Linear systems and inverses 
20070806 

From Marsia: explain how inverses are used to solve linear systems. Answered by Penny Nom. 





Direct and inverse Variation 
20070403 

From liz: how do you tell if an equation varies Directly or Inversely? ex.
x= 2y or
xy+12=3
i know that if you have three numbers (x. y, z) that it varies jointly but how do you tell if it is Inverse or Direct?
Thanks for the Help!
liz Answered by Stephen La Rocque. 





What does inverse graph represent? 
20070330 

From san: what does inverse graph represent? Answered by Penny Nom. 





Is the inverse of a function always a function? 
20070329 

From San: Is the inverse of a function always a function? Please justify. Thank You! Answered by Penny Nom. 





The angles in a right triangle 
20070328 

From Golaan: I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length.
I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters.
I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?
The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint. Answered by Penny Nom. 





Direct and inverse variation 
20070303 

From Rene: Hi I'm Rene, I'm stuck with some problems in direct and inverse variation.
I know how to solve direct and inverse problems when only one variation is in a question at a time.
EX: p varies inversely as the square root of q, and when p=12, q=36 find p when q=16
12*6 =p*4 72=4p 18=p
But how would you solve a problem like.....
If s varies directly as r and inversely as t, and s=10 when r=5 and t=3, for what value of t will s=3 when r=4 ? Answered by Penny Nom. 





Direct and Inverse variation 
20061027 

From Vishalinee:
i'm not sure how to use the words direct variation and inverse variation to describe thre relationship between: a. speed and distance b.speed and time c. distance and time. and then i need to create equations using the descriptions. i am really messed up with direct and inverse variation. Answered by Karen McIver. 





Finding the inverse of a function 
20060412 

From Sam: If g(x) = 2x+3/5 then how do I find the inverse? Answered by Walter Whiteley. 





y = log(x) + x. Solve for x. 
20050826 

From Alain:
I have the following equation:
y = ln(x) + x
How do I solve for x?
Answered by Penny Nom. 





Angle of incline 
20050515 

From Kyle: What is the degree of incline of a 12 foot plank that goes from 10.5 inches on one end to zero inches on the other? Answered by Penny Nom. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





Direct and inverse variation 
20041005 

From Abraham: Given that y varies inversely as x and x varies directly as z.If z is doubled then y is halved.Why is that true.Please explain.I'm having trouble understanding the different types of variation Answered by Penny Nom. 





An inverse 
20040909 

From Hillary: I cannot figure out the inverse of this function.
f(x)= 1/2x 1 Answered by Penny Nom. 





d varies inversely with g 
20040907 

From Ashlyn: d varies inversely with g when d=8 and g=2
a. write d as a function of g using function
notation.
b. find d(10). Answered by Penny Nom. 





The inverse of a quintic function 
20040722 

From A student: I'm really having trouble finding out the inverse of this quintic equation. F(X)= X^{5}+3X^{3}+1.I know that this quintic has an inverse because it is one to one. But I can't find a method to solve this. Finding the inverse of a quadratic or a cubic equation is a lot easier, but with this quintc I am really lost. I even know how the graph of this equation and its inverse looks like, but I'm not sure if Iam getting the right equation. Please help me out. Answered by Penny Nom. 





Finding angles 
20031202 

From Jason: I AM TRYING TO SOLVE A TRIG PROBLEM AND HAVE
FORGOT HOW TO DO IT. WHAT I HAVE IS A RIGHT TRIANGLE WITH SIDE A BEING 14
FEET AND SIDE B BEING 3 FEET, USING PYTHAGOREAMS THEOREM SIDE C SHOULD
EQUAL 14.318 FEET ON A RIGHT TRIANGLE BUT I AM TRYING TO REMEMBER HOW TO
FIND MY ANGLES OTHER THAN THE ONE THAT IS 90 DEGREES. Answered by Penny Nom. 





Differentiating inverses 
20021120 

From Amy: f(x)= x^{3}+x+1, a=1 find g'(a) (g = f^{ 1}). I am having trouble finding g(a). Answered by Penny Nom. 





Matrix 
20011121 

From Hoda: I have a question about matrix multiplication; well, actually, matrix division. I am assuming that matrices are divided the same as they are multiplied; that is, row by column. But what happens if you have to divide by zero? How does this affect the resulting matrix? Answered by Patrick Maidorn and Penny Nom. 





Proportionality: direct and indirect 
20010118 

From Nancy Ellis: What is the difference between directly proportional and indirectly proportional? Answered by Leeanne Boehm. 





cot(arcsin 3/5) 
20010107 

From Jason: Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Answered by Harley Weston. 





Direct and inverse variation 
20001212 

From Ashley: I'm stuck on this unit of direct and inverse variation..please and my problems and show me how to do each PLEASE!!! Assume that y varies directly as x If y= 4 when x = 2, find y when x= 6 Assume that y varies inversely as x If y =4 when x=2, find y when x =6 Answered by Penny Nom. 





Triangles and trigonometry 
20001130 

From Mose: If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles? Answered by Harley Weston. 





Range of a function 
20001121 

From David Bell: Given a rational function such as f(x) = (8x3)/(4x1). How can the range be found. Answered by Penny Nom. 





Using the inverse sine function 
20000531 

From Nelson Rothermel: This has me completely baffled. I have to use the laws of sine or cosine to find the angles of a triangle when I have 3 sides, so I can't go 180xy when I have 2 angles. Now, I have a triangle with values of 3, 7, and 9. Here are the steps I used (A,B,C are angles; a,b,c are opposite sides): angle A (16.1951 degrees): cos^{1}*((b^{2}+c^{2}a^{2})/(2*b*c)) angle B (40.6011 degrees): sin^{1}*(b*sin(A)/a) angle C (56.7962 degrees): sin^{1}*(c*sin(A)/a) If you notice, A+B+C does not equal 180. According to the book, A and B are correct, but C is supposed to be 123.2038 degrees. Why doesn't it work??? Answered by Harley Weston. 





Graphing cube roots 
20000427 

From Heather Jones: What do the graphs of cube roots look like? Answered by Walter Whiteley. 





Cos x = 1/2 
19991201 

From Pierre Boivin: When I factor[ 2cos (square)  5cos 3], I get (2cos + 1)(cos  3). 2cos + 1 = 0, 2cos = 1, cos = 0.5,. Using inv cos on calculator, I get 120 degree related angle. When I graph I get two values, between 90 and 180 degree and between 180 and 270 degrees. How do I find those two values. How do use 120 degree in relation with the x axis. Answered by Penny Nom. 





Domain and Range of a Function 
19991114 

From Michelle Mellott: How do you find the range of the following function: 2y^{2}/(y^{2}+5y+6)?? I know the domain is x not equalled to 2, 3. How can one easily find the range? Answered by Harley Weston. 





Inverses of functions 
19991101 

From Leanne Hickey: Let f(x) = 2x^{2} 3x + 2. Find f^{1}(4) given the fact that f(2) = 4. So the question is finding the inverse of 4, he said it's easier than it looks. Answered by Penny Nom. 





Matrices 
19980310 

From Ksya:
 A and B are matrices. If A^n=B^n, can we say A=B or det(A)=det(B) or det(A)^n=det(B)^n ? Any conditions ???
 If B^(1) is the inverse of B, where B is a matrices. Can we say [(B^(1))^n][B^n]=I, where I is identity matrices? Any conditions???
Answered by Doug Farenick. 





Inverse 
20051018 

From Pauline: Défi ! a et b désignent deux nombres distincts non nuls. Peuton trouver un nombre à retrancher du numérateur et du dénominateur du quotien a/b pour obtenir son inverse b/a? Answered by Claude Tardif. 

