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How to calculate percentage change 2007-08-03
From Galland:
I am working on graphs and I need to find the percentage of increase from one figure to another. How do I do that? For instance staff hours for 2006 were 28011 and for 2007 were 31230. How do I find the percentage of increase?
What are the possible lengths of the hypotenuse? 2014-03-07
From audrey:
The three sides of a right angles triangle measure x-2, x+5, and 2x-1 in length. What are the possible lengths of the hypotenuse?

... I'm doing the equation c2=a2+b2 and subbing in the numbers but nothing makes sense

The inverse of y = 5^x 2014-03-07
From Melody:
how do you find the inverse of y = 5^x
The diameter of the base of a cone 2014-02-23
From elwin:
i have a sector of a circle that has 120 degree and 6 cm length. What will be the diameter of the base of the cone.
and what is the diameter of the angle is changed to 180.

Selecting a card 2014-02-16
From Akarsh:
Cards numbered 1 to 1000 were put in a box.Ali selects cards at random.What is the probability that Ali selects a card containing at least one'3'?
A sequence 2014-02-10
From Joshua:
hello..the question I have today is... A sequence... 1,5,14,30,55,91 find the general terms.
Conics 2014-02-01
From Kassidy:
Hey, I have searched through all the questions about conics and how people use them in the real world, but none of them were very specific on how they are applied and the process, why it's so important etc. I have a project due asking these questions and it's been very difficult finding the right answer, if you could name jobs, how they are use and specifically applied that would be greatly appreciated.
A sequence 2014-01-30
From joshua:
hi...really struggle with one question that the teacher gave us...
The sequence is 1,2,1,5,8,1,11,___,___

Counting in base five using words not digits 2014-01-25
From Randy:
We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure - in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow - how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems?
An arithmetic sequence 2014-01-06
From paris:
find the twenty-fifth term of an arithmetic sequence whose first term is 12 and whose common difference is -6
An infinite geometric series 2013-12-24
The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series
Find the next 3 terms of the sequence 2013-12-19
From Lanelyn:
Find the next 3 terms of the sequence 2,3,9,23,48,87,__,__,__
Base 5 arithmetic 2013-11-27
From samuel:
Good day sir, please i don't understand when you say 4x4=13 in base five? In fact, am always having difficulties in addition, subtraction, division and multiplication of number in the same base other than base ten. Please can you give me one example each with details explainations?
The popcorn box problem 2013-11-07
From Dave:
We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4-corners of a sheet of card and then folding up.

What I want is to find the sizes of card that lead to integer solutions for the size of the cut-out, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.

I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1.

A union and interception problem 2013-10-19
From Zakir:
Sir, I have some problem in union there is a Question in a book find B set if A={2,4,6,8} , AUB={2,4,5,6,7,8} and A intersection B={6,8} plz tell me how can I find the B set
Base 5 arithmetic 2013-10-12
From Obassy:
(4 2 4 3)-(1 3 x 4)=( Y 3 4 4),find the value of x and y in the subtraction above carried in base five?
Base 5 2013-09-30
From Zakir:
Sir I wanna know something about base 5 number system Why we use it and who use this ? and what is the purpose of it
The markup on a country maple bedroom set 2013-09-26
From steven:
Bargain Furniture sells a five-piece country maple bedroom set for \$1299. The cost of this set is \$700. What are the markup on the bedroom set?
Intersection points and diagonals 2013-09-11
From Kenneth:
I was wondering, is there a relationship between the number of sides of a regular n-gon and the number of times its diagonals intersect?
Ie:
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on.

The sum of all whole numbers from 1 to X 2013-09-06
From Tim:
How do I develop a rule for the sum of all whole numbers from 1 to X when I have no idea how to do this
A sequence or a series? 2013-09-05
From Rahul:
Whether the following sequence is increasing or decreasing? I even do not kow whether to call it a sequence or not. an = (1/(1+n))+(1/(2+n))+....+(1/(n+n)). I am confused. It looks like a series to me. Please help.
Regards,
Rahul

8 numbers from 80 2013-09-04
From susan:
Out of 80 numbers how many combinations of 8 are there and what are they.
More than half of the people said... 2013-08-26
From Lucy:
Hi,
The question is:
Samoa 23%
Brazil 41%
Sri Lanka 52%
Senegal 39%
Armenia 37%
Croatia 20%
Why is the following statement true for the data above: More than half of the people said they were interested in Sri Lanka. The reason I don't understand the problem is that because the percentages add up to be greater than 100%, that means that the 500 people(as stated in the question) who participated in the survey got to pick more than once. Therefore, it is not 52% out of 100% anymore. Thanks for taking the time to answer my question.

Tesseract 2013-08-22
From Dan:
I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help.

The question is: for a tesseract of side length = 1 what is the distance of the center of each cube from the center of the tesseract ?

I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me.

(anyone not having a clue what I am talking about can brush up here http://en.wikipedia.org/wiki/Tesseract )

Thanks in advance - Dan V

Consecutive Numbers Question 2013-08-11
From Lucy:
Hello,
I have a question about consecutive numbers. So lets say a question tells you to find what three consecutive numbers are that add up to a certain number. To calculate this, would you use 2x+1, 2x+3, 2x+5 or just x, x+2, x+4.
Also, the same question for even numbers. Would you use:
2x, 2x+2, 2x+4 or just x, x+2, x+4.
My math book is confusing because it uses the first strategy(the 2x+…) in some situations and the second strategy(x+…) in other situations. Thus, can you provide me an explanation of why you would use the strategy that is correct?
Specifically, my book answered this question: If “n” is the first of five consecutive odd numbers, what is their average, using n,n+2….=5n+20 and average is n+4(this is the answer),.
For the question: the sum of 4 consecutive odd integers must be:
Divisible by 8 but not necessarily 16(this is the answer), it used the strategy 2k+1, 2k+3…=8k+16.

Thank you so much for taking the time to answer my question.

Practical uses of trigonometry 2013-08-06
From tharindu:
use of trigonometry
Slicing through a cone to form an ellipse 2013-08-06
From Pulkit:
we get an ellipse on slicing through a cone. Is there a relation between central axis of the cone and this ellipse?
Does it pass through the any of the foci of the ellipse?

The area of a semicircle 2013-07-28
From Lucy:
Find the area of the the figure described: a semicircle with arc length 3 pi.
A geometric sequence 2013-07-16
From Relebohile:
Find the n^th term of 3,6,9,12,24,48...
Three consecutive odd integers 2013-07-08
From sparsh:
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
Inverse trig functions 2013-05-19
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 sin-1, cos-1, tan-1. I got really confuse, I'm taking the SAT pretty soon and it would be great to get this... THANX
Points of intersection 2013-05-02
From Bianca:
Find the sets of values of k for which the line y=kx-4 intersects the curve y=x^2-2x at two distinct points.
How do i reverse this formula? 2013-04-20
From MK:
I have 22,000,000 worth of gold and wants to want to resell the gold back with a profit. Each transaction of gold will have a transaction fee of 15%, so if i resell the gold back at 22,000,000, I will only get back 18,700,000 after 15% transaction cut. The current formula is X-15%X = Y where X = 22,000,000 and Y = 18,700,000 Will u be able to come up with a new formula if we don't know the value of X but we know the value of Y
Something like this X-15%X = 22,000,000. How do i reverse this formula to find the value of X
Thanks

How do i write log_8(P) =7 in exponential form? 2013-04-14
From nancy:
How do i write this in exponential form log8P =7
If 4 cooks can bake 8 pies in 6 hours????? 2013-03-18
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?

Can someone fully explain what I need to know in order to determine what is directly and inversely proportional in the example above?

Increasing and decreasing sales 2013-03-06
From Meghan:
Pace Design's sales increased by 30% in the first year, increased by 60% in the second year, decreased by 60% in the third year and increased by 90% in the fourth year. What was the cumulative change in sales over the 4 years?
From anis:
if the customer says your profit should be 20% of your cost..

1) my selling value should be cost +20% of cost = SP

or

2)cost / 0.80 = SP which is correct...if the second answer is right how should i justify my customer

Write a rule for the sequence 2013-02-20
From Angelia:
Write a rule for the sequence. Then, find the unknown term. 1 3/8, 1 ¾, 2 1/8, _______, 2 7/8 Think: The pattern is increasing. Add 1/6 to find the next term. Rule: _______________
How can I teach how to change bases? 2013-02-20
From Tammy:
How can I teach how to change bases? For example 80 base 10 changed to base 3. Thank you!
A curve in 3-space 2013-02-14
From pardeep:
we have to show that the curve r(t)=(cos t)i+(sin t)j+(1-cos t)k ,0<=t<=2pie; is an ellipse by showing it to an intersection of a right circular cylinder and a plane. i got the eqn. of the cylinder but did not get the eqn of plane.
Is a line lying in a plane an open or a closed region? 2013-02-13
From pardeep:
please help with this question on the open and closed intervals :: Is a line lying in a plane an open or a closed region? my teacher says it is a closed region reasoning out that it contains all it boundary points. please help how is it so?
Multiplication in base two 2013-02-01
From Michael:
multiply in the indicated base

110two*11two

The multiplication table for the different bases 2013-02-01
From sylvia:
I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers.
A triangular island 2012-12-29
From Udit:
A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone?
A raised bed in the shape of an octagon 2012-11-22
From pat:
I want to make raised-bed gardens - usually 4' square, but want to be more creative by creating octagonal boxes. The ideal size for square beds is 4'x4'. The boards are 8' long, so I want to get as much out of a board as I can. If I want an octagon with a diameter of 4', I think the sides would be (rounded off) about 1.5' each using 2 full boards with a little waste and the growing space would be less than a 4' square (16 square feet). If I want to increase the length of each side to 2' each (getting the max from a board), what will the diameter of this octagon be so I can determine the growing space of the box. (The reason a 4' square is important in gardening, besides maximizing the wood, is that a person can reach into the center to plant and pick veggies without stepping on the soil, so diameter is important). My math days are long over and I'm having trouble working with octagons! Thank you!
Difference of squares 2012-11-19
From Qelibar:
Factor (6a^2-5a+1)(8a^2-6a+1)(12a^2-7a+1) 2012-11-16
From bailey:
Factorise f(a)=(6a^2-5a+1)(8a^2-6a+1)(12a^2-7a+1) thus find [f(a)]^1/2
Stairs for the new community center, part 2 2012-11-13
From Emily:
Plans for a set of stairs for the front of a new community center use the ratio of rise to run of 2 units to 5 units.

B. Sketch a set of stairs that meets the rise-to-run ratio of 2 units to 5 units.

A function with 3 asymptotes 2012-10-19
From rimoshika:
find a function that have 3 Asymptotic : y=x/y=sinx/x=-1
The nth term of a sequence 2012-10-19
From Emily:
I don't understand how to do this question:
Nth term for 9, 7, 5, 3, 1
Is there a fast way to do nth term for this question? Or in fact any question?

Revolutions per second 2012-10-18
From Crystal:
Suppose a car wheel is 26 inches in diameter.
a) If the tire completes one rotation, how far would the car travel?
b) If the car is traveling at 60 miles per hour, how fast is the car wheel spinning in revolutions per second?

Functions 2012-09-18
From nayeem:
A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
Please give me the trick of finding such functions

Answered by Robert Dawson and Harley Weston.
Functions 2012-09-18
From nayeem:
I tried with many functions but I am not getting the exact values please help me A give an example of a function whose domain equals the set of real numbers and whose range equals the set the set {-1,0,1}?
B Give an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the set of positive integers and whose range is the set of positive even integers D. Give an example of a function whose domain is the set of positive even integers and whose range is the set of positive odd integers E give an example of function whose domain is the set of integers and whose range is the set of positive integers. F. Give an example of function whose domain is the set of positive integers and whose range is the set of integers.
Please give me the trick of finding such functions

Answered by Robert Dawson and Harley Weston.
Equivalent sets 2012-09-13
From asif:
show that (-1,1)~(1,1) or give its counter example
The hypotenuse 2012-09-06
From Jeevan:
how can i find the height and base of a right angle triangle if i have the hypotenuse only ?
A security code 2012-09-01
From Breanna:
The code is made up of five two digit numbers from 01 to 20 entered in a certain order. How many different security codes are possible with this system
Minutes and seconds 2012-08-29
From Casey:
I have to write a variable equation. The questions says there are 60 seconds. but we need to write and equation to solve for minutes. Is it 1/60 or 1/s
An arithmetic progression 2012-08-22
From A student:
the 3rd term of an A.PPP is 10 more than the first term while the 5th term is 15 more than the second.find the sum of the 8th and 15th terms if the 7th term is 7 times the first term.
John's electronic store 2012-07-25
From Jora:
Electronic Store John opened an electronic store in December. During his first month, He sold 10 LCD TVs and 20 Plasma TVs. His income during that month was \$12800. In January, he sold 25 LCD TVs and 40 Plasma TVs for an income of \$27600. In February he projects to sell 30 LCD TVs and 50 Plasma TVs. If John expenses are \$28900 in February, how much money will he have after paying the expenses?
A cylinder is to be filled with peas. 2012-06-12
From Silje:
Hi! How can I solve the following question without the use of a calculator?

"A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on. This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?"

Expanded exponential form? 2012-06-12
From Ramon:
express the numbers 990 614 000 005 in expanded exponential form.
A geometric sequence 2012-06-10
From vicki:
The sum of the first three terms of a geometric sequence of positive integers is equal to seven times the first term, and the sum of the first four terms is forty-five. What is the first term of the sequence?
The area of a semicircle 2012-05-28
From Rebecca:
how do you find the area of a semi circle and then how do you add the area of a semi circle and the area of a rectangle?
Division in base eleven 2012-05-27
From Zoe:
How do you divide numbers that are in base 11?

For example;

9A7A6A divided by A

The nth term 2012-05-05
From Justin:
Which expression can be used tofind the nth term in this sequence? 94,75,56,37,18,.....
My choices are
A. -19n=113        B. -21n+115
C. -19+75        D. 21n+73

Please explain how to get the correct answer. I think it is A. but I am not sure,

How to find the base length of a isosceles triangle if only the sides are given? 2012-04-25
From aqilah:
how to find the base length of a isosceles triangle if only the sides are given?
The inverse of y = x^2 - 2x 2012-04-20
From Shona:
How do I Find the inverse of the function y= x^2 - 2x ?
A semi-circular roof gutter 2012-04-09
From Kyle:
A semi-circular roof guttering contains some water.
The cross-section of the guttering has a diameter of 10 centimetres. The surface of the water collected in the guttering is 8cm. What is the depth of water in the gutter?

1+2+4+8....= -1 2012-04-02
From Andy:
In this minutephysics video, it's claimed that 1+2+4+8....= -1 Is this true, and if so, how?

The power set of A 2012-03-24
From rashdin:
Can you find a set A, |A|=4 and define a bijective function between A and P(A)?
The length is inversely proportional to the width 2012-03-18
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
Forming a triangle from 3 line segments 2012-03-15
From rustom:
A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle.
An increase/decrease in profit 2012-03-13
From Thanikasalam:
It is understood that increase/decrease in profit for current year compared to the previous year is done by the formula (x-y)/y, with x=profit on current year and y=profit on previous year. How do we derive this formula?

If we work on this formula of calculating increase/decrease in profit, we get x/y-1

* = (x-y)/y
= x/y - y/y
= x/y - 1

How do you justify the 1 in the equation above. How to derive the formula and how do i prove it?

Four digit combinations from 1,2, ..., 9 2012-02-26
From Errol:
show me a list with all four digit combination numbers from 0 -9
A geometric sequence 2012-02-24
From Camille:
Find x if the sequence 5,10,x+2 is geometric.
If x ix directly proportional to y then ... 2012-02-19
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?

Figures with dots 2012-02-15
From A:
Okay so my daughter came home and had this question for homework from her teacher. I have no idea what it means HELP!!
The question shows a figure that is a square. It has 5 dots on the top, bottom and on the sides looks similar to this:
. . . . .
.       .
.       .
.       .
. . . . .
they want to know 3 more ways to show the number of dots in the figure. They have already shown one with just counting them and the other one that they showed was circling the four corner dots and then taking the dots in between with a number sentence set up like this: 4+4*(5-2) = 4+4*3= 16. They also besides giving 3 ways want us to write a number sentence and an algebraic sentence to show the number of dots in the figure with "n" sides. Please help! So confusing ! I don't know if my square turned out or not but it should be 5 across the top and bottom and on the sides and no dots in teh middle it is just the outside.

Can the result of the calculation be 2? 2012-02-09
From Thomas:
You have the digits 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 in a random order side by side and put randomly between two digits a colon, so that a division comes into existence. Can the result of the calculation be 2?
Answered by Robert Dawson and Chris Fisher.
A tree growth modelled by a geometric series 2012-02-08
From Steph:
a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence.
A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres

Notation for the second derivative 2012-02-06
From Shafira:
In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2?
Two sectors of a circle 2012-02-03
From Wayne:
I am not even sure what to ask. I have to two lengths of feet and an angle of degrees, and I have to find the area?
**Problem attached

Thanks,
Wayne

Properties of real numbers applied to subsets 2012-02-01
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!
1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2 2012-01-27
From Vicki:
I am trying to find out how to do show how this proof was worked.
Here is the end result 1 + 3 + 3^2 ...+3^(n-1) = 3^n - 1/2

This equation was used to find the number of white triangles in the Sierpinski Triangle

Two shapes 2012-01-06

a boy has two pieces of wire each 99cm long .he bends them into the shapes shown below.calculate the radius of each figure,giving each answer to two decimal places.figures are one is semicircle and other on is half of the semicircle.

A 46% increase 2012-01-03
From kabilan:
increase a price of £8.24 by 46% and give the answer to the nearest penny
The number of digits in a number base m 2011-12-22
From Jash:
Assume there is a number system of base m.

The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).

In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.

Find m.

Three consecutive numbers 2011-11-29
From Michael:
Find three consecutive numbers such that the second number squared is equal to the first and third added together
Converting from base 4 to base 10 2011-11-29
From anjg:
How to convert base 4 number 2^11 to base 10 number?
Four carpenters can build eight houses in 10 days. 2011-11-23
From Kenneth:
Four carpenters can build eight houses in 10 days. Two carpenters can build how many houses in 15 days?
What was the cost price of the article? 2011-11-10
From tashana:
By selling an article for \$320,the profit was 20% of the cost price.what was the cost price of the article.
The sum of a series 2011-11-07
From Rattanjeet:
Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series.
A scale drawing 2011-10-30
From aretha:
i have a scale drawing of a house floor plan, don't understand how to find the answer. the drawing is 1in: 3ft. need to find the length / width/and the actual length/width of the living room,kitchen, 3bedrooms deck,sitting room, entry, and closet
Three consecutive terms of an arithmetic sequence 2011-10-30
From Juliette:
Find X when x, 1/2x + 7, 3x -1 are consecutive terms of an arithmetic sequence.
Expanded form 2011-10-12
From Chris:
Write this number in expanded form
4 326 180 501

Thanks!!!

Three consecutive odd integers 2011-10-07
From Muneera:
Find 3 consecutive odd integers so that 3 times their sum is 5 more than 8 times the middle one?
A reservoir has the shape of an inverted cone 2011-10-03
From Roger:
a reservoir has the shape of an inverted cone whose cross section is an equilateral triangle. if water is being pumped out of the reservoir at a rate of 2m^3/sec, at what rate is the depth of the water changing when the depth is 40 meters?
58 choose 4 2011-08-26
From Jean:
Using only the numbers 1-59, how many times would the number 23 appear in combinations of 5 numbers?
... Can a list be provided as well?
Thank you very much,
Jean

Two line segments in the plane 2011-08-15
From Tim:
For this problem I actually have tried to visualise the image in my head many times. This question makes my head spin.

Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value. Prove that these segments have no common points.

A sequence 2011-08-14
From intesar:
how do i figure this out 0,1/6,2/9,3/12
The third term of a sequence 2011-08-13
From sammantha:
Find the 3rd term of the sequence, an=1.5(4)n - 1.
Infinite Logarithmic Series 2011-08-08
From Sourik:
Dear Expert,

In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between -1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof.
Thanking you,
Sourik

The nth term of a sequence 2011-07-01
From Rachel:
I am trying to help my son get ready for our Aims test and I am not much help. The sequence is 2,5,10,17 The question is which equation represents the rule for finding the nth term for this sequence

a. an=n + 1
b. an=2n2
c. an=n2+1
d. an=2n+1

The nth term 2011-04-30
From Samantha:
predict the general term, or the nth term, An for the sequence.
1/2,2/3,3/4,4/5,5/6

Find the rate at which the searchlight rotates 2011-04-17
From Meredith:
A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight.
sin x = -0.25 2011-03-29
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

A true or false trig question 2011-03-24
From Abeth:
True or False: Since cot (theta) = cos (theta)/sin (theta), if cot (theta) = 1/2, then cos (theta) =1 and sin (theta)=2. My answer before was true, but not my answer is false. Can you give me a solution on this matter. thanks.
A 15% increase 2011-03-22
From Abeth:
Bobby dela Cruz is the purchasing agent for school supplies of a certain university. Because of new research projects, Bobby ordered an additional 32,500 worth of supplies this month. This is a 15% increase from last month. What was the value of the school supplies that Bobby ordered last month?
Three consecutive odd numbers 2011-03-11
From George:
Write an equation three consecutive odd numbers whose sum is 75
A family of circles 2011-03-01
From steffi:
Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7.
Converting base 3 to 5 2011-02-28
From Harry:
Hey Math Central, I came across your website and im in need of help on my maths c assignment. I have to convert base 3 to 5 without converting back to ten. I heard that you can use patterns in 3 and 5 to make an equation but im not sure how to and i also heard you can use logarithms but i dont know how to use those so im kinda stumped.
An imaginary infinite geometric tree 2011-02-18
From Elise:
An imaginary infinite geometric tree grows 1m the first day. 2nd day 2 branches and right angles to each other and each 0.5 m long. 3rd day two new branches at ends of each of previous days' 2 branches, again at right angles, and only .25m long each.
And so on, infinitely.
Q: Use relationships of right-angled triangles and high school level knowledge of geometric series to show the tree height is limited to (4 + sqrt2)/3 m and width to (2(sqrt2 + 1))/3 m.

Reversing the digits 2011-02-08
From rejie:
if the digits are reverse , the number is 9 less than the original number.what is the equation?
Three consecutive numbers 2011-01-31
From parth:
name 3 consecutive numbers,each less then a 100,the smallest # is divisible by 6 the next is divisibel by 5 and the largest divisible by 4
A player runs from second base to third base 2011-01-30
From Marie:
A baseball diamond is a square with side 90 feet in length. A player runs from second base to third base at a rate of 18 ft/sec. At what rate is the area of the trapezoidal region, formed by line segments A, B, C, and D changing when D is 22.5
Distance A is the players distance from first base when running from 2nd to third. Distance D is his distance from 3rd base. Distance C is the distance from 3rd to 3rd to Home. Distance B is the distance from Home to First. I have found dA/dt in a previous problem.

The perimeter of a semicircle 2011-01-29
From Keith:
I have the perimeter of a semi circle of 37 but how do I calculate the diameter from this. This is all the information I have.
The sequence 2,3,5,5,8,7,11 2011-01-19
From taylor:
number relationship in number sequence 2,3,5,5,8,7,11
Answered by Chris Fisher and Penny Nom.
tanθ=1.192 2011-01-15
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.

What is next in the sequence? 2011-01-13
From jodi:
what is next in the sequence 1, 1/4, 1/9, 1/16, 1/25
Set notation 2011-01-10
From Ron:
The question asked in a handout:

8k - 5 < 35, keI

I believe the answer to k is 5. But what does the k e(E) I mean in this?

Semicircles and the Pythagorean Theorem 2011-01-09
From Jas:
Okay well, in math we are learning about the pythagorean theorem and we have to do a math journal on the question:

****Can you replace the squares (that are put on the sides of a right triangle) with semicircles and still get the same answer??

I do not understand because i tried doing an example and comparing it with a normal way of doing it and I didnt get the same answer!

A sector of a circle 2011-01-07
From Alice:
the radius of a circle is 7cm the angle of the sector is 68 how do you find the
Line segments 2011-01-04
From Izsak:
What is the formula to find the number of segments that can be named by a given number of points on a line?
[sec^2x]*[sec^2x] 2010-12-16
From Hari:
[sec^2x]*[sec^2x]=...?
A geometric progression 2010-12-15
From Abeth:
find the value of x so that 2(x-1), x+3, x will be a geometric progression.
A sector of a circle 2010-11-29
From Mel:
Find the area of a sector of a circle that has a central angle of 13pi/18 and a radius of 12cm. Round answer to nearest 10th degree
Hours minutes and seconds 2010-11-26
From beket:
I need to turn 1.486588292 into real time hours minutes and seconds. I keep getting multiple answers. Online conversions give me 1 hour 29 minutes and either 11 or 12 seconds. On the calculator I get 1 hour 29 minutes and 20 seconds. Can you explain how to turn this decimal into time?
Answered by Robert Dawson and Penny Nom.
Intersecting polygons 2010-11-17
From Laura:
How can I estimate the amount of intersection (area or better a normalized number) between two polygons if I have the cartesian coordinates of their vertices?

regards,
Laura

The perimeter of a semicircle 2010-11-11
From gayathri:
the area of semicircle is 1925sq.cm find perimeter
Three consecutive odd integers 2010-11-07
From karen:
find three consecutive odd integers such that twice the sum of the second and the third is 43 more that three times the first
How far must the pitcher travel to get to the ball? 2010-11-04
From ken:
A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball.
The base of an isosceles triangle 2010-10-24
From Brian:
how can I find the base of an isosceles triangle from the height and the perimeter?
Four consecutive integers 2010-10-21
From Mickey:
Find four consecutive integers such that the sum of the first three integers is 20 more then the fourth integer. I know that for consecutive integers the algebraic expression is x+x+1+x+2+x+3
A division sentence for an array 2010-10-05
From Laura:
On a math test Grace needs to look at an array and write a division sentence for the array. Grace writes 18/3=6 on her answer sheet. Describe what the array on Graces test looks like.
A Taylor polynomial for (lnx)/x 2010-09-29
From Dave:
I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, -3, 11, -50, 274... Ok, so the negative is an easy fix -> (-1)^n-1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this? Thanks!
rat sequence 2010-09-24
From Vishal:
this is known as rat sequence. I want to know the logic pf this :-

1,2,4,8,16,77,145

A reverse PST calculation 2010-09-23
From Manning:
Hi, I'm a manufacturing contractor in Saskatoon. The way to calculate PST for us is using total contract amount x 70% then 5%. For example, contract amount of \$100 x 70% x 5% = \$3.5 (PST). The subtotal is using contract amount + PST. \$100 + \$3.50 = \$103.50.

If you only know the subtotal is \$103.50 including PST, how do you reverse calculation to get the contract amount?

Thank you very much for your help.

A taxi ride 2010-09-22
From Jack:
A taxi ride costs you \$2 for the first km and 10 cents for each tenth of a km thereafter. Sketch a graph of the total cost \$C(x) for a ride of xkm, for 0 < x < 2. Hint: The graph is not smooth.

How will I start this question off? I tried the table of values method, and then graphed it, but it comes out as smooth,

Find the point of contact of the circles 2010-09-20
From Sandra:
If the center of circle A = (-1,-3) and the radius of it is √20, the center of circle B = (5,9) and the radius of it is √80. Find the point of contact of the circles A and B.
The nth term 2010-09-14
From Anna:
The problem is 2n-2. find the nth term. I'm lost as how to even begin
Differentiable on an interval 2010-08-12
From Dave:
Hi I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help.
An 18ft round pool 2010-07-19
From christine:
will an 18ft round pool fit on a 12x16 ft rectangular cement slab?
Remainders 2010-07-17
From GARY:
WHAT NUMBER DIVIDED BY 11 LEAVES 1, DIVIDED BY 13 LEAVES 8, AND DIVIDED BY 17 LEAVES 3.
A pattern in a puzzling sequence 2010-07-09
From Martha:
A1 2 3 B 5 6 7 C 9 10 11 D 13 14 15

THE MISSING TERMS IN THE PROBLEM BELOW:
a) H _ _ _ b) R _ _ _
c) _ _ 50 _ d) _ _ _ 63
e) _ @#\$ where @ + # + \$ = 258

The product of 2 consecutive integers 2010-06-28
From Sharon:
the product of 2 consecutive integers is -6 less than the square of the larger number. find the smaller number
The intersection of two graphs 2010-06-27
From Austin:
In depth explanation of how to find the intersection points of functions y=-4t+300 and y=-4.9(t-5)^2+300
Selling price, cost and profit 2010-06-22
From Alex:
The profit on a certain television set is 16.5% of the cost price. If the profit is \$330, Find:
a) the cost price
b)the selling price of the television

The area of a circle 2010-06-12
From grier:
what is the area of a semicircle with arc length 3pi?

A cylindrical vessel with belled ends 2010-06-01
From George:
surface area of a vessel with a cylindrical length of 60 feet, a diameter of 10 feet, and with belled ends of 5-foot radius
Math in the workplace: nursing 2010-05-24
From Taylor:
How is math used in the workplace - Nurse Anesthetist?
The number of gallons of water in a basement 2010-05-23
From George:
A basement with dimensions 68 ft long by 42 ft wide by 10 ft deep is flooded to the ceiling calculate the number of gallons of water in the basement. 70
Divisibility by 3 2010-05-23
From Cathleen:
To math central. I have to do a maths extension question that I don't understand. At first I thought I did. It is about the dividing by three. In one part of the question, it asks me to show that the rule of division by three does not work for 23142 with a little 5 down the bottom. What doe base 5 mean? We first thought that the little 5 down the bottom meant multiplying y the power of five. Can you please tell me what it means so I can finish this question?
The hypotenuse of a triangle 2010-05-22
From linda:
find the length of the hypotenuse of a triangle with legs of 12in. and 17in. round to the nearest hundredth
Percentage increase 2010-05-20
From Rebecca:
Question from Rebecca:

In 2008 my land was valued at \$84,000. In 2009 my land was re-valued at \$235,000.00. What is the percent increase between the two values? I want to be able to express "the value was increased by x%."

The product of two consecutive even integers 2010-05-11
From Terry:
The product of two consecutive even integers is 14 more than their sum. Find the integers.
The nth term 2010-05-09
From Jessica:
what is the nth term of 3, 9, 19, 33, 51

A geometric progression 2010-04-30
From Kalyani:
sum of infinite geometric progression is 9 and common ratio is 1/10 then sum up to 8 terms is?
Sales taxes in Quebec 2010-04-28
From carole:
I work at a company where we use transport companies and we often get credits on their invoices. I need to know how to subtract the sales taxes from these credit amounts. (5% TPS and 7.5% TVQ). Is the equation: Amount / 1.05 = then this amount / by 1.075=?
4 + 10 + · · · + (6n − 2) 2010-04-21
From Lan:
Find the sum 4 + 10 + · · · + (6n − 2). The answer is 3(n^2) + n. How?
The area of semi circle 2010-04-16
From sagir:
how to find the area of semi circle?
A sequence 2010-04-13
From Essence:
hello, I am having trouble doing my math homework. It asks me to write the first five terms of each sequence .I can not figure it out because it is a fraction.

The Problem Is:

{2n+1/2n}

A geometric sequence 2010-04-13
From glen:
A geometric sequence has a first term of 0.1024, a second term of 0.256, and a middle term of 156.25. how many terms are there in the whole sequence? i know that r=2.5 but i dont know how to find how many terms there are.
Counting by sevens 2010-04-13
From Larry:
Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted three of the following numbers, which number did Lee NOT count?

a. 107
b. 184
c. 534
d. 641

Answered by Robert Dawson and Penny Nom.
The area of a field of view 2010-04-07
From Frank:
I know we have a field of view of 90 degrees and the distance we can cover is 6 miles. What is the area we can cover/view?
A formula would be nice to have since the diameter or distance of the wedge area can change and the degree of the field of view can also change.
Thank you and I look forward to hearing from you.
Frank

Body measurements 2010-04-06
From Amirul:
Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student. My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist? I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..

But teacher said that it is golden ratio...so nothing interesting... =( really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question??

1/1+1/2+1/3... 2010-03-31
From Mohd:
you explained the way of getting the summation of 100 series numbers but what is the summation of the numbers 1/1+1/2+1/3+1/4+1/5.............................+1/100
The angle of intersection between two lines 2010-03-25
How to find the angle of intersection between a line x=249 and another line which is of the form y=m*x+c; Line1 has a slope of infinity so what does the angle of intersection turn out to be? Or how can i find it?
Water in a culvert 2010-03-18
From Chip:
Hello, I have a problem to which I know there must be an analytical solution - but as it has been 50 years since I studied math I can't remember quite how to do it!! I have a 12" round culvert in my yard that runs water all year. I would like to be able to calculate the flow through the culvert by measuring the depth of water flowing through and measuring the speed of the current. I can measure the depth and the speed, but I forget how to calculate the cross section of the flow. If you could help I would greatly appreciate it. Thank you
Angular velocity 2010-03-17
From Lindsay:
Determine the angular velocity, in radians per second, of a 14-inch car wheel, if the car is traveling at 60 miles per hour
A 14 side well house cover 2010-03-12
From Kenneth:
I am 35 yr I am wanting to build a well house cover. I'm trying to figure out how long the pieces need to be and what angle they need to be for a 4 ft dia with 14 side well house. I would love an answer but would also like to know how to figure it in the future. Thanks Kd
Prove A intersect B =X iff A = X and B = X 2010-03-06
From Gloria:
how would you prove A intersect B =X iff A = X and B = X
The base area of rectangular prism 2010-03-05
From Desiree:
How do you find the base area of rectangular prism that has 4 cm by 4cm by 6cm ?
2+3 =10 and 7+2=63 and ... 2010-03-01
From brenda:
if 2+3 =10 and 7+2=63 and 6+5 =66 and 8 +4 = 96 then 9+7+ ??????
its driving me crazy !!

Answered by Penny Nom, Claude tardif and Melanie Tyrer.
The hypotenuse 2010-02-27
From Dannielle:
how do you find the hypotenuse if a=8 and b=6?
The test for some disease is 99% accurate 2010-02-24
From baaba:
Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease?
A geometric sequence 2010-02-22
From Kelsey:
_, 2, _, _, 250, _

i don't know how to fill in the missing terms

The first five terms of a sequence 2010-02-14
From Joanne:
Find the first five terms of the sequences with the nth term given as follows. n^2+3n
Can a line segment curve over two planes? 2010-02-14
From Graham:
I am working on a math fair project. Can a line segment curve over two planes? Such as, if I had a three dimensional L bracket and I drew a line segment on it with a marker starting on the bottom of the L and had it curve around the corner and up the top, would it still be considered one line segment? Or is that two line segments? Is there a rule that a line segment can only occupy one plane? Thank you. Graham
A square corner 2010-02-11
From Trevor:
I am building a new house and wish to set it out on site with the use of profile boards and string. I want to be certain it is correct in terms of squareness. I have a vague idea that the square on the hypotenuse should be equal to the sum of the squares of the other two sides.

I get a little lost here and need some help. The building is a rectangle measuring 40x30 feet to exterior brickwork. I guess that the length of the hypotenuse should be exactly the square root of the combined squares of the two sides.

Using the above measurements could you give me calculations from nuts to soup as to the correct length of the diagonal. And what adjustments are needed if everthing is not in accord.

Trevor.

A sequence 2010-02-07
From Shalev:
hi,

i had a job interview yesterday. it had mathematical questions. couldn't solve 1. i m obsessed with it. please find out what the answer is..

it goes like this: 2,4,5,5,8,6,_,_,14,8

thank u very much

The perimeter of a semicircle 2010-02-04
From Sarah:
The perimeter of a semicircle is doubled when the radius is increased by 7. Find the radius of the semicircle.
A sector of a circle 2010-02-04
From trisha:
Given a circle with a radius of 6 inches. Find the area of the sector that is formed by an arc of 36 degrees. Round your answer to the nearest tenth of an inch.
Consecutive even integers 2010-02-03
From cassandra:
find 2 consecutive even integers whose sum is 34

find 3 consecutive even integers such that 3 time the middle interger is 10 more than the greatest.

A sequence 2010-01-27
From Haku:
if there are 8 dots in the first shape, 13 in the second, 19 in the third, and 26 in the fourth, then what is the formula?
A sequence 2010-01-22
From brahmaji:
0 7 26 63 _ 215 342 fill the blank? find the missing number
Angle of incline 2010-01-20
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
Percentage increase from a negative to a positive 2010-01-12
From Greg:
If a company had a net lost in 2005 of \$11,234 and net income of \$3231 in 2006, what is the percentage annual growth in income between the two years?
Improper fractions 2010-01-12
From Blanca:
Between which two consecutive natural numbers does the improper fraction 57/56 lie?
The domain, range and inverse of a relation 2010-01-08
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.
The area of a sector 2010-01-07
From angelkem:
how do you get the area of the circle, the sector, the shaded sector, non shaded sector and its total area if the diameter is 20 cm and each area of the circle is 45 degrees?
Consecutive odd intergers 2010-01-06
From keyanna:
list five consecutive odd integers, starting with -3
Holiday for 7 golfers 2010-01-05
From Andy:
I am having difficulty scheduling pairings for a forthcoming Golf holiday. There are 7 players and we will be playing 7 rounds - each round will be a 3 ball and a 4 ball. I am trying to work out a schedule that means everyone plays with each other roughly the same number of times (with a minimum of, say, 3 times if possible). Also, we are looking to ensure everyone plays in roughly the same number of 3 and 4 balls. Any suggestions would be much appreciated (we leave in 10 days time). Thank you.
Profit increase from 10% to 15% 2010-01-03
From taha:
A shopkeeper sold a pen for \$13.20 to a make a profit 10 percent.In order to earn a profit of 15 percent,he should have sold it for?
Triangles on a base of 2.4 meters 2009-12-26
From Allan:
Please,How do I calculate the height of a triangle when I only know the width of the base line,It is 2.4 mtrs.
Thankyou very much.

The acute angle formed by intersecting lines 2009-12-17
From Katie:
To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x - 2y = -2. Was is necessary to find the intersection point?
The second derivative of y = x³ (x² + 5) 2009-12-14
From Kyrie:
Find d²y/dx² for this function:

y = x³ (x² + 5)

A circle problem 2009-12-14
AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm. Find the length, in cm of AQ.
Bases larger than ten 2009-12-14
From Nick:
For numbers in bases larger than ten, what are the digits by mathematicians' conventions?

I assume the first 10 are always 0-9. I know two computer science conventions (for hexadecimal (A-F case-insensitively) and for base 85 (case-sensitivity plus 23 other characters)) and as a school student I learned that base 12 uses either T and E (which confused me when I thought they stood for Eleven and Twelve) or A and B, the latter as capitals only. Clearly, these conventions are in conflict.

I saw your reply in http://mathcentral.uregina.ca/QQ/database/QQ.09.99/magin1.html as accessed a few minutes ago but hope that in the 10 years since then mathematicians have arrived at a convention. Have they?
Thank you.

--
Nick

A number base that's not a positive integer 2009-12-11
From Nick:
Is it possible for a number to have a base that's not a positive integer? Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.

Thank you.

Nick

Answered by Robert Dawson and Claude Tardif.
7 36 14 18 28 9 56 x y 2009-12-06
From lisa:
what is the sequence of x and y
7 36 14 18 28 9 56 x y

What number comes next? 2009-11-25
From Mark:
Can someone help and give me the break down of how to solve. 5,3,1,-1
The point of intersection of the pair of straight lines 2009-11-19
From Stephanie:
Find the point of intersection of the pair of straight lines:
y=-3x-9
-y=4x+2
x = _______ and y = ________

A baseball diamond 2009-11-18
From maelee:
the official distance between home plate and second base in baseball diamond is 120ft. Find the area of the official ball diamond & the distance between the bases.
Answered by Robert Dawson, Chris Fisher and Penny Nom.
6 numbers from 53 numbers 2009-11-17
From MIGUEL:
IM A STUDENT IN HIGH SCHOOL AND IM HELPING THE SOCCER COACH WITH PLAYS SO I NEED ALL THE POSSIBLE NUMBER COMBINATIONS OF NUMBERS 1- 53 IN SETS OF SIX THE NUMBER CAN ONLY BE USED ONCE IN EACH SET.
A sequence of letters and numbers 2009-11-10
From Maria:
What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old. J1F8M1A0M1J0J1
Answered by Robert Dawson, Claude Tardif and Harley Weston.
A drawing of a baseball diamond 2009-11-09
From Beth:
My husband has a drawn diagram on a piece of paper of a baseball diamond. He knows that on the paper 1 1/16" (1.6875") = 90 actual feet. How do we calculate how many feet 5 7/8" on the paper would be?
Consecutive odd integers 2009-11-09
From Erin:
I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2 and so on, but if its odd then do the numbers change to odd ones? i don't know the question is: the sum of four consecutive odd integers is -72. write an equation to model this situation and find the values of the four integers
Answered by Robert Dawson and Penny Nom.
What's the next term? 2009-11-03
From bharat:
if
1=5
2=25
3=325
4=4325
5=?

Answered by Robert Dawson and Penny Nom.
The extended real numbers 2009-11-02
From Justin:
Hello there, I was wondering is the set of extended real numbers a closed set or an open set?

Justin

Consecutive positive integers 2009-11-01
I'm doing my homework, and there are questions on Consecutive Positive Integers. I was just wondering, what is a consecutive integer? Or to be more specific, what is a consecutive POSITIVE integer?
The intersection of two graphs 2009-10-30
From asma:
by using the suitable scales,draw both the graph of x/2 + y/4 =3 and y=2 on the same graph paper.Find the points of intersection of the two graph.
Graphing y=(4-x^2)^5 2009-10-25
From natalie:
I want to graph the curve of y=(4-x^2)^5 without using a graphing calculator. To do this, I'm suppose to find: domain, y and x intercepts, asymptotes, intervals of increase/decrease, local max/min, concavity and points of inflection. I got all the way to the step where I'm solving the concavity and I'm stuck. I found the f"(x) and it came out to be really large polynomial. I want to know how I can solve for the x of f"(x) without the use of a graphing calculator, when the polynomial has x^6 and x^8. Thank you so much, natalie
Four consecutive odd integers 2009-10-24
From Tonya:
the sum of four consecutive odd intergers 2008 what are the intergers
What jobs use conics? 2009-10-22
From denise:
i have to type a paper on what jobs use conics and i can not find anything can you help

thanks
Denise

The inverse of f(x)=-1/x^2 2009-10-22
From Jasmine:
how to solve f(x)=-1/x^2 --> find f-1[x], than state if its a function
A sequence 2009-10-20
From Alyce:
The rule of this sequence is k=1/8n. Find the 8th term of the sequence.

1/8, 1/4, 3/8, 1/2, ...
Thanks!

The hypotenuse of a right triangle 2009-10-18
From steven:
the perimeter of a right triangle is 20 cm. its area is 15 sq cm. find its hypotenuse.
The next three terms 2009-10-16
From Shawn:
I'm a parent and don't know how to help my 6th grader solve for this problem.

Name the next tree terms in this sequence and tell the rule used to find each:

-1,0,1,0,1,2,3,8,25,.....

What is the next term? 2009-10-04
From julia:
patterns 18 46 94 63 52 61 what is the next one?
How many terms are there in this sequence? 2009-09-28
From tabby:
How many terms are there in this sequence?
5,1,-3,...,-111

Seven circles 2009-09-20
From Bobbi:
try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circles--vertical, horizontal, and diagonal -- add up to 12. Each number can be used only once.
Segments of a ring gasket 2009-09-20
From Robert:
I am in the process of making an Excel spreadsheet in which our sales team just needs to enter the outside diameter, inside diameter, and number of segments to price ring gaskets that are too big to fit on a sheet of material and need to be cut into segments. With your help I was able to create a spread sheet that can calculate the Chord lengths, and Segment height on a single gasket segment. I am now stuck trying to come up with a formula to figure out the height of the second segment when it is stacked on the first segment, then use it to add more depending on the quantity of segments needed. I have an illustration below showing 2 segments (of a gasket that was segmented into 4 pieces) stacked together. I need to find a formula to get the dimension from "A" to "B".
A sequence 2009-09-19
From Oliver:
I am struggling to work out the missing terms in the following sequence:

1, 3, _, 7, 11, 18, _

Cubes and squares 2009-09-16
From Stanley:
What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square?
A sequence 2009-09-15
From Derek:
what are the next four numbers in this sequence 1/8, 1/4, 3/8, 1/2...
The nth term of a sequence 2009-09-11
From Michael:
My son has this question as part of his key stage 3 maths homework-

The nth term of a different sequence is n - 2/n^2.

We've got to find the first three terms of the sequence.

Bisecting rays 2009-09-09
From frank:
Ray OC bisects angle AOB, ray OD bisects angle AOC, ray OE bisects angle AOD, ray OF bisects angel AOE, and ray OG bisects angle FOC: if angle BOF=120 degrees, then find angle DOE? Confused!
The intersection of two graphs 2009-09-02
From Jaqueline:
Find the points of intersection of the graphs of the equations

x^(2 )+ y^2=25 and 2x + y = 10

Price increases and decreases 2009-09-02
From craig:
I work for an industry that bases it price increases and decreases on commodity pricing - Customer get confused on how/why we calculated new prices due to movement in the market - Price go up x% for every \$10 of movement in the market -

For this example-
Movement went down by \$30 and it is 2% for every \$10 - so price decrease was 6%.
Customer's price is currently \$100.
We say - \$100/1.06= new price of \$94.3
Customer says - \$100*.94= new price of \$94.

They don't understand that if board went back up \$30 which would be 6% increase, they wouldn't be back at \$100 if they multiplied on the price decrease.
\$94*1.06=\$99.64 vs. \$94.3*1.06=\$100 (Back to the original price)

What is the best way to explain to customer besides using this example?

Any help or info is appreciated.

Craig

Arithmetic Sum & Sequence 2009-09-01
From Alice:
Find the 24th term of this sequence 6.8,8.0,9.2... Find the sum of the first 21 terms
Cardinality of infinite sets 2009-09-01
From Brian:
I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong.

I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers.

Please correct me if I am wrong, but I believe those two sets are -- pardon the expression -- equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa.

For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321 -- I could write it out algebraically, if you want, but you get my point)

Am I wrong?

Thanks, Brian

Sequence problem 2009-08-18
From James:
I have the equation: tn = (n)(n+1)/2 Which gives the sequence: 1, 3, 6, 10, 15 etc. However, I'd like to be able to solve for n. So that a t of 6 would give me the answer of 3, and t of 10 would give me the answer 4 etc.
Answered by Stephen La Rocque and Victoria West.
Subtraction base 5 2009-08-09
From Nikki:
can you help me how to do subtraction in base 5 notation. example is 3434 - 51? how do you do this in base 5?
can you please explain how you do this & the answer as i have no idea.

Thank you kindly
Nikki

An infinite set 2009-08-07
From Islam:
How can I prove that the set of all odd natural numbers is an infinite set. Thank you.
Percentage decrease 2009-08-04
From Bill:
How to calculate the Percentage Increase or Decrease of a \$ value.
Example -
Site Spend for 01-01-2008 thru 07-31-08 was \$ 3,465,660
Site Spend, 2009 YTD as of 07-31-09, was \$ 1,673,405
Site Spend down what % between these two amounts ?

Angular speed 2009-08-04
From Mary:
The engine of a sports car rotates at 5000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second. Use 2 radians = 1 revolution.
Intersection of Two Curves 2009-07-27
From Amarah:
Find the coordinates of the point A( this point is where the two lines intersect). Justify answer question : here is a curve x^y =y^x (for x,y>o)
How can I trisect an angle? 2009-07-27
From Nazrul:
How can I trisect an angle?
The inverse of F(x)=x^2-6x+13, for x>3 2009-07-26
From Juan:
The function F is given by F(x)=x^2-6x+13, for x>3.

A. Write F(x) in the form (x-a)^2+b

B.Find the inverse function F^-1

C.State the domain of F^-1

Finding the Common Difference and Number of Terms of an Arithmetic Sequence 2009-07-24
From Juan:
In an arithmetic sequence, the first term is -2, the fourth term is 16 and the nth term is 11,998 A. What is the common difference? B. What is the value of n.
A sundial on an elliptical cylinder 2009-07-22
From Leo:
I want to build a sundial where the shadow falls on an elliptical cylinder. I can calculate the coordinates of the points on the cylinder that I want to mark. My problem is that I will have to make the surface as a flat sheet and bend it into an elliptical shape. However, I cannot work out a scheme to transfer the coordinates I know into a distance that will work when I bend the shape. Help!
Annular sector 2009-07-20
From Ed:
What is the name for the section of a flat ring (annulus)? Similar to a section on a radar screen, a quadrilateral but the top and bottom are curved.
Finding the Line Joining Perpendicular Feet 2009-07-16
From mukulu:
Please help I've been tryng to search in your data but i failed to get the solution Find the equation of a straight line joining the feet of the perpendiculars drawn from the point A(1,1) to the line 3x-3y-4= 0 and 3x+y-6=0.
A sequence 2009-07-11
From jamie:
what is the next number in the sequence and what is the relationship of the numbers? 36,16,20,10,12, _
A base 7 number and a base 9 number 2009-07-09
From koteawarao:
Find a base 7 three-digit number which has its digits reversed when expressed in base 9.

ans: (281) base 7 and (182) base 9

A binary equation 2009-07-07
From Chinonyerem:
Find a bitwise solution (i.e find xi so that each xi E {0,1}) to
32 = x1 + 2x2 + 4x3 + 9x3 + 20x5

The retail price for an ice cream scoop 2009-07-05
From Patricia:
Hi - I am trying to figure out the fairest retail price for an ice cream scoop. We have an ice cream parlor and the cost of the ice cream we buy by the bulk container has recently been increased so now we must charge more for our scoops. We pay a wholesale price of \$25.40 for 242 ounces of ice cream. The cost per ounce is \$0.105. What is the formula for figuring out how much to charge retail per scoop? This is probably so simple but confusing to me. Please help. Thank you!
Prove that the set of all positive odd integers is an infinite set 2009-06-20
From Nazrul:
How can I prove that the set of all positive odd integers is an infinite set.

Successive differences 2009-06-18
From Jonathan:
I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help.
Answered by Robert Dawson and Penny Nom.
Subsets 2009-06-16
From Tracy:
Suppose C is the subset of D and D is the subset of C.

If n(c)=5, find n(D)

What other relationship exists between sets C and D?

Two ships and a lighthouse 2009-05-27
From Chelsey:
I have a question in regards to how do I know when to use tangent or cosine when determining angles. The question is: Looking north from the observation deck of a lighthouse 60 m above the sea, a lighthouse keeper sees two ships. The angles of depression to the ships is 5 degrees and 10 degrees. How far apart are the ships?

I don't understand which one to use when solving the equation.

A sequence 2009-05-26
From Jay:
what is the equation that would give me the next 3 numbers in this progession: 0,1,5,14,20
What type of conic section is this? 2009-05-22
From Donna:
What type of conic section is 3x² + 3y² - 4y - 8 = 0
An infinite geometric series 2009-05-18
From terri:
find the sum of the infinite geometric series

14 -7 +7/2 -7/4 +.....

A. 7007/13 B. 2002 C. 28/3 D.5005/7

A sequence 2009-05-18
From Richard:
This is my question about sequences. Write down the nth term of the following sequences.

1/2, -3/4, 9/8, -27/16

Plz help me solve the question!

A number sequence 2009-05-08
From alicia:
what is the next number 1,2,6,42,1806------? is it 1954?
Answered by Robert Dawson, Chris Fisher, Penny Nom and Claude Tardif.
How do you convert 1248 to base 6? 2009-05-02
From Tamara:
How do you convert 1248 to base 6?
Stairway construction 2009-05-02
From Olivia:
Hi, I'm Olivia and I'm in 8th grade studying algebra 1. I'm having some trouble with my math project. It has to do with rules of stairway construction. It says that there are two generally accepted rules to building stairs. Rule 1: x+y=43 and x+y=46 (cm) Rule 2: 2y+x=61 and 2y+x=64 (y is the riser and x is the tread length) I cant figure out how to graph them...it says they're supposed to intersect to make a square which is like the safety zone for building stairs (the stairs' rise and tread lengths are plotted as points) any points outside of that square are considered unsafe. Did i explain it ok? Thanks for your help. --olivia
2+6+12+20+30+42 2009-04-24
From fredy:
what is the sigma notation for the series 2+6+12+20+30+42?
Miles per hour and feet per second 2009-04-22
From mary:
A car traveling at 60 miles per hour, how many feet per second has it traveled?
Percent increase from a negative number to a positive number 2009-04-21
From Brian:
I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = -110,333.00
2008 Net Profit = 66,054.00

Brian

The center of an ellipse 2009-04-21
From Nae:
what is the ellipse center of 5x^2+3y^2=15
\$65.09 is 70% greater than the average price 2009-04-11
From Kelly:
Hello! I know you might be thinking that I didn't look through your previous answers, but I really did. Here's my dilemma- I have a percent increase equation that is missing the 'old" value. I know that \$65.09 is 70% greater than the average price, but I do not know the average price. How do I go about finding that? I tried to set up an equation, but its throwing me off because the unknown variable is in there twice, and it's been a long time since I've taken math

The axiom of choice and constructibe sets 2009-04-10
From sydney:
The axiom of choice asserts the existence of certain sets, but does not construct the set. What does "construct" mean here? For example, does it require showing the existence and uniqueness of some function yielding the set? In general, what does it mean to require the existence of a mathematical object be tied to a construction of it?
Direct and inverse relationships 2009-04-06
From allison:
A piece of string is cut into n pieces of equal lengths L (1) does n vary directly or inversely with L
Three consecutive odd integers 2009-04-02
From Brian:
Find the greatest of three consecutive odd integers if the product of the second and third is 8 more than 13 times the first.
A 25 team league 2009-03-31
25 teams are in a league in which each team plays everybody once how many games must be scheduled ?
From Lucy:
If you are working in base 6, what do you have to add to 4(base 6) to get 10(base 6)????
Uses of Pythagorean theory 2009-03-27
From Britta:
Please, give me some complex real life situation examples where the pythagorean theory is used. It must be a grade 8 or grade 9 level of thinking as that is what is my teacher's demands.
The base of a triangle 2009-03-25
From yinna:
how do I find the base of a triangle who's height is 2 times the base and the area is 9?
The base and height of an isosceles triangle 2009-03-23
From Chris:
How do you find the base and height of an isosceles triangle that has 2cm legs?
An equation for a line with a changing slope 2009-03-21
From Ben:
Is there anyway to write an equation for a line with a changing slope. e.g. A cell [hone company has a initial fee of 50\$ paying for the first 100 minutes, the rate then increases to 10 cents per minute, then at 500 minutes the rate is 5 cents per minute.

Thanks

A plane cuts a line segment 2009-03-17
From Manis:
Find the ratio in which the line joining (2,4,16) and (3,5,-4) is divided by the plane 2x-3y+z+6=0.
License plates and poker hands 2009-03-14
From CC:
You have a license plate it can have 6 numbers/letters you can use the numerals 0-9 and the letters A-Z how many combos are possible and how did you figure it out?

Question 2,

Your dealt an Omaha hand You have KKKQQ, how many different hands can consist of the same cards.

A sequence 2009-03-13
From Shelly:
Which sequence satisfies the rule n/4?
Three consecutive odd integers 2009-03-11
From Susan:
Find three consecutive odd integers such that the sum of the first, twice the second, and three times the third is 70
A sequence 2009-03-11
From Vly:
2; 6; 26;126;626 find the nth term
The angles of a triangle 2009-03-11
From Marissa:
The angles in a triangle measure 7x-1, 18x+2, and 5x+10. Determine whether the triangle is acute, obtuse, or right. State your reasons clearly.
Trifecta 2009-03-09
From Annie:
I want to know how many combinations are there for the first 3 horses in a race of 20 horses. For example, the horses can come in 1, 5, 7 or 7, 5, 1 which are totally different combos. I've only found formulas where the 1, 2, 3 and 3, 2, 1 are counted as the same combo. In horse racing every combo is different. Thank you.
A property that decreases in value every year by 10 percent 2009-03-07
From PEter:
there is a competition problem where a cottage is worth 25000 years, but it decreases in value every year by 10 percent. Without a calculator, is there a way to find after how many years, the cottage will be worth 2500? (besides multiplying it out and besides logs)
The ratio test 2009-03-06
From Haley:
Use the ratio test to determine whether the series in convergent or divergent. (2/5)+(4/10)+(8/15)+...
Infinite sets and infinite limits 2009-03-06
From Justin:
Hello, I know I have asked a similar question before but I was just wondering if set theory applies to the lim x->0, y=1/x=infinity and if so, what type of infinity would it be? Thanks a lot for your help with this question!

Regards,

Justin

Answered by Robert Dawson and Harley Weston.
Direct, inverse and indirect proportionality 2009-03-04
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

Convergent or divergent? 2009-03-03
From Betsy:
Use the ratio test to determine if the series is convergent or divergent. 1+1/2^2+1/3^3+1/4^4

I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1) but I can't simplify r=lim(n->inf.)=n^n/(n+1)^(n+1)

An array with 2 more rows than columns 2009-02-28
From Mario:
Write a division sentence modeled by an array that has 2 more rows than the number in each row.
Where do X, Y and Z go? 2009-02-27
From Aj:
A E F H I K L M N T V W
B C D G J O P Q R S U

where do X, Y and Z go?

1 3 6 10 15.... 2009-02-26
From Allie:
1 3 6 10 15.... i know the pattern is +2 +3 +4 +5 and so on...but i dont know how to write an equation to find the nth term. help!
Answered by Robert Dawson and Claude Tardif.
Multiplying in different bases 2009-02-25
From Susan:
11 base 2 X 22 base 3 + 33 base 4 = _________ base 5
wo consecutive numbers with a product of 9506 2009-02-25
From sofie:
find two consecutive numbers with a product of 9506
Pressure at Given Depth 2009-02-22
From Tamara:
A sea is 3km deep. The average density of sea water there is 1020 kg/m^3. What is the water pressure at the bottom?
One vertex angle of a regular octagon is trisected 2009-02-19
From Chelsy:
Suppose one vertex angle of a regular octagon is trisected as shown in the figure. Each side of the octagon measures 4 units. Find the area of the shaded area.
The volume of a cylinder 2009-02-18
From jim:
given the volume of a cylinder at 565m^3 and the height of 20m how do i calculate the cross section area in order to determine the compression strength of the cylinder
More on infinity and Set Theory 2009-02-17
From Justin:
I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x->0, y=infinity?

Justin

Miles per hour to kilometers per second 2009-02-17
From Tamara:
If a car goes 60 miles in an hour how many kilometres will it go in a second?
Infinity and Set Theory 2009-02-17
From Justin:
I was just wondering is the limit x->0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory?

Justin

The second derivative of h(x)=f(g(x)) 2009-02-16
From Kristina:
If h(x)=f(g(x)), and is differentiable, then find h"(x).
In what base is 3x3= 10? 2009-02-14
From David:
In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one?
y = p q^t 2009-02-12
From Conor:
y= p x (q (to the power t) ) ; y= 100 when t = 2 and y= 4 when t= 0

a) find p and q
b) hence find y when t=4

A semi circular room 2009-02-11
From Taylor:
being 450pi (the area of a semi circle)

how much money would it cost to lay carpet at \$2.57 per foot???

if the area of a semi circular room is 450 pi ft then what is the volume being that the diameter is 60 feet and the ceiling is 16 feet tall

Answered by Robert Dawson and Penny Nom.
Seating around a circular table 2009-02-09
From Jenny:
A committee of 15 -- 9 women and 6 men -- is to be seated at a circular table (with 15 seats). In how many ways can the seats be assigned so that no two men are seated next to each other?
Congruent line segments 2009-02-05
From casie:
marica drew one-line segment on a graph with endpoint of (0,9) and (0,4). she drew another line segment with endpoints (1,1) and (6,1). are the line segment congruent?explain
The sequence 5, 12, 19, 26, ... 2009-02-04
From Vickie:
Hello, Here's the question. Ryan wanted to play basketball on a team, He started practicing shooting everyday to improve his skills. The first day he make 5 shots, the second day he made 12 shots, the third day he made 19 shots, and the fourth day he makde 26 shots. If the first day was March 1 and the pattern continues, how many shots will Ryan make on the last day of April and the last day of July? My daughter's answers were 425 for April and 1069 for July. Are these correct and what would be the formula for this question? ? +N=? I don't know please help. Thank you, Vickie
Answered by Robert Dawson and Penny Nom.
A piecewise function for monthly salary 2009-02-03
From Josh:
A sales rep for a drug company is paid on the following scale. His base salary is \$1600 per month. He is also paid a commission of 2% of sales over \$20,000. When his gross sales reach \$30,000 he is then paid 4% on the amount above that until his sales reach \$50,000 after which point his commission becomes 6%. His commission reaches 8% when his sales total goes over \$100,000 for the month. Set up a piecewise function for the information above.
Calculating markup 2009-02-03
From Tonya:
I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my cut to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my cut once I pay the commission and I don't want it to do that. Thanks
What do I need to pass the course? 2009-02-02
From Lynnette:
If I received 100% on my assignment which is worth 20% of my total mark and 87% on my midterm which is worth 40% of my total mark what would I need to get on the final exam which is worth 40% of my mark. To pass the course I must have 80% or above. Thanks.
The sequence 2n! - 1 2009-02-01
From Penny:
I am trying to help my son with this problem. Find the first five terms of the sequence that can be written from the formula A= 2n !-1.
The intersection of two lines 2009-01-30
From kaylee:
how do you find and graph the intersect of these two equations: y=2x-4 (and) 2y=x thanks, kaylee
From John:
I have been asked to tutor a 7th grader who is very good in math. He is taking the most advanced course that his school offers to 7th graders. This course will cover Algebra 1 over a period of two years, using McDougal Littell's Algebra, Structure and Method, Book 1, a book I like a lot.

I have been hired not to help him with his schoolwork, which is too easy for him, but to guide him through something in math beyond his schoolwork. This was his idea, an idea which surprised his parents, but one which they support.

Do you have a suggestion for me? If so, I would be very grateful to hear from you. I think this could be a lot of fun for me and my new student, if I pick the right path.

Thanks and best regards, John John

Answered by Robert Dawson, Victoria West and Walter Whiteley.
Percentage increase 2009-01-19
From Destiny:
In 1990 there were 25 springs in the park. This year there are 35 springs in the park. What is the percent increase?
The point of intersection of the straight lines 2009-01-18
From Kieran:
Find the point of intersection of the straight lines

y=2x+4, and y+2x-16=0

Answered by Robert Dawson and Penny Nom.
Segments of a sphere 2009-01-16
From Herman:
How do I solve for a segment of a sphere so that the orange peel or pie shaped section is converted to a flat surface with dimensions. I form large diameter domes, elliptical and sphere heads on a press. I enter the diameter say 30 feet with two segments above and below the equator and the total number of segment around the circumference at say 18 so the widest part of the pie shaped section will fit my press. How do I take the upper or lower course above or below the equator and figure the height of the orange peel shape, the chord length at top and bottom, and solve for the right angle at 2 degree increments down the arc length of the pieces so I can layout the flat plates prior to pressing. Thanks for your help.
A seven card poker hand 2009-01-12
From Sean:
from a standard card deck, seven cards are chosen at random. find the probability that the set chosen contains exactly three of each of two different face values.

the second part of the problem asks the probability that the card hand contains exactly three 2's and exactly three 5's.

(a x b) intersect (b x a) 2009-01-08
From sean:
is it possible to have two sets such that n((a X b) intersect (b X a) =3
A union B and A intersect B 2009-01-07
From Jim:
Suppose A and B are sets and (A union B) = (A intersect B). Is it true that A=B.
y varies jointly as x and the square of z and... 2009-01-05
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?
The area enclosed by a curve and the x-axis 2009-01-04
From Rogerson:
Find the area, S, enclosed by the curve y = -x^2 + 6x - 5 and the x-axis in the interval 0≤x≤4.
Determine y'' by implicitly differentiating twice 2009-01-04
From Walter:
Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution?
What is f^-1(3) when f(x)=2x-1? 2009-01-03
From Peter:
how do you do functions like f^-1(3) when f(x)=2x-1?
Jon's bank account 2009-01-03
From Abigail:
Hi, i have an exam soon (monday =[ ) in my revison book, it shows two peoples bank accounts- and then it says

"write a formula to show the balence of Jon's bank account after n weeks of 2003" this is the table show

Jon's Bank account

 Weeks Balance(£) Week 1 Week 2 Week 3 Week 4 Week 5 970 1035 1100 1165 1230

A spill of oil on a flat surface 2008-12-19
From Phillip:
Hello, my question is: If I spilled 25 gallons of diesel fuel on a flat surface how much area would the spill cover? How would I mathematically figure it out? Thanks!
Answered by Robert Dawson and Harley Weston.
The inverse function for F(x)=x^3+x 2008-12-18
From alireza:
I want inverse function for F(x)=x^3+x
The middle term of an arithmetic sequence 2008-12-15
From Leigh:
Find the sum of the first fifteen terms of an arithmetic series if the middle term is 92
Annual percent growth 2008-12-13
From Joe:
If Wall-Mart had sales of \$58,200,000,000 in the year 2002 and \$90,800,000,000 in the year 2006.

1. Find what percent that increase is of the 2002 sales? I came up with (9.08*10^10 - 5.82*10^10) / 5.82*10^10 * 100 = 56.01% increase. Is this correct?

2. What was the percent GROWTH in Wal-Mart's sales from 2002-2006? I am having trouble figuring out how to do the Growth problem. I would appreciate any help.

The third vertex of a right triangle 2008-12-10
From prashant:
how to calculate coordinates of third vertex in a right angle triangle given the coordinates of hypotenuse as (1,3) and (-4,1)
Division in different bases 2008-12-02
From MICHELLE:
DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5
A log base 2 problem 2008-11-26
From dave:
solve for x

(log base 2 of x) - (log base 2 of (x-2)) = 3

Sec(2x) 2008-11-23
From Evan:
Prove that this is an identity...

sec2x = sec^2x / 2 - sec^2x

The nth term of a sequence 2008-11-20
From kim:
Find the next 2 terms of the sequence.
11n+2.5

The height, base and perimeter of a triangle 2008-11-17
From Zack:
How would i calculate the height of a triangle if the base is 10cm and the area is 50cm²? If possible how would i calculate the length around the the triangle.
From Clayton:
Okay, so in this situation a license plate must have four letters (A-Z) and four numbers (0-9), ex. ABCD-1234, where repeating a letter or number is allowed ex. AAAA-1234, or ABCD-1111, or AAAA-1111. The order of letters first numbers second, or number first, letters second is allowable, and each state has its own plates, so ABCD-1234 from New York, and ABCD-1234 from Minnesota are considered different combinations, how many different license plates could there be?
The nth term of a sequence 2008-11-16
From Robin:
How do I solve for the next term in the following sequence, I just don't want the answer...I want how to do it to. x,x -1, x -2

Also, how do I solve for the nth term? I can't understand the explanations I've found. He has numbers subscripted in his equations.

The midpoint o a line segment 2008-11-15
From Jane:
The vertices of a triangle are at (1,7), (6,-1) and (0,3). Find the coordinates of the midpoints of the sides.
A cross-sectional area 2008-11-13
From David:
I am doing a science project examining the tensile strength of seaweed fronds. I need to calculate the cross-sectional area from the major and minor diameters of the elliptical central axis of the seaweed frond. What formula would I use to get this. The strength of the segments is expressed in terms of cross-sectional area of the frond at the test site.
1/8, 2/7, 1/2, 4/5, ..., ... 2008-11-06
From katie:
Inductive reasoning, what 1/8, 2/7, 1/2, 4/5, what would be the next two in th sequence.
An arch is in the form of a semi ellipse 2008-11-03
From jessica:
An arch in the form of a semi ellipse has a span of 10 meters and a central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis.
A sequence 2008-10-26
From Nicole:
what is the rule to this sequence 3,6,12,24,48.....
The sequence 49,48,46,43,39... 2008-10-26
From Kyle:
What number comes next in the series 49,48,46,43,39...?
The sequence 6,1,6,2,6,4,6,8,6, 2008-10-26
From Kyle:
What number comes next in the series 6,1,6,2,6,4,6,8,6,?
The amount of diesel fuel in a tank 2008-10-26
From Mike:
I have an cylinder shaped oil tank that holds approx. 283 gals of diesel fuel. The tank is laying on on its side, (like taking a garbage can and laying it down on its side). What is the formula to calculate how much oil is in the tank at any given time. If the tank was sitting on end it would be easy to figure out, but it is not.
nth term 2008-10-22
From jen:
what is a nth term and how do i find the nth term of any sequence
A canal with cross section a semicircle 2008-10-19
From Connor:
a canal with cross section a semicircle is 10m deep at the centre. Find an equation for the semicircle and use it to find the depth 4m from the edge
An arithmetic series 2008-10-17
From Laura:
In an arithmetic series 5+9+13+...+tn has a sum of 945. How many terms does the series have? What formula do I use?
Bags of wheat seed 2008-10-16
From Gayle:
If you want to plant 26 seed per square foot (wheat) on one acre of land and the seed comes in 50 lb bags and there are 13,500 seed per pound (675,000) per 50 pounds, how many bags do you need to plant per acre?
Bags of pennies 2008-10-11
From paul:
jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag?
Answered by Penny Nom and Victoria West.
The volume of fluid in a semi circular trough 2008-10-10
From Kerry:
How do I find the volume of fluid in a semi circular trough?
A 10% increase in supply 2008-10-10
From Irena:
How do you find begining inventory if after 10% increase in supply you got 27.5 units
Three consecutive integers 2008-10-07
From pam:
Find three consecutive integers such that the greatest increased by twice the least is 293.
Answered by Penny Nom & Chris Fisher.
The rise over the run 2008-10-07
From Mak:
what is the ratio of the rise to run?
Area of a semicircle 2008-10-06
From Benjamin:
How do you find the area of a semi-circle if the diameter is a variable.
Does an oval have sides? 2008-10-02
From reid:
My 6 yo neice came home with her math homework and she was supposed to identify which objects had sides.One of the objects was an oval.I don't believe it has sides because it is curved and I don't think that would make it an object with sides.What would be the correct answer?Thanks,Reid
The empty set 2008-09-29
From wahab:
Why a null set is called a set? the definition of set includes that a set is a collection of well defined objects But a null set is having no value.
The nth term 2008-09-29
From shauna:
The first five numbers in a sequence are
40, 37 34, 31, 28
Find an expression for the nth number in the sequence.

3,6,10,15,and 21 2008-09-28
From jarred:
i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time.
The area of an arched transom 2008-09-28
From Ivan:
What is the formula for figuring out the square footage of arched transom windows & doors?
Increase pricing by 5% 2008-09-28
I am working to increase pricing by 5%. If the price is 100, I would typically use the formulas 100 * 1.05 = 105, which is a \$5 increase. An associate suggests I divide to get the desired increase. For example, using \$100 with a 5 percent increase. I would use the forumula 100/.95 = 105.26. Thas is a 5.26 increase. Can you explain this method to me an why the different increases? Which one is correct.
Two consecutive numbers 2008-09-21
From tomas:
what is the two consecutive numbers with a product of 4160?
The area of a garden 2008-09-20
From Hannah:
How do you find the area of a semi circle when no measurement is given? The question is find the area of the garden which is semi circular. The measurements are 24m and 26m and the semi circle's height is 10m!
Finding the Pattern in a Sequence 2008-09-16
From sjp:
please could you help me find the nth term for 8 4 0 -4 -8 and -4 -1 4 11 20 Thank you
The nth term of a sequence 2008-09-13
From lavett:
what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4...
The height and base of a triangle 2008-09-12
From Bailey:
The length of the base of a triangle is 1cm less than 5 times the height of the triangle. The area of the triangle is 21 square cm. What is the the height of the triangle and the length of the base of the triangle?
0.151515...=15/99 2008-09-08
From Emma:
This week, my Algebra teacher told us about the pattern between infinitely repeating decimals and their corresponding fractions. (ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.) I was just wondering the reason why this pattern occurs. Is there a certain element that causes this pattern to occur?
Thanks
-Emma

An exclusion zone around a triangle 2008-09-07
From Awrongo:
A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone?
Answered by Stephen La Rocque and Penny Nom.
A security camera 2008-09-07
From Rita:
A security camera in a neighborhhod carnival is mounted on a wall 9 feet above the floor inside a video gallery. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?
Answered by Stephen La Rocque and Harley Weston.
The selling price 2008-09-04
From Robert:
Client wants to sell his property providing he is left with 100000.00\$ net. How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov. I'm taking the real estate class and this one really got me.
Half a circle 2008-09-04
From brandon:
what are the area and perimeter and area of half a circle??
Aboriginal number groupings 2008-09-04
From Barbara:
Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently?
Four weights 2008-08-25
From Darla:
A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use?
Eccentricity of an Elliptical Orbit 2008-08-20
From Gina:
A satellite has an elliptical orbit around the earth with one focus at the earth’s center, E. The earth’s radius is 4,000 miles. The highest point that the satellite is from the surface of the earth is 800 miles, and the lowest is 200 miles. What is the eccentricity of the satellite’s orbit?
The intersection of the medians 2008-08-18
From Katie:
Q: A Triangle is positioned with one side on the x-axis, the coordinates for the triangle are (-a,0), (a,0), (b,c)

a) Find the coordinates of the point of intersection of the perpendicular bisectors of the sides
b) Find the coordinates of the point of intersection of the medians
c) Find the coordinates of the point of intersection of the altitudes

A 3% increase 2008-08-18
From RENEE:
I need to know how to do a 3 percent increase for \$118,200......x's it by 3% will not work please answer fast
Graphing a piecewise function 2008-08-12
From Shanti:
how do you graph a step function or piecewise function such as
u^2 if u is greater than or equal to -2 and less than 1
2- u if u is greater than or equal to 1 and less than 4

The base of a triangle 2008-08-10
From Mark:
What is the formula I need to use to find the base of a triangle sail that is 16 feet high and has an area of 64 square feet.
Answered by Stephen La Rocque and Penny Nom.
Angles in a regular tetrahedron 2008-08-07
From Carla:
Hi guys, A regular tetrahedron has all its edges 8cm in length. Find the angles which an edge makes with the base. Thanks. Carla
Arc-length and sector-angle 2008-08-06
From Benson:
If chord length, radius are given, How to find the sector angle and arc-length
Cost of pencil is rising every year since 7 years ago 2008-08-06
From Mari:
Cost of pencil is rising every year since 7 years ago. If the cost of pencil last year was 60 cents which is the sum of the cost from the last two previous years, what is the cost of the pencil now, the cost seven years ago.
Demographics 2008-07-25
From shahrukh:
Each year for 10 years ,the population of a city increased by 5% of its value in the previous year. If the initial population was 200 000 ,what was the population after 10 years ??
The midpoints of the sides of a quadrilateral 2008-07-22
From JOEL:
A QUADRILATERAL A,B,C,D HAS THE CO -ORDINATE [2,5],[8,7],[10,3]&[0,1] RESPECTIVLY [B,E,G,H] ARE THE MID POINTS OF THE SIDES AB,BC,CD&DA RESPECTIVLY FIND THE MID POINTS OF [FG]&[FH]
Taking two math classes 2008-07-21
From Bailey:
i am going into the 7th grade, but i am going to be taking 9 th grade math. i was wondering if anyone could help survive doing two different math classes at the same time.
Three consecutive positive integers 2008-07-20
From AC:
find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third
Choosing 5 numbers out of 39 numbers 2008-07-18
From robert:
Please list the way I can choose 5 numbers out of 39 numbers, without repeating them, starting at number 1.

Please send me a list of all 120 combination.

Does the sequence 1 2 4 8 16 32 etc have a name? 2008-07-17
From Richard:
Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name?
1, 2, 4, 8, 16, 32 ... 2008-07-15
From eve:
I have to find out the fomula for:

1, 2, 4, 8, 16, 32 ...

A reflected line segment 2008-07-14
From Peter:
Segment AB has endpoints A(-1,2) and (3,1). Segment AB is reflected over the y-axis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'?
Choosing a number from 1 - 400 2008-07-04
From Peter:
The numbers 1-400, inclusive, are put into a hat. What is the probability that the first number chosen at random is a multiple of 4 or 17? Express your answer as a common fraction. How do you do this the question without a calculator?
A series solution of y' = xy 2008-07-03
From sasha:
I've to find the power series solution of the differential equation: y' = xy.

Percentage increase 2008-06-29
From Paul:
Could you please help me with this question. I was paying \$98.00 a month for my health insurance premium, now it is up to \$125.83 How much of an increase is that as a percentage increase, and how can I do this on a calculator. I'd like to know how much my increase is as a percentage.
A 7-digit odd number 2008-06-26
From Godryk:
I am the smallest 7-digit odd number. my ones digit is the sum of my thousands, and ten thousands digits. What number am I?
Product of Two Integers 2008-06-25
From devin:
two consecutive integer have a product of 240. what are they
How do you change bases? 2008-06-17
From Peter:
How do you change bases eg. 121 from base 3 to base 5?
A piecewise equation 2008-06-16
From John:
AT&T charges \$39.99 for 450 minutes per month. It charges 45 cents per minute over the 450 minutes. How can I make a piecewise equation of this problem?
An ellipse and circle with the same area 2008-06-09
From Michael:
The area of the ellipse if equal to the area of a circle with radius=40 ft. Find the values of a and b using appropriate algebraic techniques, not basic math computations. A=pi ab and satisfy the constraint a+b=100????
Geometric sequences 2008-06-08
From Rita:
A geometric sequence is given. Find the common ratio and write out the first four terms.

(1) {(-5)^n}

(2) {(2^n)/(3^(n - 1)}

90% of gross leaseable footage 2008-06-07
From Rosalind:
90% of gross leaseable footage in the shopping center, being 394,577, excluding that square footage leased by major anchor tenants, being 284,747. Would you deduct the 284,747 from the 394,577, then multiply by the 90%. Or would you multiply the 394,577 by the 90%, then deduct the 284,747?
A recursive formula for 9, -18, 36, -27, ... 2008-06-05
From Rita:
I am having trouble understanding how to write formulas (I should say create formulas) from a given sequence. It does not matter what sort of sequence it is. The confusion remains. I have not found a textbook or easy math book that explains this process for the average Joe to grasp. Here are the two questions:

(1) Write a recursive formula for the sequence
9, -18, 36, -72, ...

(2) Write a recursive formula for the sequence
3, 3(sqrt{3}), 9, 9(sqrt{3})

The path of a baseball 2008-06-04
From Tom:
How high would a batter have to hit a ball to clear the stadium roof in right field if the distance to the right field fence is 320 feet from home plate? Is this solvable?
Calculating a price based on markup 2008-06-03
From Sheldon:
I know the most common form for retail businesses of calculating a price based on markup is: Cost/(1 - Markup), but how is this supposed to work for a business that desires a markup of over 100%.
Two consecutive negative even numbers 2008-06-03
From Chelsea:
The sum of the squares of two consecutive negative even numbers is 100. Find the integers,
Inverse variation 2008-05-22
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.

How much seed do I need per plot? 2008-05-13
From Jaye:
The plot size is 5 m X 2 m. The seeding rate is 12Kg/ha. How much seed do I need per plot? I have failed to get a proper answer. Thank you.
Selling price 2008-05-10
From Roxane:
I'm trying to figure out the formula for the following, I have a product that I want to receive a certain profit margin, but with this product I also have to pay a percentage of commission to someone. I need to know how to calculate my new selling price taking into account the markup percentage, but I don't want my gross margin to be lowered. I have calculated the markup percentage to get my new selling price with the commission, but it lowers my profit margin once I pay the commission and I don't want it to do that.
The area of a sector of a circle 2008-05-10
From lupio:
a problem asks for the area of a sector in a circle,no central angle,in circle is given only 5cm radius, three answers 180-90-35
can't find a way to start.Help

The inverse of a function 2008-05-03
From keith:

h(t) = 2 + 4 ln(1-5t)

The standard form of an ellipse 2008-04-30
From Rebecca:
I have to write the following equation into standard form of an ellipse:

9(X-1)^2 + (Y+1)^2 = 1

Answered by Stephen La Rocque and Harley Weston.
3-3+3-3+3.........up to infinite terms = ? 2008-04-25
From Jatin:
3-3+3-3+3.........up to infinite terms = ?
Two intersecting circles 2008-04-17
Hi, how can we find the perimeter and area of the region common to two intersecting circles of radii 6 cm and 4 cm with centers 7 cm apart.
Conic sections 2008-04-14
From Christine:
In my analysis class we are learning about conic sections. Our project is to create a genral statement of the definition of conic sections. Truthfully, I have absolutely no clue on how I should write that. Could you help me?
The maximum area of a pizza slice 2008-04-12
From charles:
A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when o is the central angle in radians, the area of the sector is given by A= r^20/2and the length on the circle is given by s=r0
Two function problems 2008-04-10
From keith:
find the domain: F(x)= 1/ {ln (x+5) - ln (7-x)}

find the inverse: g(t)= sqrt {2-3 ln (1-t)}

cosec [arccos (1/y)] 2008-04-09
From Tom:
I am having trouble with this question. For y > 1, the value of cosec [arccos (1/y)] is?
1-(1-P)^75=0.05 2008-04-05
From Amy:
1-(1-P)^75=0.05
Answered by Stephen La Rocque and Penny Nom.
Two consecutive odd integers 2008-03-24
From Jarrod:
the sum of two consecutive odd integers is 24. Find the two integers
Circles and semicircles 2008-03-23
From sally:
Hi i am sally ,

i need to know what is the formula of :

Find perimeter and area of a semicircle ?

Find the area of a circle whose circumference ?

5 9 1 6 10 12 2, where does 3 fit in and why? 2008-03-22
From Cassidy:
number sequence

5 9 1 6 10 12 2, where does 3 fit in and why?

4,12,24,40,60,84 2008-03-18
From kirsty:
Here are the first six terms of a sequence.

4,12,24,40,60,84

Find in terms of n, an expression for the nth term of teh sequence.

Distance seen 2008-03-18
From Nev:
formule: Distance Seen
S = 1.225 x square root of H
S = Distance seen in Miles
H = Height in Feet

What dose 1.225 Relate To ?

The nth term 2008-03-16
From ryan:
1, 1, 2, 3, 5, 8, 13, ___ ___ ___ 2008-03-13
From Karen:
What is the rule for the following pattern, and what would come next?

1, 1, 2, 3, 5, 8, 13, ___ ___ ___

Inverses of functions 2008-03-13
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
Two consecutive odd positive integers 2008-03-12
From Sarah:
The sum of the squares of two consecutive odd positive integers is 74. What are th integers?
Estimate the cube root of 270 2008-03-11
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 Newton-Raphson 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.

Base 5 arithmetic 2008-03-06
From Jana:
Hello, my name is Jana, i have asked a question here previously about how to count in base-5. I am happy now because i can convert any number now and it is very easy for me. The only thing i am having trouble with is understanding how to do a maths sum or times base-5 numbers. it is just a bit hard for me. So do you think you could explain how to do a sum in base-5 and how to do a multiplication sum. Please help...Thankyou Jana!!
What was the ostrich's speed in miles per hour? 2008-03-03
From jacob:
If it took an ostrich 2.5 seconds to travel 110 feet and the average speed is 44 feet/ seconds, what was the ostrich's speed in miles per hour?
Convert from base 6 to base 12 2008-03-02
I am trying to convert 13405 base 6 to a base 12 number. I am not allowed to go into a base 10 number. How will can I base 12 without doing anything with base 10? Thank you kindly.
Answered by Stephen La Rocque and Penny Nom.
The perimeter of a sector of a circle 2008-02-28
From erica:
What is the perimeter of a sector if the radius is 18 and the middle arc is 150?
3 consecutive odd integers 2008-02-28
From Pat:
For 3 consecutive odd integers, twice the first integer, plus 5 more than the second integer, plus three less than four times the third integer equals -85. Find the 3 consecutive odd integers.
The surface area of an ellipse 2008-02-25
From paritosh:
how is the surface area of a elliptical dome be calculated when the two diameters are 55 metres and 35 metres and the height of the structure is 13.4 mts?
Counting in base 5 2008-02-24
From Jana:
my name is Jana, i really need help with a maths question at school. Im confused about how to count up from1-20 in a base-5 format! I'm in year 5 and i really don't get all the complicated stuff.
Actural cost, selling price and commission 2008-02-21
From LiSa:
I have a question about a few things if anyone can answer... ex. actual cost (AC) = \$1000 selling price (SP) = \$ amount earned for company (C) = 15% of... selling price? commission 1 (C1) = 2.5% commission 2 (C2) = 2.5% How would you calculate how much the company's commission amount would be as well as the amounts for the other 2 that get 2.5%? And what would the selling price be? (the 15% \$ + 2.5% \$ + 2.5% \$ ?) Is the 2.5% taken from the original amount? I am soooo confused! If anyone could help, that would be great!
Find the next terms 2008-02-20
From Darrin:
I was given a number sequence and can't figure out the next terms to this

2,9,20,35,66,91......

Classifying a triangle 2008-02-07
From kevin:
scalene triangle 8 ft base right side 9.5 left side 12 ft what is the angles
The perimeter of a semicircle 2008-02-02
From Lisa:
How do you find the perimeter of a semi circle when you are only given the diameter, say 24 units?
Cross-sectional area of a fire hose 2008-01-27
From Tom:
My question is this I know the equations for the final answer but the book skips how to get to one section of the equation. Q=(a)(v) A= The cross-sectional area of the conduit in square feet (ft2). So if you have a 5 inch hose how do they get A=0.136 ft2 ? And I know the velocity already v= velocity in ft per second.
How do I convert mcg to ml? 2008-01-27
From David:
How do I convert mcg to ml?
O.T.T.F.F.S.S 2008-01-25
From Omar:
What is the next letter in the following sequence:

O.T.T.F.F.S.S

Three consecutive odd integers 2008-01-24
From daniel:
find three consecutive odd integers such that three times the second minus the third is 11 more than the first. help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while.
1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 2008-01-22
From Neil:
Find the next two terms in the following number sequence

1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128

Find a general rule for the nth term of the sequence

Choosing 6 numbers from 42 2008-01-19
From Marcus:
If i have 42 numbers to choose from and i could only choose 6 numbers at a time without choosing the same number twice in the same row, how many possibilities are there?
A sector of a circle 2008-01-17
From Amandsa:
What is the formula for finding the sector of a circle?
A large concrete shape 2008-01-16
From Keith:
what is the cubic yards of an area that is not a perfect 1/4 circle? The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth?
The area of a sector of a circle 2008-01-11
From Serenity:
A denotes the area of a sector of a circle of radius r formed by the central angle theta. Find the area A if r=10 meters and theta = 1/2 radians.
Multiplying numbers in bases other than 10 2008-01-08
From Imaiya:
In class we've been learning about numbers with a base other than ten. For example, base 7, base 5, and base 6. What's really stumping me is how to multiply these numbers, when they aren't a base of 10. I've had it explained to me once, but don't seem to understand it. Here are the equations, and I've listed the first few numbers for that particular base.

Base 5: 0,1,2,3,4,10,11,12,13,14,20 etc... The Equation: 34 x 42 Base 9: 1,2,3,4,5,6,7,8,10,11,12,13,14, etc... The Equation: 56 x 78

If you could explain to me how to multiply numbers with any type of base, I'd really appreaciate it. Also if you could show me how to do one of the questions that I listed, that would really help me =) Thanks so much, and once again, thank you for your great site!

Practical applications of sequences 2008-01-01
From carl:
can you give me examples of different kinds of practical applications of sequences?
Find the lengths, and explain in a 'let statement' 2007-12-20
From Cordilla:
the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'.
Answered by Stephen La Rocque and Harley Weston.
A 45-45-90 triangle 2007-12-13
explain to me please how to do the 45-45-90 theorem when one of the legs(not the hypotenuse) is 3. How do you find the remaining two sides? please help me out.
How many houses must they paint? 2007-12-12
From Natalie:
The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds. If they work for four months of the summer and their expenses are 152 pounds per a month, how many houses must they paint for each of them to have one thousand pounds at the end of the summer?
Imprecise measurements 2007-12-09
From Sara:
Hi! A water tank, in the shape of a cuboid (length 1.6 m, height 1.2 m, breadth 0.8 m), is full of water. Water is drained from the tank at a rate of 8 litres per minute. The dimensions of the tank are given to the nearest 10 cm. The rate at which the water is drained from the tank is given to the nearest 0.5 litres per minute. (a) Calculate the smallest possible time to drain the tank. (b) Calculate the greatest possible time to drain the tank. Many thanks!!!
Three consecutive numbers 2007-12-08
From Aris:
The product of 3 consecutive numbers is 1716. Find their sum.
A portion of a circle 2007-12-07
From Richard:
please could you tell me the formula and answer to the following. I have a circle portion with a radius of 150mm and an angle of 120 deg. If an arc is drawn from one point to the other as the radii touch the circle circumference, i need to know the area of the segment and the formula to carry out the answer. Many Thanks
A right triangle 2007-12-06
From Shubhomoy:
The co-ordinates of a hypotenuse are (1,3) and (-4,1). Find the equations of the perpendicular sides.
Representing different bases 2007-12-05
From Sudhir:
What does a number subscripted to another one denote? (I know that a number superscripted to another denotes the power, but the subscript number is something I have never seen before.)
Percentage increase in profit 2007-12-04
From Dee:
If I had a certain % increase in profits for the entire year, why can't I add the profits I made for the first 1/2 of the year to the profit I made in the second 1/2 of the year to get the total year end profit percentage? Or how can I compare the increase/decrease for each 1/2 of the year to the total % increase/decrease?
Proving a quadrilateral is a rhombus 2007-12-03
From Jeanie:
How do you prove that a quadrilateral is a rhombus because the diagonals of the quadrilateral are perpendicular and bisect each other using the 2-column proof method?
O,T,T,F,F,S,S,?,?,? 2007-11-28
From Kim:
What are the next 3 letters in this sequence?

O,T,T,F,F,S,S,?,?,?

Direct and inverse variations 2007-11-27
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.
Elimination of mayan prisoners 2007-11-19
From Jim:
An evil Mayan emperor decides to make an example of 1,000 prisoners. He stands them in a circle with numbers one to a thousand marked on their shirts. He then starts counting: "one in, two, in three out" The third man is immediately executed. This continues round and round and round the circle. While the number in the circle shrinks, every third prisoner is pushed out and executed. And it continues even when there are only two prisoners left alive. What number is on the last prisoner's shirt?
Sides and vertices 2007-11-17
From derek:
What is the correct name for a 2D geometric shape that would look like one slice from a round pizza and how may sides and vertices would it have? I believe you would say it has one vertex and two sides with the curved boundary not resulting in vertices or a side. Your help is much appreciated.
Answered by Chris Fisher and Walter Whitelty.
A matrix equation 2007-11-16
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

Two sequences 2007-11-14
From Kim:
Pattern........what comes next?

1,4,9,16,25,_____,____
1,4,9,16,27,40,__________,_______

Answered by Penny Nom and Gabe Potter.
From abdulai:
a circular saw with diameter 18.4cm rotates at 2400rpm. What is the angular speed of a point on the edge of the saw blade in radians per second?
What number best completes the series? 2007-11-12
From Grace:
What number best completes the series?

2 3 7 13 27 ____

Answered by Stephen La Rocque, Penny Nom and Harley Weston.
The sequence 3,12,26,45.... 2007-11-12
From Tra:
I can seem to find the realtionship in these sequence of numbers, I am looking for the next three. How can I determine that, I have tried everything??!!!

3,12,26,45....

Meters per second to miles per hour 2007-11-08
From Niecey:
If Greg was timed at 0.91 seconds for 10 meters running the 100 meter dash, at that speed, could he pass a car traveling 15 miles per hour in a school zone?
The base and height of a triangle triangle 2007-10-31
From mike:
How do you find the length of the base or the height of a triangle if the area is 30 square feet?
Subsets of a set 2007-10-30
From Snehal:
1. Let an denote the number of subsets of f{1,2, 3.... n}including the empty set and the set itself.)
a) Show an = 2an-1
b) Guess a formula for the value of an and use induction to prove you are right

Dividing a segment into 3 congruent parts 2007-10-30
From Carolyn:
I am doing construction. I have a line segment drawn. I need to divide a segment into 3 congruent part. How do I do that?
Variation 2007-10-29
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 8th-grade student is \$8.56 per week, what is the average weekly allowance of a 5th-grade

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?

Combinations and horse races 2007-10-28
From Ian:
How do I calculate the number of combinations for: Horse races,1 horse in each race.I want all combinations covered. e.g.5 races, 1 horse in each race. R 1&2, R 1&3,R 1&4, R 2,3,4,5, R 1,2,3,4,5 etc etc.I have worked it out manually to 27 combinations but if I want to cover more than 5 it will be a big excercise to work out the cost manually. Many Thanks
Is there a practical use for radian measure? 2007-10-26
From Paula:
Is there a practical use for radian measure in any profession? Which professions might us radian as opposed to degree measure?
The perimeter of a circle sector 2007-10-25
From sara:
Hi! The area of a sector of a circle is 25 sqcm. The radius of the sector is 6 cm. Calculate the perimeter of the sector. Many thanks!!!
A sixfold increase 2007-10-24
From Fred:
If I have \$500 and it grew to \$3,000, what is the correct description of the increase? Is it a sixfold increase (sextupled), or a fivefold increase (quintupled)? When I divide \$3,000 by \$500, the result is six, therefore, a sixfold increase?
Converting bases 2007-10-24
From Johanna:
Is there an easy way to convert from base to base. For example, base 5 to base 9 or base 2 to base 4 etc
Answered by Stephen La Rocque and Penny Nom.
The nth term 2007-10-18
From shannon:
Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term.
Paying with silver - Part 2 2007-10-17
From Shanna:
The paying with silver problem. I understand how to do the problem, but could you please explain how you would use base 2 arithmetic to solve it.
the sum of two consecutive integers is 51 2007-10-17
From Keira:
the sum of two consecutive integers is 51
0,1,2,3,6,11,20,37,68... 2007-10-16
From Pat:
Describe the rule for this pattern: 0,1,2,3,6,11,20,37,68... Thanks
How much water is in a hose? 2007-10-12
From Bryan:
I need to know how much water (gal) is in a hose thats 100' long by 5" in dia. Thanks
77,49,36,18,... 2007-10-11
From Kim:
Find a pattern and predict what comes next in this sequence 77,49,36,18,________________.
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.
Base 10 to base 5 2007-10-09
From Angela:
I've been searching online for the past week and I cannot find an Algorithm to convert from base 10 to base 5. Can anyone give me a step-by-step instruction on how to do this?
Equation of a circle circumscribing a triangle with given vertices 2007-10-01
From Randy:
How do I determine the equation of a circle when it is circumscribed by a triangle whose vertices are (-1, 6), (3, -2), and (2, 5)?
A sequence of numbers 2007-09-30
From eleanor:
can you find the nth term of the sequence ( n starts at three)

1=?
2=?
3= 4
4= 10
5=20
6 = 35
7= 56

i only hand the 3rd 4th 5th 6th and 7th numbers in the sequence

can you please tell me how to find the nth term and what is it :)

Answered by Stephen La Rocque and Victoria West.
The nth term 2007-09-29
From zoe:
what is the nth term for the following sequence...
5, 2, -1, -4

Describe the pattern 2007-09-29
From Baffled:
Given a rule, extend a pattern and describe it in informal mathematical language:

a) 1, 6, 16, 36, _

b) 2, 6, 14, 30, _

c) 1, 8, 22, 50, _

d) 3, 9, 27, _

e) 2, 7, 17, 37, _

Answered by Stephen La Rocque and Penny Nom.
Four consecutive integers 2007-09-28
From Joshua:
We were given a question that involved consecutive integers. I can not seem to solve this question and I am the top student in my class.The question states: Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91. How do you solve this question? Thank you very much for your support.
Answered by Penny Nom, Stephen la Rocque and Claude Tardif.
A sector of a circle 2007-09-26
From A student:
hi im stuck on this question. i have tried to do some, could you please che= ck it and help me.the answers i have worked out are in red. the question is= attached. thank you.
The nth term 2007-09-25
From Bobby:
whats the nth term of 2,12,22,32 ?
A geodesic dome 2007-09-25
From Roger:
In my Science-Fiction series, I have a Dyson's Sphere tiled with regular hexagons. The number of hexagons is over 300,000 and the radius of the Sphere is roughly 80,000,000 miles. The actual size of the Sphere and hexagons have been left flexible until I can come up with a definite number of hexagons that would fit. My problem is the pattern of hexagons which would fit within the sphere without leaving gaps or overlapping.

My best guess has been to use four equilateral triangles composed of 78606 hexagons, (396 per edge) arranged around the sphere with six 'zippers' to connect them and four 'caps' at the points, for a total of 316804 hexagons. Given the fact that each Hex is the same size, does this seem plausible? Is there some pattern formula I can use to play with these figures? Simple divsion of areas will not work if the number derived will not fit into the pattern to leave a perfectly tiled surface. Thank you.

The sequence 2,4,7,11,16,22 2007-09-22
From Simon:
I thought i understood how to explain how to work out the nth term on a sequence of numbers until my son had this sequence to work out - 2,4,7,11,16,22
We have worked out the 2nd differance is +1 but nothing else seems to fit. Im sure the answer is staring us in the face but cant see the wood for the trees!

Answered by Denis Hanson and Steve La Rocque.
Finding equations, intersection point of two lines at right angles 2007-09-22
From Yaz:
Find the equation of the line joining A(-1,-9) to B(6,120). Another line passes through C(7,-5) and meets AB at rigth angle of D. Find the euation of CD and calculate the co-ordinates of D.
A fraction sequence 2007-09-21
From marissa:
i have read the examples you have on fraction sequences, but i am still having a hard time understanding how to figure this out. for example:

__ 1 2/5 __ 3 __ __ __ __7

Letter number sequence 2007-09-21
From Hope:
The challenge problem of the week in 6th grade math is a letter number sequence. J 1 F 8 M 1 A 0 M 1 J 0 J 1 _ _ _ _ _ _ _ _ _ _ They are to find the next 10 letters and numbers in the line. They were given a hint : look at the letter sequence by themselves and you should recognize it. Does it just repeat starting with the F 8 M 1 etc.? Thank you for your help.
The hypotenuse 2007-09-20
From Kasey:
What is the hypotenuse of 96 squared and 108 squared?
What is the inverse function of y=x^3 +x? 2007-09-19
From saman:
what is the inverse function of y=x^3 +x
Number sentences 2007-09-15
From jen:
list the addition number sentences that can be written using two sets of cards with the numbers 5 6 and 7. which number sentences have the same addends but show a different order?,,,,,,,,,,,,,,Ithis is for my son in 3rd grade and for the life of us we can't figure it out,,thanks for this elementary help
The nth term 2007-09-13
From Rookin:
Can you help me find the nth term for this ... 20,17,14,11,8 i'm really confused oh and could you also tell me how you got the answer?
Answered by Steve La Rocque, Claude Tardif and Harley Weston.
The perimeter of a semi-circle 2007-09-11
From Confused:
What are the next two terms? 2007-09-11
From Sassy:
I can't figure out what the next two integers in this pattern are 3,9,6,12,9 are.
A sequence of fractions 2007-09-10
From mitch:
find an expression for T(n), the nth term of the sequence
1/5, 3/8, 5/13, 7/20, 9/29

Segments on a line 2007-09-10
From Cathy:
This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments.
The nth term 2007-09-09
From Conor:
Please can you help me with this question on the subject of the Nth term. 3.5, 5, 6.5, 8, 9.5

5.1, 7.2, 9.3, 11.4...

nth term in this series 2007-09-07
From danii:
im trying to solve the nth term for this pattern.

1 3 6 10 15 21 28

any help would be appretiated

The next term 2007-09-07
From Ariel:
Please explain to me why -3^2 is a -9. One calculator give me an answer of positive 9.

WHAT IS THE NEXT TERM IN Each sequence/ What is its term number?

1/2, 2/3, 3/4, 5/6 6/7

1, 1/4, 1/9, 1/16

A sequence 2007-09-06
From aimee:
i have the sequence 1,5,14,30,55 and i have been told to use An squared times Bn times C and my working should look like this

1 5 14 30 55
4 9 16 25
5 7 9
2 2

But how do i do this

A sequence of fractions 2007-09-05
From Arjun:
1/2 3/5 5/8 7/11- need to find the nth term.

I did search the data base & found one for fractions but what I want to know is when calculating nth term for the denominator in the example give in your database how do we get (n-1)? When we deduct the actual term with the one that is in the table give in your example it is more that one. Could you please explain solving the above example?

The first five terms 2007-09-04
From JP:
Find the first five terms of a sequence with the nth term n^2+2n+1 and 2^n.
Speed of sunrise 2007-09-04
From Robert:
Facing west in a car, you are watching the sun rise (through the rear view mirror). It peaks the horizon, you take off driving. How fast would you have to drive, to see it rise again?
2,6,7,21,22,66,67 2007-08-28
From EDWIN:
this doesnt make any sense to me....... i cant find the pattern...

2,6,7,21,22,66,67

Answered by Leeanne Boehm and Stephen La Rocque.
Applications of sequences and series 2007-08-27
From Trish:
I'm a grade 12 learner working on a math project based on sequences and series. I'd like to know the different types of sequences and series such as fibonacci, fourier, farey, etc.

I've already used the Fibonacci Sequence and Harmonic Series and need two more. The simpler the sequence or series type the better.

I'd also like to know in which non-mathematical areas use sequences and series and how. Areas such as engineering or science.

Where do you use trigonometry? 2007-08-21
From jenny:
where do you use trigonometry besides architecture and engineering?
The tens digit 2007-08-21
From Arul:
Hi.. Please help me on this question.. Sequence 2, 7, 22,…after the first three terms, each term is three times the previous term plus 1, a(n+1)=3an + 1. What is the sum of tens digit 33rd and tens digit of the 35 term?
Common factors 2007-08-19
From John:
Answered by Leeanne Boehm, Steve La Rocque and Penny Nom.
Percentage change 2007-08-19
From nona:
If inputs increase by 30% and outputs increase by 15%, what is the percentage change in productivity?
Area and perimeter 2007-08-16
From sheryl:
a 50*70 horse pen is 240 feet and 3500 square feet a 60*60 horse pen is 240 feet and 3600 square feet why is there a 100 square feet difference?
Percentage change 2007-08-13
From Karen:
I need a formula for calculating percentages in Excel. For example, we = sold 4 units of an item one month, and 105 units the next. I need a = formula to calculate the percentage increase in sales units. Also, if = 5251 were sold one month and 651 the next, what is the formula for = calculating the percentage difference? Please help, thank you.
Twenty dining tables 2007-08-13
From priya:
Utkarsh bought 20 dining tables for Rs 120000 and sold these at a profit equal to the S.P of 4 dining tables.Find the S.P of one dining table.(give the answer in statements)
A right triangle 2007-08-11
From Peter:
Ok, is it possible to find the height and base of a right triangle when all the information you are given is the length of the hypotenuse?
I also know that the angle between side b and the hypotenuse is 45 degrees. please help.

4,18,48,100, __ 2007-08-07
From Jeremy:
What is the next number in the following sequence?
4,18,48,100, __

Answered by Leeanne Boehm and Stephen La Rocque.
Linear systems and inverses 2007-08-06
From Marsia:
explain how inverses are used to solve linear systems.
Angular speed 2007-08-05
From Virginia:
the engine of a sports car rotates at 5,000 revolutions per minute (rpm). calculate the angular speed of the engine in radians per second. use 2n radians = 1 revolution
A sequence of numbers 2007-07-27
From Shamik:
Question: A sequence of numbers is defined in the following way.
B(1) = 1
B(n) = B(n-1) + {Sum of the digits of B(n-1)} for n > 1.

B(1) = 1
B(2) = 2
B(3) = 4
B(4) = 8
B(5) = 16
B(6) = 23
B(7) = 28
B(8) = 38
B(9) = 49
::::::::: and so on ...

Is the number 123456789 a term in the given sequence?

Shamik

Countable and uncountable sets 2007-07-24
From Mac:
Hi, i tried to read few webpages related to the countably infinite and uncountable sets. Even i read few questions from this forum.

But i am not convinced with this explanation. If you have any good book that explains this in layman term, please redirect me to that.
1) Can you please explain what is the difference between these too ?
2) How could you say set of Natural number and set of even numbers are countably infinite ?
N={1,2,3,...} and Even= {2,4,6,...}
When an element in the even set is some 2n, we will map it to 'n'.So now we have a bigger number(2n) right ?
Sorry, i didn't understand that.
...

Equality of sets 2007-07-23
From Mac:
Hi, I learnt set theory recently. My teacher and few of the weblink actually give different definition for basic set. Can you please solve this ?

My teacher says, {1,2,3} and {1,1,2,3} is also set.
But in this link http://library.thinkquest.org/C0126820/setsubset.html it says,
"A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice."
and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}"

My question is,
1. Whether duplicates allowed in the set or not ?
2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ?

Answered by Penny Nom and Harley Weston.
Comparing flow rates of two pipes 2007-07-14
From Kenneth:
If two water pipes are 3 feet long, but one of them has a 1 foot diameter and the second has a 1 1/2 foot diameter, what simple mathematical method can be used to determine how much faster one pipe can drain water than the other pipe?
Can't find circumference of an ellipse 2007-07-06
From Michele:
I need to figure the circumference of an oval and I know the height and width.
Log base 2 of log base 2 of x 2007-06-27
From alex:
y = log base 2 of lag base 2 of x The slope of the tangent to the given curve at its x-intercept is..?
The area of part of a circle 2007-06-21
From Sarah:
Hi, I need help finding the area of a part of a circle that involves a chord. I need this answer/help very soon if at all possible. I have attached a drawing of what I am trying to solve. Thank you for your help! Sarah!
Finding the center of an ellipse 2007-06-20
From Sima:
find the center of the ellipse with the equation 3x^2 +4y^2+18x-32y-5=0
What is the 100th term? 2007-06-15
From George:
I have the sequence 50,120,235,406,644

the 1st difference is 70,115,171,238
the 2nd difference is 45,56,67
the 3rd difference is 11,11

i used the a*n^3+b*n^2+c*n+d rule but the a turns out to be a decimal because 11/6 is 1.833333333 and so i cant find the formula for the 100th term term.

Percentage increase and decrease 2007-06-13
From Anna:
I just want to if the following formula is used for the computation of a PERCENTAGE DECREASE:

Old Value - New Value/ Old Value x 100%

My immediate superior is under the impression that the said formula works ONLY for the computation of a percentage INCREASE. He believes that the formula for a percentage DECREASE:

Old Value - New Value/ NEW Value x 100%

On this score, I want to know the correct formula for the computation of percentage decrease. Thank you so much.

Composition functions 2007-06-12
From Gilligan:
Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start.

A sequence of circles 2007-06-11
From Ann:
Please help with solving the following problem!!! A circle is inscribed in an equilateral triangle with a side of length 2. Three circles are drawn externally tangent to this circle and internally tangent to 2 sides of the triangle. 3 more circles are drawn externally tantgent to these circles and internally tangent to 2 sides of the triangle. if this process continued forever, what would be the sum of the areas of all the circle? the answer 1 parent came up with was Pie over 2, but we don't know how he did it. Can you please show the work or explain the answer to this problem? Thank you Ann p s my daughter is in 9th grade math.
Answered by Steve La Rocque, Chris Fisher and Penny Nom.
How many terms in this sequence? 2007-06-11
From Jesse:
How do I find how many terms are in the sequence? 51, 48, 45, ...., -75
Answered by Stephen La Rocque and Penny Nom.
The intersection of two planes 2007-05-31
From Sarim:
How to find a intersection of two planes?
Water tank volume 2007-05-29
From Cecelia:
I HAVE A SEMI CIRCULAR TANK AGAINST A WALL MEASURING 6'10" ACROSS THE WIDEST PART AND 3' FROM THE WALL TO THE FRONT OF THE TANK. THE DEPTH IS 14". PLEASE HELP ME TO CALCULATE THE VOLUME OF WATER IN THE TANK.
A point on a semicircle 2007-05-28
From arun:
a semi circle is drawn with ab as diameter from p a point on ab a line perpendicular to ab is drawn meeting circumference of semi circle at c, ac = 2cm, cd = 6cm find area of the semi circle?
The surface area of a fire hose 2007-05-26
From Vanessa:
Why do we need to find the surface area of a fire hose (cylinder).
The circumference of an ellipse 2007-05-25
From Graham:
I have an ellipse that I need to find the circumference of. It is 40ft at its longest point and 25ft at its shortest
Normal distribution 2007-05-24
From Paula:
Consider a data set that is normally distributed. The mean of the data set is equal to 10,000.
a.) Suppose that, for this data set, 10,625 has a "z-value" = 2.5. Solve for the standard deviation of the data set.
b.) Solve for the "z-value" of 9,900.

Base seven 2007-05-19
From Dan:
A number X is converted to base 7 and becomes a four digit number. Its leftmost digit is removed and written again as the rightmost digit. The number thus obtained is twice X. Find the decimal representations of all such numbers X.
Parabolas in the real world 2007-05-18
From Katherine:
Hi, my name is Katherine, and my mean old math teacher just assigned us a test in which we have to write two examples of how parabolas are used in the real world, each one page single spaced, size 12!! I know you have already answered some questions like this, but I still don't understand the whole baseball thing, and any other way parabolas are used. And how I can write a whole page on it. But that's my problem, not yours, I just need help with a little explanation on how parabolas are actually used today. I know this might be kind of confusing for you, but imagine how it is for me!!
Comparing the areas of various shapes 2007-05-16
From Kathy:
If the perimeters are the same, which has the greater area, a circle, a square, an ellipse, or an octagon?
Maximizing the volume of a cone given the slant length 2007-05-14
From Christina:
A coffee filter for a new coffee maker is to be designed using a conical filter. The filter is to be made from a circle of radius 10cm with a sector cut from it such that the volume of coffee held in the filter is maximised. Determine the dimensions of the filter such that the volume is maximised.
Answered by Stephen La Rocque and Kerstin Voigt.
Finding the hypotenuse without Pythagorus 2007-05-11
From Shelbie:
How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs?
Probability of H.I.V. tests 2007-05-07
From Danielle:
A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.?
A point inside a circle 2007-05-04
From edgemitter:
There is a point inside a circle (but not in its center) where two perpendicular secants intersect, dividing the circle into four regions with different area. Calculate the area of the four regions
Hypotenuse 2007-05-03
From ashley:
how do you find the hypotenuse
3, 6, 12, 21, 33, 48, 66 2007-05-02
From Siew:
I need to find the nth term formula for the sequence :

3, 6, 12, 21, 33, 48, 66

Percentage change 2007-05-01
From katie:
The sum of two or more consecutive integers 2007-04-26
From nana:
some numbers can be written as the sum of two or more consecutive integers(we consider positive integers only) other number (eg. 4) cannot be express in this way.
let us call a number which can be expressed in this way a SOALTCI( sum of at least two consecutive integers)
a). list the first few SOALTCI and conjecture the general formula.
b). Prove that any number of the given form(in your answer (a)) is a SOALTCI

A triangle problem 2007-04-23
From Dimitri:
In the triangle ABC, M is the midpoint of AB and N is the midpoint of AC. Prove that CM and BN cannot bisect. (I can prove it by contradiction if it is a scalene triangle, but i cant seem to prove it for isosceles)
Two lines intersect at a right angle 2007-04-20
From ellen:
The line with the equation 3x + by = 6 intersects with the line 6y + ax = c at right angles at the point (4,6). Determine the values of a, b & c.
The second derivative 2007-04-14
From Gerry:
In mathematical context,what do you understand by the term "Second Derivative"
Intersection of a line and a circle 2007-04-12
From gaby:
The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers.
Answered by Steve La Rocque and Melanie Tyrer.
Choosing 6 from a set of 12 2007-04-12
From Darren:
there are 12 numbers (1-2-3-4-5-6-7-8-9-10-11-12) how many times can i pick 6 different numbers?
Where will volume 13 go? 2007-04-12
From Shawn:
A novice librarian shelved a twelve-volume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will volume 13 go?
Answered by Stephen La Rocque and Penny Nom.
Pythagoras was right 2007-04-11
From Vineet:
in a right angle triangle, hypotenuse side is less than the sum of other two sides, how the square of hypotenuse is equal to the sum of squares of other two sides?
What are the first 3 terms of this sequence 2007-04-10
From kyrie:
what are the first 3 terms of this sequence n-2 divided by n squared
4,7,16,43,... 2007-04-04
From claire:
What is the explicit definition for the sequence 4,7,16,43,...?
Answered by Stephen La Rocque and Penny Nom.
What is the hypotenuse of a right traingle 2007-04-04
From debbie:
what is the hypotenuse of a right triangle with sides of 38 meters and 24.2 meters.
A set of points in space 2007-04-04
From Lenny:
What is a set of points in space the same given distance from its center point called?
Algebra 2007-04-03
From Emily:
9,365 and 2,242 added to the difference between 255 and half of a number is 11,784. What is the number?
In what base does 25+25=51? 2007-04-03
From Jenna:
In what base does 25+25=51?
Answered by Stephen La Rocque and Penny Nom.
A geometric series 2007-04-03
From jessica:
If a geometric series includes 54-18+6-2 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive.
Direct and inverse Variation 2007-04-03
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

What does inverse graph represent? 2007-03-30
From san:
what does inverse graph represent?
Is the inverse of a function always a function? 2007-03-29
From San:
Is the inverse of a function always a function? Please justify. Thank You!
A beam on a lighthouse 2007-03-28
From Lisa:
A beam on a lighthouse 2000 metres away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500 metres from P?
The angles in a right triangle 2007-03-28
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.

The foci of an ellipse 2007-03-27
I am trying to figure out how to find the foci of an ellipse x^2/7 + y^2/16 = 1. Since 16 is the largest denominator I know the major axis is going to be the y axis. Do I now take 7-c^2=16. c^2=16-7, c^2=9, c=3. So is my foci (0,+-3).
An inheritance problem 2007-03-23
From Carl:
A father of 3 boys, who owns 17 horses dies. He leaves his first son 1/2 of the horses. The sons hate each other. The father leaves the second son 1/3 of the horses. They are ready to kill each other. He leaves his youngest son 1/6 of the horses. Without cutting the horses into pieces how do they split the horses? I heard this puzzle when I was 12 years old. 1968 The preacher rides up on his horse and said "If I give you my horse will you quit fighting ? They agree to stop fighting?" Why?
Two consecutive odd numbers 2007-03-19
From Alicia:
The sum of two consecutive odd numbers is divisible by 4.

Can you make similar statements about the sum of three consecutive odd numbers and of four consecutive odd numbers? Generalize your findings.

I tried :
n= smallest odd number therefore the next = n, n+2 and the second =n+4 and the third = n+6 Now n+ n+2+n+4+n+6/4

Choosing numbers with no two consecutive 2007-03-15
From Meghan:
How many combinations are there of 3 numbers chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 but where no 2 of the 3 numbers are consecutive?

Thank you! -Meghan

A truncated cone 2007-03-10
From Russell:
Hello, I have attempted to use two of your answers already given and had no real success. This young lady is making a cat food dispenser using a truncated cone. The top of the cone as a diameter of 5 inches with a height of 6 1/2 inches and diameter of 3 inches for the bottom.

Could you please map out a solution for the both of us to understand? Thank you so much for your time and for this wonderful service.

Russell

Seven digit account numbers 2007-03-09
From Miranda:
Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!!
A circle is stretched horizontally by a factor of 2 2007-03-07
From bob:
I was wondering if you could double check my work?

the question is as follows:
The circle X^2+y^2-2x-3= 0 is stretched horizontally by a factor of 2 to obtain an ellipse what is the equation of this ellipse in general form?

Finding the vertical height of a roof 2007-03-05
From Zainab:
The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o
Direct and inverse variation 2007-03-03
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 ?

The intersection of two lines 2007-02-28
From Tamara:
I was told to make a graph to help solve this question. I was given two equations. One was x-2y=3 and the other was 2x+y=-4. We have to change it to the equation of the line format. Then we graph the line and find the point where they meet. I've been trying to do that, but when i check the answer, It turns out wrong. It's meeting in the wrong spot. I need help please.
Find the nth term 2007-02-27
From Dinky:
My teacher has set us a project, but i am having trouble finding the nth term for this. the numbers are: 1, 2, 6, 24, 120 could you please help me? thank you dinky113
Answered by Stephen La Rocque and Penny Nom.
Social security numbers 2007-02-27
From Tish:
Social Security numbers are in the form ###-##-####, where each symbol represents a number 0-9, how many are possible with this format? Will we ever run out of Social Security numbers?

(This is one question with two parts, I saw some examples but I am still confused because if there are 1 million possibilities then how have we been able to issue out numbers to over 280 US citizens?) (For the second part a yes or no answer is sufficient)

Cutting the top off a circle 2007-02-25
From Daniel:
If a circle as a diameter of D I cut off a straight part at C from the top What is the formula to find the area of the left over part?
Arithmetic Series 2007-02-18
From Krista:
Question- The sum of the first 4 terms of an arithmetic series is -8 and the sum of the first 5 terms is 500. Determine the sum of the 3 terms.
What is the index of the term '119' in the sequence 2, 5, 8, 11? 2007-02-16
From joey:
What is the index of the term '119' in the sequence 2, 5, 8, 11?
The nth term 2007-02-13
From Sarah:
The sum of a sequence 2007-02-11
From joey:
find the sum of the first 98 terms of the sequence 3, 5, 1, 3, 5, 1, 3,
Piecewise Functions 2007-02-09
From Steph:
h(x)={-2 if x<0
{x+1 if 0< x <10

Find the next 3 terms of the sequence 2007-02-07
From rose:
find the next 3 terms of the sequence 2,3,9,23,48,87
A triangle inscribed in a semicircle 2007-02-06
From Benneth:
Consider a triangle inscribed in a semicircle with a radius of R. What are th possible perimeters for the triagle? And the areas?
A 3-digit number in base 7 has its digits reversed when expressed in base 9. 2007-01-28
From Ashley:
A 3-digit number in base 7 has its digits reversed when expressed in base 9. Find this number.
The area of a ellipse 2007-01-25
From Ranjit:
I have a task in which i have to find the area of a ellipse. i find this difficult because i have only been provided with the perimeter, which is 1000m.
Line segments on dot paper 2007-01-21
From Khaori:
The three line segments below are drawn on centimeter dot paper.

a. Find the length of each segment to the nearest ten-thousandth of a centimeter.
b. Could these line segments be arranged to form a triangle? If no, explain why or why not. If yes, answer this question: could they form a right triangle? Explain why or why not.

5,8,11,14,17 2007-01-18
the sequence i was given was 5,8,11,14,17 what is the nth term and what is the 10th term ?
Points of intersection 2007-01-18
From Mark:
Find the points of intersection of the given pair of curves. 2x - 3y = -8 and 3x - 5y = -13
Answered by Steve La Rocque and Haley Ess.
An octagonal bird house 2007-01-13
From Soren:
I'm in the process of building a birdhouse that is an octagon (based on previous questions, looks like that's a familiar tune). The essential elements are known, but I get stuck when trying to determine the angle for the cuts that would be made to the thickness of the wood so that they all fit together when assembled. Each octagonal section is 7 inches in width and the peak of the roof will be 2 inches higher than the sides. My sense is that the angle cuts that need to be made to the 'height' of each piece of wood. By height I mean the thinnest part of the wood that is neither the length nor the width to use colloquial terms. While it's clear that a slight angle is needed, it would seem that the angle would necessarily change as the distance from the top of any one side to the peak changes. Please advise if more clarification is needed. The 2 inches is random and can be changed if more convenient. Whew!
What is the percent of the decrease? 2007-01-10
From Bill:
if the value of xyz company stock drops from \$25 per share to \$21 per share, what is the percent of the decrease?
Three consecutive odd integers 2007-01-08
From Emma:
Find three consecutive odd integers such that the sum of the first and second is 27 less than 3 times the third.
Twice the smaller of two consecutive integers is the larger increased by 5. 2007-01-08
From Evan:
Twice the smaller of two consecutive integers is the larger increased by 5. find the integers.
Answered by Stephen La Rocque and Penny Nom.
13.78g /11.3mL 2007-01-05
From Judd:
13.78g /11.3mL
How do I determine the length of an ellipse if the width and area are known? 2007-01-04
From Tom:
How do I determine the length of an ellipse if the width and area are known?
Answered by Steve La Rocque and Karen McIver.
An octagonal birdhouse 2006-12-30
From Verner:
I am building a octagon birdhouse,what degree would I cut each side of each piece of wood to assemble the birdhouse?
Percentage increase 2006-12-21
From Wang:
The last week of a month a car dealership sold 12 cars. A new sales promotion came out the first week of the next month and the sold 19 cars that week. What was the percent increase in sales from the last week of the previous month compared to the first week of the next month?
Find the total distance the swing traveled before it stopped. 2006-12-17
From Leah:
Rebecca's little sister liked for her to push her in the swing at the park. The other day Rebecca pulled the swing back and let it go. She would have kept pushing, but she suddenly saw a friend at the other end of the park. The swing traveled a total distance of 10 feet before heading back the other way. Each swing afterwards was only 80% as long as the previous one. Find the total distance the swing traveled before it stopped.
1, 3, 6, 10... 2006-12-15
From Lisa:
What is the nth term for the sequence, '1, 3, 6, 10...' and could you say how you got the anwser.
Answered by Stephen La Rocque and Penny Nom.
The nth term 2006-12-15
From Lisa:
I have worked out that the nth term for 1, 4, 9, 16 is n squared and 3, 5, 7, 9 is 2n - 1, so what is the rule for the sequence 1x3, 4x5, 9x7, 16x9?
The nth term 2006-12-14
From Hepzibah:
what is the definition of nth term and n?
Base 5 2006-12-11
From Shelley:
how do you convert decimal numbers to a given base for example 2,875 to base five?
Sectors of a circle 2006-11-30
From Maithreyi :
A circle of diameter 21m is divided into three sectors with central angles 60degree,120degree and 180degree. Find the area of each sector?
Percentage increase 2006-11-29
From Toya:
I have some statistics from year to year based on drug seizures.(units= lbs) e.g. in 2005 123lbs seized in 2006 1518lbs seized. now i worked out the percentage increase as to be in the thousands which from looking at the figures is correct however i don't want to say 1000% increase.

using another formula current- previous *100 I got 92%. what exactly does this 92% represent and how can i use this number when presenting my answers instead of using 1000 + %

Answered by Stephen La Rocque and Penny Nom.
An arithmetic series 2006-11-28
From Jillian:
Find the sum of 21 terms of an arithmetic series that has an eleventh term equal to 30.
A geometric sequence 2006-11-28
From Jillian:
Find x so that 2x, x + 5, x - 7 are consecutive terms of a geometric sequence.
A problem involving logs 2006-11-26
From Beth:
any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!!

log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4

Answered by Stephen La Rocque and Penny Nom.
Arithmetic with base -2 2006-11-26
From Yuva:
can we do arithmetic ,base -2. If yes, how and if not, why.
The area of a semicircle 2006-11-25
From Melinda:
If the radius of a semi-circle is 9ft what is the area?
Answered by Karen McIver and Penny Nom.
An Easement 2006-11-21
From Ms Porter:
I need to acquire a 20 feet easement for a project and I need to know how many square feet are in a 20 feet easement?
The Fibonacci sequence 2006-11-21
From Ross:
Let f0 = 0; f1 = 1,... be the Fibonacci sequence where for all n greater than or equal to 2 fn = fn-1 + fn-2. Let Q = (1+square root of 5)/2. Show that for all positive n greater than or equal to 0, fn less than or equal to Q^(n-1).
Conic sections 2006-11-19
From Joyce:
My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation.
On day 1 on which day will 96 students donate food? 2006-11-19
From Veydee:
during a canned food drive the number of students who donate food doubles each day. If three students donate food on day 1 on which day will 96 students donate food? we have to find the term rule for this pattern
Induction 2006-11-16
From John:
Find a formula for
1/(1x3)+1/(2x4)+1/(3x5)...+1/(n(n+2))
by examining the values of this expression for small values of n. Use mathematical induction to prove your result.

Sigma from 0 to infinity of (n^3 / 3^n) 2006-11-15
From Cedric:
I'm wondering how you would find if this series converges or diverges?

Sigma from 0 to infinity of (n^3 / 3^n)

Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then?

The empty set is a subset of every set 2006-11-14
From Narayana:
The empty set is a subset of every set
Answered by Stephen La Rocque and Penny Nom.
Some applications of conic sections 2006-11-13
From Burt:
how are circles, ellipses, and hyperbolas used in everyday life
Piecewise functions 2006-11-08
From Kait:
We discussed how to graph piecewise functions today and I'm very lost!! I'm sitting here staring at this problem that says:
f(x){2x+1, if x <1
f(x){-x+4, if x is greater than or equal to 1.

1,4,9,16,25,36..... 2006-11-06
From Teje:
i cannot find the next number for this sequence 1,4,9,16,25,36..... could u help please
From Caroline:
Can you tell me how to calculate a grade based on a percentage formula where 15 assignments account for 40% of the grade and 3 tests account for 60% of the semester grade.
Kilowatts and Horsepower 2006-11-03
From Michael:
How many Kilowatts=1 Horsepower or Horsepower=1 Kilowatt?
The sum of 2000 consecutive integers is 1000 2006-10-29
From Matias:
if the sum of 2000 consecutive integers is 1000, then the sum digits of the greatest of these 2000 integers is?
Three consecutive integers 2006-10-29
From Jimmy:
Basically i want to know how you prove that the product of any 3 consecutive integers is a multiple of 6
The real numbers with decimal representations consisting of all 1s. 2006-10-29
From Ivessa:
Determine if the following set is countable or uncountable : the real numbers with decimal representations consisting of all 1s.
Answered by Steve La Rocque and Walter Whiteley.
How many sequences are possible? 2006-10-28
From Sam:
A fair eight-faced die with faces numbered 1,2,3,4,5,6,7 and 8 is tossed six times and the sequence of numbers is recorded. How many sequences are possible?
Direct and Inverse variation 2006-10-27
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.

Three consecutive odd numbers 2006-10-21
From Pige:
The sum of three consecutive odd numbers is 387. Find the numbers.
A trillion seconds? 2006-10-16
From A student:
How many years, days, hours, minutes, and seconds in a trillion seconds?
Percentage increase 2006-10-15
From Amanpreet:
in yr 7, bill was 1.28 m tall, in yr 9 he was 1.67m tall. calculate his percentage increase in height
How many feet tall is the tunnel 2006-10-14
From Charles:
A tunnel in the Smoky Mountains is semicircular. At a distance of 12 feet from the center of the tunnel, the tunnel has a height of 16 feet. How many feet tall is the tunnel at its center?
Plotting percentage change 2006-10-11
From Beckie:
I have worked out a set of percentage differences which are all percentage decrease. Should i express them as a negative percentage as -20%? I also need to plot them on a graph and am not sure whether to just use the percentage difference as it is, in which case i get a positive gradient, or include a negative axis and plot them in this way, in which case i would get a negative gradient. I think the slope of the curve will be the same either way so it might not matter!
One-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5 2006-10-09
From Hina:
If one-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m.
Answered by Steve La Rocque and Claude Tardif.
The area of an oval 2006-10-08
From Bruce:
area of an oval: 60" x 120"
How many line segments are necessary? 2006-10-04
From Varun:
If you place 35 points on a piece of paper so that no three are collinear, how many line segments are necessary to connect each point to all the others?
A number pattern 2006-10-02
From Tim:

The patterns that went in 2s, 4s and 5s we got, but we are stuck on the pattern that doubles. We can't come up with the rule or equation that solves it.

With the first number being the term number and the second being the term, this is the pattern:

1-1
2-2
3-4
4-8
5-16
6-32
7-64
100-128

What is the rule for this?

Answered by Stephen La Rocque and Penny Nom.
The hypotenuse 2006-10-02
From Ashley:
How do you find the hypotenuse of a right triangle? I don't understand how to find c.
The focus of a parabola 2006-10-01
From Lily:
I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me?
2 5 11 17 23 31 ? 2006-09-28
From Bernice:
How do you determine the next number in the following sequence:
2 5 11 17 23 31 ?

Piecewise functions 2006-09-24
From Claudia:
hi! i was just looking at a question by someone else about piecewise functions, but i still don't get it.
my problem is
g(x){x+2 if x <-2}
g(x){2x - 1 if x> or = -2}

Find the nth term 2006-09-13
From Shakira:

my question is - Find an expression for the nth term of each sequence.

a. 6,15, 28, 45, 66

b, 1/5, 3/8, 5/13, 7/20, 6/29 - these are fractions

-5, 3, -2, 1, -1, 0, __, __ 2006-09-12
From Sherrie:
next two terms in the sequence: -5, 3, -2, 1, -1, 0, __, __
Brackets and more brackets 2006-08-29
From Michelle:
Feeling stupid asking but it's been awhile ... {{{2}}} ...what is this really saying ....are the outer brackets = null?
Points of intersection 2006-08-20
From Gianella:

Find the points of intersection by solving this problem analytically.

y= x cubed
y= x

Find the points of intersection 2006-08-18
From Ingrid:

The question says find the points of intersection of the graphs of the equation, and check your results analytically.

x squared + y squared=25
2x+ y=10

A concrete semicircle 2006-08-15
From John:
I have to figure out how many yards of concrete I need for a semicircle. I have a radius of 21 feet and the concrete is 4" thick. I took 3.14 x (21)^2 then divided by 40 to get how many yards of concrete but that doesn't seem right.
Marking out a circle 2006-06-28
From Peter:
given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius.
Answered by Stephen La Rocque and Penny Nom.
The area of a house 2006-06-28
From Michael:
I would like to know how to measure the area of a house?
The area of a sector and a triangle 2006-06-23
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.
As close to 841 as possible 2006-06-21
From Alan:
using these numbers by either add subtract division multiply come up with the answer as close to 841
100 25 10 7 6 3

13 57 91 11 31 51 ?? 2006-06-15
From Chastity:
im trying to determine the missing number in the sequence 13 57 91 11 31 51 ??
Answered by Claude Tardif, Steve La Rocque and Natasha Glydon.
The perimeter of a pool 2006-06-05
From Troy:
How many Linear feet would a pool be if the pool was 18 by 38 foot oval
What is the value of csc (-2pi/3)? 2006-06-04
From Kishor:
What is the value of csc (-2pi/3)?
What is the sum of the first 100 whole numbers? 2006-05-31
From Jo:
what is the sum of the first 100 whole numbers?
Answered by Natasha Glydon, Paul Betts and Penny Nom.
The area of part of a circle 2006-05-29
From Larry:
need to find area of a circle between a given line (cord) to the circumference of the circle (see attachment). I often review blue prints of homes and many times have to know the area the home.
Answered by Stephen La Rocque and Penny Nom.
The nth term of a sequence 2006-05-24
From A student:
please could you give me a formula for the following numbers for my teacher 3 8 15 24 35
Three purses 2006-05-22
From Marcee:
If you take \$20 from the first and put it into the second of three purses, the second would then contain 4 times as much as remains in the first. If \$60 of what is now in the second is put into the third, the third will contain twice what is in the first and second together. Now, if \$40 be removed from the third and put into the first, there will be half as much as in the third. What did each purse originally hold?
We are 2 pairs of consecutive 2 digit numbers ... 2006-05-13
From A perent:
We are 2 pairs of consecutive 2 digit numbers that are factors of the number of feet in a mile. Who are we?
A person is given 3 true or false questions 2006-05-11
From Larry:
A person is given 3 true or false questions. They have no idea of the answers. What is the probability of the person getting them all correct? Could you show me a tree for this.
Small pipes and large pipes 2006-05-09
From geece:
A large fresh water reservoir has two types of drainage system. Small pipes and large pipes. 6 large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir?
From Lisa:
When I have a total that is the sum of consecutive numbers, how do I figure out what the numbers are?
Geometric sequence and basic functions (graphs) 2006-04-20
From Marlene:
Which of the basic functions is related to the geometric sequence: Linear, Quadratic, Rational, or Exponential? Can you give me an example of how it would be used in normal life?
Arithmetic and Geometric Sequences 2006-04-19
From Skye:
If the 1st, 4th, and 8th terms of an arithmetic sequence are consecutive terms in a geometric sequence, find the common ratio of the geometric sequence.
Reverse percentage 2006-04-19
From Mike:
How would I calculate a reverse percentage? Let me give you an example. I have two values that calculate to a success rate of 93.32. Total=1546051 Failures=103302. (1546051-103302)/1546051=93.32% success. Now how much would I need to increase the total value to get the success up to 95%?
Overlapping area of two circles 2006-04-15
Given two identical circles where the radius (6 units) is the distance between the centers, what is the area of the overlapping region?
What is the cost price? 2006-04-14
From Purushotham:
If the selling price is 120 and the profit is 20%, what is the cost price?
The product of successive terms in sequences 2006-04-13
From Forrest:
1) Find three successive terms in an arithmetic sequence such that their sum is 24 and their product is 440 2) Find three successive terms in a geometric sequence such that their sum is 21 and their product is 216
Finding the inverse of a function 2006-04-12
From Sam:
If g(x) = 2x+3/5 then how do I find the inverse?
Arithmetic Sums 2006-04-12
From Angel:
(a) In a particular arithmetic sequence, u6 = 344.5 and u20 = 88.3. Find S28. (b) In a particular arithmetic series, S10 = 495 and S15 = 1005. Express S15 in sigma notation.
Sum of a Geometric Sequence 2006-04-11
From Andre:
In a particular geometric sequence, U3=-3.6 and U10=12.9. Find S16 and S17.
A plant increases its height by 1/2 the first day,... 2006-03-30
From Andy:
A plant increases its height by 1/2 the first day, 1/3 the second day, 1/4 the third day and so on. How many days did it take to grow to 100 times its height?
Can an equilateral triangle have an obtuse angle? 2006-03-26
From Chris:
Can an equilateral triangle have an obtuse angle?

I'm thinking not, because all sides must be equal, but
does that also imply that all angles are equal?

The cartesian product of a countably infinite collection of countably infinite sets 2006-03-25
From Geetha:
Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite?
How much fabric do I need? 2006-03-25
From Michelle:

I AM DECORATING A STAGE FOR A BOARD OF DIRECTORS MEETING AND I NEED TO BUY FABRIC AND I DON’T WANT TO WASTE \$\$ BY BUYING TOO MUCH FABRIC OR NOT ENOUGH FABRIC.

THE AREA THAT I’M NEEDING MATERIAL FOR IS, 12ft HIGH BY 34ft WIDE.

THE FABRIC COMES IN ROLLS OF 60” (inches) x 100 yards.

SO HOW MUCH FABRIC SHOULD I NEED TO FOR THE AREA I’M WANTING TO COVER?

Answered by Stephen La Rocque and Penny Nom.
Piecewise functions 2006-03-21
From Kris:
First Problem:
Southeast Electric charges .09 cents per kilowatt-hour for the first 200 kWh.The company charges .11 cents per kilowatt-hour for all electrical usage in excess of 200 kWh. How many kilowatt-hours were used if a monthly electric bill was \$57.06? The answer I came up with is 360, is that right? and also how do I set it up in an equation form?

Second Problem:
A construction worker earned \$17 per hour for the first 40 hr of work and \$25.50 per hour for work in excess of 40 hr. One week she earned \$896.75. How much overtime did she work? I came up with 8.5 hrs over-time worked. Again I don't know how to set up the equation to come up with the answer.

I need some pointers on how to figure out story problems! If you have any suggestions that would help me out I would be very grateful.

How far from Earth is Neptune? 2006-03-21
From Scott:
A laser beam travelling at the speed of light bounces off the planet Neptune and returns to Earth in 29 960.72 s. The speed of light is 299 792.5 km/s. How far from Earth is Neptune?
The square footage of an area in my backyard 2006-03-17
From Kim:
I need to find out how to calculate the square footage of an area in my backyard that is in the shape of a "slice of pie". There are two sides that are straight lines that come together at the top to form a point, and then at the bottom is a curved line that joins the two other lines together. I need to figure out how to calculate the square footage that is inside the area.
Divide the product of three consecutive positive integers by their mean 2006-03-12
From Sandy:
When I divided the product of three consecutive positive integers by their mean, I got 99. What is the smallest of the three numbers?
Two consecutive even integers 2006-03-11
From Cheryl:
Find two consecutive even integers that have a sum of 450
How many of these cubes have no wax of them? 2006-03-10
From Iban:
cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm. How many of these cubes have no wax of them?
8,_,4,9,1,_,10,3,_,0 2006-03-08
From Rachel:
I cant figure out this sequence if someone could help me 8,_,4,9,1,_,10,3,_,0
A nine digit number 2006-03-06
From Ryan:
What is the total number of possible combinations of a nine digit number (ie., social security number) including repeating numbers?
Answered by Stephen La Rocque and Penny Nom.
2,4,9,6,5,6,____,____,____,... 2006-03-06
From Mike:
I am having problems figuring out the following sequence:

2,4,9,6,5,6,____,____,____,...

We were able to guess that the pattern simply started to reverse itself, but I was wondering if there were other possibilities.

The nth term 2006-03-05
From Umar:
my question is what is the nth term for a house of cards 4 stories high if you use the following numbers:
2 7 15 26

A 5900% increase 2006-03-03
From Pat:
I want to find out the % of production increase from 250 dolls a month to 15,000 dolls a month. i think it is 5900% but that seems too high.
A cone with an oval as base 2006-03-01
From Richard:
I am trying to find the volume of a cone that is not round but oval.
Luke and Slim have only one horse. 2006-02-26
From Emily:
Luke and Slim have only one horse. Luke rides for the agreed on distance and then ties up the horse for Slim, who has been walking. Meanwhile, Luke walks on ahead. They alternate walking and riding. If they walk 4 miles per hour, and ride 12 miles per hour, what part of the time is the horse resting?
The nth term of a sequence 2006-02-21
From Mike:
I'm having trouble finding the nth term in an equation, can you help me?
Percent gain 2006-02-14
From Bill:
If a stock is bought at \$3.50 and sold at \$5.80, what percent was the gain?
Base pi 2006-02-13
From Joe:
How would you convert the number 10 from the decimal system of numeration (base 10) into a system of numeration of base pi.
Find two consecutive integers whose product is 182 2006-02-09
From Anthony:
Find two consecutive integers whose product is 182
The intersection of a line and a circle 2006-02-02
From Bernice:
if i am given an equation of a circle and 2 points in a line how do i know if the line intersects the circle and how do i determine the points of intersection
Arithmetic progressions 2006-01-31
From A student:
1)the sum to n terms of a particular series is given by Sn=17n-3n2

a)find an expression for the n term of the series
b)show that the series is an arithmetic progression

2)a particular arithmetic progression has a positive common difference and is such that for any three adjacent terms ,three times the sum of their squares exceeds the square of their sum is 375.Find the common difference

An array problem 2006-01-31
From Cynthia:

Write a number sentence for this array........

It's a rectangle box 3 down and 4 wide.

Percentage increase in sound intensity 2006-01-29
From David:
I am doing some emotion response mapping. Being a composer I know how to push the heart beat tempo by a % increase of BPM in my music. I want to know how to calculate an increase in intensity of sound. Now I have 60 decibels. I want an increase of intensity by a factor n% with out going over 156 decibels.
how can i find the height of a triangle if i have the base and the hypotenuse 2006-01-27
From Kelsey:
how can i find the height of a triangle if i have the base and the hypotenuse
Sectors and arcs 2006-01-25
From Wael:
How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived?

Finding the nth term in fractions 2006-01-23
From Zarina:
Each term in this sequence is made by increasing the numerator by 1 and the denominator by 3. here are the first five terms:

1/4, 2/7, 3/10, 4/13, 5/16, ...

(a) write an expression for the nth term:

A sequence of circles and tangents 2006-01-16
From Paul:
Consider a circle whose center is (2,2) and whose radius is 1, and the straight line that goes through the origin and that is tangent to this circle so that the intersection between them is as shown in the attached picture. With this new point we make a new circle whose radius is half of the first one, and we calculate the corresponding intersection point with the same suppositions as in the first case. We repeat the process to the infinite. Find the distance between the center of the circle in the infinite and the origin (point (0,0)).
Percentage change when you start from zero 2006-01-02
From Joseph:
I am not sure if my meaning for calculation for a percent change (C-P/P)x100) is correct. In this case, C=10, P=0, does this mean 100 percent increase from previous period?
The area of a sector of a circle 2006-01-02
From Natashia:
How do you find the area of a shaded sector of a circle?
Joey had 8 drinking glasses, all of different sizes. 2005-12-29
From Danielle:
Joey had 8 drinking glasses, all of different sizes. he has lined them up from smallest to largest and numbered them #1 (smallest) to #8 (largest). he knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold!

He experiments by filling up different glasses with water and pouring the water back and forth into other glasses. Her are his results:

Percent change 2005-12-17
From Marie:
What is the percentage change when 1500 becomes 2000?
Percentage increase 2005-12-15
From Luiz:
I would like to know how much net income in % we have increased from 2005 to a 2006(projection).
2005 Net Income Actual: \$1,599,887
2006 Net Income Budgeted: \$2,067,339

Find the nth term 2005-12-14
From Kevin:
How do i find the nth term of 1 4 9 16 25 36
The stair problem 2005-12-06
From Arnold:

My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?

1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations

An Arithmetic sequence 2005-12-01
From Aana:

The first term in an arihmetic series is 25 and the 3rd term is 19. Find the number of terms in the series if its is 82.

Here's what I did to find d
a+2d=19; 25+2d= 19 ;19-25=2d d=-6/2=-3

This is where I'm stuck. Can you please provide me with some guidance.

The sum of n consecutive integers 2005-11-27
From Craig:

If 875 is expressed as the sum of n consecutive integers (n > 1), then the number
of possible values of n is?

A) 15
B) 8
C) 7
D) 16
E) 4

Notation for the second derivative 2005-11-08
From Mussawar:
my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x.
How many passengers boarded the plane in Phoenix? 2005-11-03
From Vish:
Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix?
A tangent to a parabola 2005-11-02
From A student:
Find the point on the curve y=x2 where the tangent to the curve is parallel to the secant line connecting (-1,1) and (2,4)
2, 6, 12, 20, 30, ... 2005-11-01
From Rebecca:
I have a sequence of I have a sequence of 2, 6, 12, 20, 30, and have no idea how to figure out the nth term please help!
The area of an irregular semi-circle 2005-10-14
From Bob:
Is there a way to compute the area of an irregular semi-circle i.e. one in which the arc length is not determined by the diameter; and is therefore not technically any part circular - yet still possessing an arched side?
Calculer la clé 2005-09-29
From Un eleve:
Chaque individu a un numéro INSEE de 13 chiffres auquels est adjointe une clé de deux chiffres. voici comment est calculée cette clé :
Open dots and closed dots 2005-09-29
From Cynthia:
When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot?
Find the next 5 terms 2005-09-24
From Grant:
n+7, 2n-0.5, 4n. Find the next 5 terms of each one and explain the sequence in words
Converting from base ten to base five 2005-09-21
From Julie:
My sister is home schooled and we are trying to convert from base 10 to base 5. We are trying to teach and we have never had this in school. If we could have some examples of some problems and how to do them we would appreciate this.
Percentage increase 2005-09-19
From Dory:
Last year sales was 120,000 \$ and this year sales is 280,000 \$, there was an increase in sales. what I would like to know is the percentage increase between the years with the formula.
A 3-dimensional pie shape 2005-09-17
From Bill:
Your site appeared in my search for the name of a 3-dimensional pie shape. 2-d would be a sector of a circle. As it it curved, I don't believe it is in a the polyhedra family. Can you help me find the mathematical term for it?
Find the first five terms of this sequence? 2005-09-17
my homework says can you find the first five terms of this sequence? 5n-6 i can`t figure it out.
Elliptic trigonometry 2005-09-15
From Krystal:
I'm currently searching for a science project topic and i have the idea of deriving elliptic trigonometry analogous to circular trigonometry. My questions are: Is this project "possible" to do?
Answered by Chris Fisher and Harley Weston.
A piecewise function 2005-09-15
From Duncan:
A child is assigned to your care and she has a headache. The parent has authorized the administration of Children's Tylenol. Read a box of Children's Tylenol (or any other similar drug) and find the directions for administration. Note the child's weight and the corresponding dosage. (Be sure the drug you choose has a minimum of 4 weight intervals.)
Finding the nth term 2005-09-12
From Paul:

Hi , Im having a problem helping my daughter to find the Nth Term in the following sequences.

1/3 1/2 3/5 2/3

and

1 3 6 10

The sum of a series 2005-08-31
From Aamod:
Find the sum of the given series till n terms:

(14\1*3) + (24\3*5) + (34\5*7)............... till n terms

1,4,9,1,6,2,5,3,6,4,9,6,4,8,1 2005-08-30
From Liz:
Find the next four numbers to the sequence 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,___,___,___,___.
cos x * cos 2x * cos 4x * cos 8x 2005-08-29
From Leandro:

A = cos x * cos 2x * cos 4x * cos 8x

What's the value of log A at base 2?

Answered by Chris Fisher and Penny Nom.
y = log(x) + x. Solve for x. 2005-08-26
From Alain:

I have the following equation:

y = ln(x) + x

How do I solve for x?

Is this percentage change or percentage increase? 2005-08-15
From Betty:
When calculating a percentage, if the formula is A(new) - B(old)/A(new) Is this percentage change or percentage increase?
The Maclaurin series generated by f(x)=x^ cosx + 1 2005-08-10
From Latto:
f(x)=x3·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
The equation of an ellipse 2005-07-17
From Allan:
I working on a problem that asks me to give the equation of an ellipse when only the location of the directrix and the length of the latus rectum are given. No other points on the ellipse are given. Again, the only "givens" are:

Length of latus rectum = 12
Location of directrix is x = 16

If I could determine the eccentricity, I could proceed from there by taking the ratio of the distance from a focus to the latus rectum point to the distance of the point from the directrix, but I lack the x coordinate of c. I've searched the text, and feel I've "missed something" somewhere! I note that the latus rectum segment is unique in one respect in that it is parallel to the directrix, where any other line segment on the ellipse to the focus would not be. Please indicate where I'm going wrong.

A lighthouse is located on a small island,... 2005-07-14
From Brittnee:
A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
Percent change 2005-07-01
From Betty:
Can you tell me the difference between Percentage Change, Percentage Increase, Percentage Difference and please give an example of each, I am very visual.
A geometric sequence 2005-06-21
From A student:

The first three terms of a geometric series are 3(q+5), 3(q+3), (q+7) respectively.
Calulate the value of q.

The circumference of an oval pool 2005-05-18
From John:
I have an oval pool of which I am trying to find the circumference. it is 38 feet long and 19 feet wide
Angle of incline 2005-05-15
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?
From Yas:
i need some help with my work which is to investigating sums of consecutive numbers for example: 15= 4+5+6 and 15=1+2+3+4+5
A 5% increase 2005-04-27
From Debra:
How can I determine the increased percentage of a dollar amount? I.e.: One dollar amount is \$202 and another is \$150, how can I determine the 5% increase from last year on the \$202 dollar amount?
The least integer of a set of consecutive integers 2005-04-19
From Lucia:
The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in the set?
Percentage increase 2005-04-19
From Tom:
What is the percentage increase from (negative -\$9262.00) to (positive \$3840.00)?
A Taylor series for ln(x) 2005-04-16
From Anood:
i have to represent ln(x) as a power series about 2

i`m not getting the final answer which is ln 2+ sigma (((-1)(n+1)/ (n*2n))*(x-2)n). i don`t get the ln 2 part

i show you my trial

f(x)= ln x.

f-(x)=(1/x) .

f--(x)= (-1/x2)*1/2!

f---(x)= (2/x3)*1/3!

f----(x)= (-6/x4)* 1/4!

so the pattern shows me that f(n)= ((-1)(n+1))/xn *n)

so f(2)= sigma ((-1)(n+1))/2n *n) *(x-2)n

so as you see i don`t get ln 2

Two overlapping circles 2005-03-20
From Safi:
I have a problem to calculate the area of two overlapping circles because two circles are overlap then how i calculate the overlap area to subtract from the area of both circle.
Dimensions of a roof 2005-03-18
From A roofer?:
A right triangle (roof of a house) has a base of 7 feet and a 22 degree angle. What is the height of the roof and what is the hypothenus of the triangle.
Biodiesel 2005-03-08
From William:
My son is doing an demonstration for science class about how to make biodiesel. we are having problems with the conversion. for instance we think there are approx 190 liters in 50 gallons. Is this correct? Also if you needed 3.5 grams of lye per liter, would that be 662g of lye.
Spraying roses 2005-03-03
From A student:
A litre and a half of water has 0.045 grams of herbicide added for spraying roses. How many grams of herbicide per litre is this?
Reverse pecentage 2005-03-01
From Nathan:
Question for you. If I have spent \$10.00, what is the mathamatical equation to
figure out what the G.S.T (7%) was?

Also if I were to spend \$80.00 on a hotel, and I would like to know how much

A countably infinite collection of countably infinite sets 2005-02-26
From Feroz:
Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set?
Each interior angle of a particular polygon is an obtuse angle... 2005-02-22
From Victoria:
Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?
arcsech x 2005-02-10
From Monica:
Prove that arcsech x = ln[(1 + (1-x2)(1/2)) / x ]
A seating arrangement 2005-02-03
From Kay:
If you have 5 married couples, how many arrangements can be made if they must sit across from each other?
A line segment connecting two vertices of a polygon 2005-02-02
From James:
What is a line segment (not a side) connecting two vertices of a polygon called?
Sum to n terms of the series i.(2^(n-i)) 2005-01-28
From Satya:
Sum to n terms of the series i.(2n-i)
From Usman:
Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and e-mailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject.
An elliptical table 2005-01-03
From Roger:
Want to make an elliptical table, say the long (major) axis is 4 feet, and the short (minor) axis is 3 feet. I can construct this figure, but I'm trying to figure out what the exact dimension of a rectangle within this ellipse will be if I make the table a drop leaf type where the drop dimensions are equal for each end of both the long and short axes. Intuitively, it looks like there is one and only one solution.
A line from the center of the patch to the periphery 2005-01-01
From Sandrine:
I am currently researching a patch disease of grasses. These patches are roughly circular. I need a term for a line from the center of the patch to the periphery. Since the patches are not perfectly circular, my supervisors tell me I cannot use the word 'radius'. What else could I use?
Answered by Denis Hanson and Harley Weston.
An arithmetic progression 2004-12-24
From A student:
the 4th and 5th term of an arithmetic progration 47 and 52 respactively find
a)d
b)a1
c)a50

Irrigation and a sector of a circle 2004-12-23
From Chuck:
A friend of mine is a farmer and uses Pivots to irrigate portions of his land. The crop rows are in straight lines that all form chords of a large circle. The intent is to determine area between any two "boundary" rows expressed in acres.
The gradiant of a hill is 9% 2004-12-18
From Jim:
The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees?
Two intersecting lines 2004-12-18
From James:
Imagine a vertical line 1.107' tall. Leaving the top of this line, sloping down to the right at a 4:1, at what horizontal distance will the line strike a second line, which leaves the the bottom of the vertical line sloping down to the right at a rate of .02 ft/ft (or 2%)? There is a fairly easy solution to this, but I have lost my notes!
A sequence 2004-12-11
From Amanda:
Find the nth term of the following sequence

4, 10, 28, 82

Geometric sequence 2004-12-04
From Lesa:
Find a formula for the geometric sequence: (√3 - √2), (4 - √6), (6√3 - 2√2), …
Cost before the markup 2004-11-23
From Norman:
the sum of eg \$130 includes the markup of 30%. However I need to calculate the percentage to apply to the \$130 to assess the cost ie \$100.
Proof by induction 2004-11-20
From Vic:
Problem: Find the first 4 terms and the nth term of the infinite sequence defined recursively as follows:

a(1) = 3 and a(k+1) = 2a(k) for k -> 1.

Note: Quantities in brackets are subscripts
-> means 'equal to or greater than'.

Using the recursive formula, the first 4 terms are; a(1) = 3, a(2) = 6, a(3) = 12, a(4) = 24

The nth term a(n) = 2n-1 x 3 (equation 1)

Equation 1 must be proven using mathematical induction. This is where I am having a problem.

A sequence 2004-11-19
From Liucy:
Find the Nth term: 10 40 90 160 250
A 40% reduction 2004-11-10
From Cathy:
I'm having trouble figuring out how to figure a percentage??? it's easy to find what 40% of any given number is, but how would i accurately figure out what is the final number is when i know the number after the 40% has been removed? when i add 40% to this number it obviously is lower than it should be. the best i could figure is; x=?-40% ---------------> x-?=-40% i'm all confused????
The points of intersection of two graphs 2004-11-05
From Benjamin:
How do I find the points of intersection of the two functions:
1) y =
2 - e-x 2) y = 1 + x2

A 40% increase in garage space 2004-10-20
From Dianna:
A bus company recently expanded and no longer has enough room in its garage for all of its buses. Twelve of the buses have to be stored outside. If the company decides to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company own?
The third derivative 2004-10-15
From Holly:
Why would you ever take the third derivative?
Direct and inverse variation 2004-10-05
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
1,3,6,11,18,29,__ 2004-09-21
From Guillermo:
How do you get to the answer of this sequence 1,3,6,11,18,29,__
f(x) = x-4 if x<2 2004-09-21
From Dani:
Hi, my name is Dani. I'm in tenth grade Algebra 2, and I'm learning about a lot of different kinds of functions, and I can't quite seem to understand how every part of the piecewise function works. I understand most of it, I think, but I've been looking at an example in my math book, and I'm not sure how they got the answer they did. The part I don't understand reads: "Graph f(x) = x-4 if x<2" and "Identify the domain and range." The picture in the book shows an open circle at (2,-2), with an arrow going down and to the left with the slope being one. How did they get the open circle to be at (2,-2), and why does the arrow point where it does?
B={A,{A}} 2004-09-20
Let A be a set and let B = {A,{A}}.

(a) Explain the elements of set B (with some example)

(b) Prove that A is not a subset of B.

The hypotenuse of a right triangle 2004-09-20
From Shannon:
I am trying to find the hypotenuse of a right triangle with only the length of the opposite side. What is the formula as I don't have the length of the adjacent side? Can I compute it without knowing what the other two angles are?
Perimeter and area of a semi_circle 2004-09-18
From A student:
I want to know how to find the perimeter and area of a semi-circle and a quarter-circle.
A challenge 2004-09-17
From Lasse:
xy
xx
xyx
xxx
xyxx

"x" and "y" each represents a number. Find out the system to make the next line

The length of a cut 2004-09-17
From Florita:
My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures: a=4squared, b=6squared.

She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square".

1+3+5+...+(2n+1) 2004-09-10
From Emma:
Prove that 1+3+5+...+(2n+1)= (n+1)2
An inverse 2004-09-09
From Hillary:
I cannot figure out the inverse of this function.
f(x)= 1/2x -1

The nth term 2004-09-08
From Alex:
What is the nth term?... Like what is it?, How do I find it?, and how exactly is used?...
d varies inversely with g 2004-09-07
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).
The intersection of planes 2004-09-07
From Joshua:
I was wondering about the intersection of planes. Can planes intersect?
Nine minutes 2004-09-02
From A student:
You have two hour glasses-one measures 7 minutes and one measures 4 minutes.How can you time 9 minutes?
The radius of a circle 2004-08-24
From Peter:
If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius?
The series from i=1 to n :ai 2004-08-18
From Ken:
a.) Explain the difference between
the series from i=1 to n :ai
and the series j=1 to n :aj

b.) Explain the difference between
the series from i=1 to n:ai
and the series from i=1 to n :aj

The intersection of two graphs 2004-07-28
From JJ:
Is there a way to find the intersections of these graphs algebraically?

x^2 + y = 4 & 2x - y = 1

I got (1.45, 1.9) and (-3.45, -7.9) with a graphing calculator.

AND THESE...

y = 3.29x & y = 5.5(x^0.5)+ 10000

I got x at 3133 with a graphing calculator.

The railing around a pool 2004-07-26
From Bob:
I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun.
The inverse of a quintic function 2004-07-22
From A student:
I'm really having trouble finding out the inverse of this quintic equation. F(X)= X5+3X3+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.
The number of blocks in a mile 2004-07-18
From Valerie:
I don't know if you can help me but I was wondering how many blocks are in a mile in Ocean City, New Jersey?
Two puzzles 2004-07-13
From Fred:
A young man's car developed a flat tire while he was driving along a deserted street. He pulled over to the curb and did all the usual things; removed the hub cap; unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them rolled down a nearby grate. Peering through the bars of the grate the man thought he could see the lugs about 6 feet below in a shallow water puddle. He had a problem, how do you think he solved it?

It is noon, your lunch hour, but you can not go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine the sun will be shining in 36 hours? Justify your answer.

An Octagonal playhouse 2004-07-13
From Levi:
I'm building an octagon playhouse for my son that is 8 feet wide. what would be the measurements of each of the eight sides.
Choosing 5 numbers from 1,...,36 2004-06-30
From A lottery player?:
how many combinations are there for the numbers 1thru 36 when only using each number once in groups of five
Jack's social security number 2004-06-08
From A student:
Jack's social security number contains each of the nonzero digits exactly once. By examining the digits from left to right, he also found that 1 divides the first digit evenly, 2 divides the sum of the first two digirs evenly, 3 divides the sum of the first three digits evenly, and so on, until 9 divides the sum of all the digits evenly. What is Jack's social security number?
The base of a triangle 2004-05-25
From Ralph:
With a 30 degree angle at the top of a triangle and a height of 15 what is the base?
Programming without trig functions 2004-05-25
From Derek:
I am a programmer trying to calculate the following.

What is the formula to find the cross-sectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?

I am using a PLC (programmable logic controller) to do this and trig functions are not available.

Setting up an equation 2004-04-30
From Matt:
I am trying to determine the dimensions of a 22 megapixel digital camera chip that has a 3:2 ratio. We know then, that: 3x = 2y (or 1.5x = y)

and that

xy = 22

Beyond this, I don't know how to hook those 2 seemingly unrelated facts together.

The sum of 4,0,-4..., -156 2004-04-28
From Christina:
find the requested sum of the arithmetic sequence

4,0,-4..., -156

Related rates and baseball 2004-04-26
From Bethany:
A baseball diamond is the shape of a square with sides 90 feet long. A player running from second to third base at a speed of 28 feet/ second is 30 feet from second base. At what rate is the player's distance from home plate changing?
A geometric sequence 2004-04-13
From Michael:
In a geometric series, the sum of the 2nd and 3rd terms is 60, and the sum of the 3rd and 4th terms is 240. Find the sum of the first 7 terms.
What is the nth term 2004-04-07
From Jason:
1 4 10 20 35 56 84
what is the nth term

Trisecting an arbitrary angle 2004-04-06
From Joe:
Where can I submit my effort on trisecting an arbitrary angle with only a straightedge and a compass? I can do it but I do not have the smarts to prove it.S
The intersection of two graphs 2004-03-31
From Benjanim:
How do I find the points of intersection of the two functions:

1) y = 2 - (e^-x)
2) y = 1 + (x^2)

I know that I have to set them equal to each other, but I can't solve for x. Please help :-)

The degree sequence of a graph 2004-03-31
From Ali:
How can i find out {6,6,5,5,5,3,2}is not the sequence of the points of a simple graph,without drawing it?
Sections, area and acres 2004-03-23
From Tony:
An acre , it can be any size right . so when they refer to a section of a township which is 640 acres, also 1 square mile does this mean that 1 sections length if sqaure and there is 5,280 ft in 1 mile does it meanthat if you took 1 side of the square of of 4 sides the lenth would be 5,280 feet long and by multiplying 5,280 x 5,280 it would give you the square mile in square feet. i guess what I 'm asking is what is the perimeter of 1 acre if it was shape like a square. sorry to make this confusing but if you can help I would appreciate it.
What's the next term? 2004-03-22
From Garrett:

A friend hit me with these questions and won't tell me the answer nor how... please help? I've racked my brain and did all sorts of formulas, but I can't get it to work out... please...

What's the next number in this series... 5, 12, 17, 29, 46, ?

And this series... 12, 19, 28, 39, 52, 67, ?

and these... ocoa, boco, oboc, dobo, odob, ?

Baseball games 2004-03-14
From Fabian:
Let's say I have 12 different Baseball games. There is one of only 2 possible outcomes for each of the 12 games. How would I fugure out how many combinations there are for the 12 games and for 11,10, and so fourth.
Equivalent sets 2004-03-06
From A student:
If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ?
Cosine of 35 degrees 2004-03-03
From Jason:
How do you find the exact solution to cosine 35 degrees.
An elliptic cone 2004-02-24
From Ben:

I am building a model for my architecture class. I need to build a elliptic cone out of chipboard and i have no idea how to do this.

The cone needs to be 20in tall and the ellipse has a max radius of 10in and a min radius of 8in.

So my question is how do i lay this out on a piece of paper so that i can form the cone after i cut it out.

A worm crawling home 2004-02-18
From Cindy:
A worm is crawling to his home which is one meter away. The longer he crawls the weaker he gets and the less he can crawl the next day. If he crawls within 1/3000 of a meter of his home, he will find food. He must eat within twelve days. The first day he crawls 1/2 meter. The second day he crawls 1/4 meter. The third day he crawls 1/8 of meter. This pattern continues for twelve days. Make a Chart that shows the distance he has covered at the end of each day and the total he has covered at the end of each day. Does he make it to the Food in time?
Geometric sequences 2004-02-03
From Alan:
hello, I am a junior in precalculus. we started working on geometric sequences today, it makes perfect sense on how it works. but why is it called that? if you could send me an answer to why geometric sequences have that name, I would be much appreciative.
Intersecting a line and a curve 2004-01-29
From Senthil:
between line and curve how can i find intersection point? could you write me the formula and explanation also sir.
Sets 2004-01-27
From Susan:
My child has the following problems to solve, and we are puzzled. 1. Compare the subset symbols to the inequality symbols of less than or greater than.

2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C?

A problem with sets 2004-01-20
From Jason:

Given that the universal set S is the set of all sports fans, and

F={x|x is a football fan}
H={x|x is a hockey fan}
a)Describe (F^B)' (f intersect b)' in words
b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans.

The product of any n consecutive integers 2004-01-18
From Fazia:
I have to prove that the product of any n consecutive integers is divisible by n!(eg:the product of five consecutive integers is divisible by 5!) It's easy enough to plug in numbers and prove it is true, but i'm finding it difficult to come up with a proper proof.
Two consecutive negative integers 2004-01-17
From Amanda:
Find two consecutive negative intergers whose product is 182.
37 with four 4'2 2004-01-03
From Myra:
Using four fours and only four fours to get an answer of 37.
Percent increase 2003-12-24
From Frank:
How does one figure the percent of increase or decrease in the cost of an item?
An elliptical race track 2003-12-16
From Judy:
the inner rail of a race track is a perfect ellipse. the track is a standard width all the way around. how can i prove that the outer rail is a ellipse?
Finding angles 2003-12-02
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.
A point and a line 2003-11-19
From Meenakshi:

Given a line segment L(x1,y1) to (x2,y2) and a Point P(x3,y3).
I need the formula to find a point on the line L that is closest to the point (x3,y3).

The 4th difference 2003-11-17
From Jack:
If i had a sequence which was the same at the 4th difference, aka difference to the 4th, like:

1 5 14 30 56 96 (sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1

then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an4+bn3+cn2+dn+e

Divisibility by 7 2003-11-14
From A student:
how do you test a number to see if it is divisible by 7 or not?
root24 = 2 root6 2003-11-13
From Burke:
I know that all algerbra can be represented visually, for example: Y=9x+3 is a line on a two dimentional plane. Could Math Central please send me a visual representation of the proccess of simplifying square root like root24 equals 2root6
Chisenbop 2003-11-06
From Jaclyn:
Hi there i was wondering if you would have any information on "counting on your fingers" or " Chisabop".
Knitting gauge and felting 2003-10-27
From Sara:

I wish to create a pattern to knit an item that will then be felted, thus, shrink as a result. In order to determine the proper gauge to use in creating the item, I produced a gauge swatch, noted the original properties and then the post-felting properties. They are as follow:

Before Felting:

20 stitches(width) x 20 rows(height)yielded:
Gauge: 3.2 stitches(width) and 4 rows(height) = 1"
Dimensions: 6.25"(width) x 5.25"(height)

After Felting:

20 stitches(width) x 20 rows(height)
Dimensions: 4"(width) x 3"(height)

How do I calculate the percentage change in size to accurately determine the number of stitches and rows needed to produce the desired dimensions for the finished (felted) item?

From Jimmy:

From 1989 to 1990, the population of Nevada increased b y 157,000, and that of Maine increased by 30,000. In 1990, the population of Nevada was 1,206,152, and that of Maine was 1,233,223. If the populations of the two states continue to increase at the same rates, when will the populations of Nevada and Maine be the same?

Write a verbal model for this problem
Write an equation for the model
Solve the equation and answer the question.

Arithmetic in bases other than 10 2003-10-22
From Kim:
how do you add, subtract, multiply and devide in base 3, base 5, etc?
Squares in a rectangle 2003-10-21
From Raj:

Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle.

If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares.

Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle.

Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle?

1 + 1 = 10 2003-09-17
From David:
could you please explain to me how 1+1=10 thanks
The mean house price 2003-09-10
From Carol:

Question:
I have to find the mean from the following example:

Price Range £000 No of Houses
55 and under 60 3
60 and under 65 6
65 and under 70 13
70 and under 80 21
80 and under 100 15
100 and under 130 7
130 upwards 1

I know when calculating the mean you use the mid points of the classes, but how does this work for the 130 upwards class? Also, does this still work given the difference in the classes (ie. 1st class is 5, 5th class is 20, etc). Any help to get me started would be greatly appreciated.

Converting from base 10 to base 5 2003-09-10
From Susy:

My son, who is 9 in grade 5 has been asked to convert base 10 numerals into base 5.

His first question of:

24(10) he has calculated to be 4x5 + 4x1 = 44 (5)

The next question however is the tricky one.Ý We know the answer is supposed to be 100 but we find it difficult to get this in the way he understands it.

25 (10) = _________________ 100 (5)

Can you help us figure out how we reach the answer.

Answered by Claude Tardif and Penny Nom.
Consecutive integers 2003-09-07
From Amy:
I was wondering if there was a proper way to write the solution to a problem requiring consecutive integers? Is it okay to write the solution as 5,4,3,2,1 or must it be written as 1,2,3,4,5?
Can 2 vertical planes intersect? 2003-09-06
From Erin:
My question is can 2 vertical planes intersect?
One million seconds 2003-09-04
From Vince:
If you can write a number each second for one million seconds, how many hours would it take?
Grooming the king's horses 2003-09-04
From Janelle:
the stable boy had 90% of the kings horses groomed.the next day the king acquired 25% more horses. Now there was 105 horses not prepared for the kings men. How many horses did the king originally have?
Converting to base 10 2003-08-28
From Karen:
My son is in 5th grade.Ý He is learning how to convert numbers from base 2 to base 10, and base 5 to base 10.Ý Can you explain it to me in the simplest terms?
Graphing a piecewise function 2003-08-24
From Amber:
How do i begin to graph a piecewise function, absolute function or step function?
39 consecutive natural numbers 2003-08-19
From A student:
Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11.
Percentage decrease in sales 2003-07-31
From Linda:
If I had sales in January of 2002 that were \$42,493.73 and sales that were \$37,281.59.Ý The difference is \$5374.50.Ý What is the percentage of decrease in sales?
Is 3/5 CLOSEST to 0, 1/2 or 1? 2003-07-09
From A student:
I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2.
Setting up a word problem 2003-06-30
From Christie:
A rectangular corral is forty feet longer than it is wide. If the perimeter is 220 feet, determine the length and width of the corral.
Sesame Street on Stage 2003-06-25
From Christie:
Sesame Street on Stage has different ticket prices for adults and for children under 6. Beth and her two children, ages 3 and 4, paid \$15 to gain entrance, while Jamie and John Jacobs and their 2-year old daughter got in for \$19.50. What is the ticket price for adults?
A 40% markup 2003-06-12
From Nick:
I am attempting to determine the Retail price of an item that costs me 11.00. Our company wants to sell it at a markup of 40%. I calculated this two ways, first the way I thought it should be done. Second, the way the calculator does it (and my accountant).

1. Cost + Cost*(percentmarkup/100)= retail price 11.00 + 11.00*.40 = retail price 11.00 + 4.40 = 15.40 retail price

2. Using the calculators Mark Up key the answer is 18.33. Or 7.33 more than the cost or 67%.

I am confused by this Mark Up key and how it calculates. I used a cost of \$10.00 and marked it up 50%. I thought it should equal \$15.00 but the calculator says \$20.00? This seems to be 100% markup, yes?

Can you explain the difference between the way I did it and the way a Business calculator does it?

From Joel:

I have this project to do about crosses and I can't think of what the answer is for the following questions: What is the area rule of the crosses (the table below will help you)?
Cross NumberArea sq cm
15
213
325
441
561

I also need to know what the formula is for it?

From A teacher:
I am going to be teaching second grade next year. How can I differentiate instruction in mathematics to meet the needs of all of my students, from those who need intervention to those who need challenges? What are some techniques I can try for this grade level?
\$1/week for week 1 and then double each week 2003-05-28
From A student:
I AM DOING A PROJECT FOR MATH I AM TRYING TO CREATE A SEQUENCE BASED ON: MAKING A SALARY OF \$1/WK FOR THE FIRST WEEK WITH IT DOUBLING EVERY WEEK FOR 52 WEEKS, SO MY SEQUENCE LOOKS LIKE THIS: 1,2,4,8,16,32,64,128,256,512,1024 ETC. THERE WOULD BE 52#'s TOTAL IN MY SEQUENCE.I BELIEVE IT IS CALLED A FINITE SEQUENCE. MY QUESTION IS HOW DO I CREATE A FORMULA/RULE FOR THIS PARTICULAR SEQUENCE? MY GOAL BEING TO FIND THE 52nd TERM IN THE SEQUENCE.
Two sequences that agree in the first 4 terms 2003-05-26
From A student:
Is it possible to have two formulas that define sequences that agree on the first four terms but not the rest?
The cross-section of a football field 2003-05-25
From Francis:
Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly.

height from base to highest point- 45.75 centimetres distance of the field- 50 metres

a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the cross-section is a parabola, find the algebraic model that describes this shape.

b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line.

A trig identity 2003-05-20
From Patty:

1/ tanx + cotx = sinxcosx

R= 5.3lnx + x. 2003-05-11
From A student:
Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition?
positive multiples of 10 that are the sum of four consecutive integers 2003-05-01
From Taurus:
How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers?
Profit for a dance studio 2003-04-28
From Craig:
A dance studio charges \$80 per student for a series of 2 hour lessons. The studio's costs are \$30 per hour for the instructor, \$15 per lesson for the room rental, and \$3 per student for miscellaneous expenses. If x is the number of students enrolled in the class, express the studio's profit P(x) in terms of x. Find the profit if 10 students are enrolled in the class.
The product of four consecutive integers is 3024. 2003-04-25
From pillar:
The product of four consecutive integers is 3024. What are those numbers.
One one 2003-04-22
find the next two rows of numbers?
```     1
1 1
2 1
1 1 1 2
3 1 1 2
1 1 1 2 1 3
```

Chopping trees 2003-04-19
From Tamara:

The master needs some of the trees (twenty, to be exact) at the back of his spooky old mansion cleared to make way for a new evil laboratory, so he decides to send some his slaves to do the work for him.

He initially sends out four of his men, armed with axes, to chop the trees down. Due to the fact he is very impatient, every ten minutes he sends out another man to help with the work.

Assuming that it takes one man 30 minutes to chop down 1/3 of a tree, how long till all twenty trees are chopped down?

How many hits? 2003-04-06
From Jack:

My name is Jack. I'm a uncle. Student is in the 5th grade email is above.

If a baseball player at sping training had a good season with the following:

one seventh of his hits were doubles.
12.5% of his hits were home runs.
But didn't have any triples.
How many hits did he have?

Can you give me an explanation of you solved the problem.

Uses of conic sections 2003-04-01
From William:
My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful.
Friends and enemies 2003-03-24
From Becky:

Consider a room that contains six people. Any two people are either friends of each other, or they are enemies.

A. Argue why there are three people, all who are friends, or there are at least three people, all who are enemies

B. Rephrase the situation using graph terminology, using all of these terms correctly: vertex, edge, graph, complement, clique, independent set, and bipartite.

A sequence that converges to e 2003-03-16
From Dane:
Something I noticed fooling around with a calculator about 30 years ago.
Considering e = 2.718281828459045....
Using Window's Calculator you will find

1.111 = 2.8531167...
1.01101 = 2.731861...
1.0011001 = 2.71964085...
1.000110001 = 2.71841774...
1.00001100001 = 2.7182954...
1.00000110000011 = 2.178231875...
1.000000110000001 = 2.178219643...

There apears to be a pattern. My conjecture is:

1.'infinite number of zeros'11'infinite number of zeros'1 = e.

A section of land 2003-02-25
From Bev:
How many acres in a section of land? How many square miles is in a secion of land?
Percentage decrease 2003-02-20
From Hope:
What number decreased by 331/3% is 30?
Numbers in base 5 2003-02-16
From Lori:
I'm trying to help my 6th grader with converting numbers like 82 to base 5 and 182 to base 12. We saw your examples on 613, but still are confused.
Finite differences 2003-02-10
From Jenny:

I need to find a formula that will work with any number.
I am finding the volume of a 3d cross- shape. Here are my results so far:

```Term Number      0   1    2    3     4      5
nth term         1    7   25   63   129    231
1rst diff           6   18   38   66     102
2nd diff              12    20   28   36
3rd diff                  8     8    8
```

I can't seem to find a formula that will work with any number. Any help would be much appreciated.

Three consecutive positive intergers 2003-02-09
From Yew:
Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.

ex. (7)(8)(9) = 504 = 6 (84)

The sum of the first 1000 even integers 2003-02-06
From Jill:
What is the sum of the first 1000 even integers?
Arithmitic sequence 2003-02-01
From A student:
I am having problems solving this arithmetic sequence... 1, 5, 10, ___, 50, 1.00, ___, 10.00, ... I believe the answers to be 25 and 5.00 but I can't figure why.
1+2+3+...+500 2003-01-31
From Brian:
What is the sum of the numbers from 1 to 500 inclusive?
25% more 2003-01-16
From Charlie:
If I buy something for \$10 and want to sell for 25% more, do I multiply by 1.25 or divide by .75? Or another way - why do I get \$13.33 when dividing by .75 ?
Collinear Points 2003-01-13
From Gary:

Which of the 4 points are collinear when you construct the following concurrent lines or rays of a triangle?

1. P(1), the point where the angle bisectors intersect.
2. P(2), the point where the altitudes (or extensions) intersect (inside or outside of the triangle).
3. P(3), the point where the medians intersect.
4. P(4), the point where the perpendicular bisectors (or extensions) of the three sides of a triangle intersect.

This is for my 9-12 high school class in geometry.
My name is Gary

Gary

Answered by Harley Weston and Chris Fisher.
What is larger than infinity? 2003-01-12
From Dana:
What is larger than infinity?
Answered by Claude Tardif and Harley Weston.
A rectangular prism 2003-01-09
From Julie:
How many faces on a rectangular prism and how many bases? Can the base also be a face and can a face also be a base?
Repeating decimals 2003-01-08
From A student:
If k=.9repeating, and 10k=9.9repeating then 10k-k=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating

It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify?

Constructions of polygons 2003-01-03
From Garrett:
Our teacher just finished the constructions unit, and he mentioned briefly about odd sided figures such as pentagons and septagons, only that they're very hard. My question is, how do you draw, with a compass and a straight edge, a pentagon and septagon?
The intersection of conics 2002-12-19
From Glenda:
We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them?
Answered by Chris Fisher and Harley Weston.
A bouncing ball 2002-12-14
From Eman:

Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m.

1. Find the maximum height to which the ball rises after two bounces.
2. Find the total distance that the ball has traveled when it hits the floor for the tenth time.
3. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels.

A geometric sequence 2002-12-02
From Wanda:
the fifth term of a geometric sequence is 5/16. the common ratio is 1/2. What are the first four terms of the sequence.
Combinations of 1,2,3,...,10 2002-11-27
From Gord:
If I had the numbers from 1-10 how many different combinations would i have.....would it be 100....since that is 10 squared.
Making 7 2002-11-26
From Bill:
At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, -, /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer.
A two stage rocket 2002-11-26
From Hoda:
a two stage rocket accelerates in free space by ejecting fuel at a constant relative speed , v(ex). the full fuel load makes up 80% of the initial mass of the entire two stage rocket . the rocket accelerates from rest until at the end of the first stage when 75% of its fuel has been burnt. find an expression for the speed of the rocket at the end of the first stage in terms of v(ex).
Differentiating inverses 2002-11-20
From Amy:
f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a).
The horse race 2002-11-19
From Pat:
The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed?
The volume of water in a hose 2002-11-13
From David:
I trying to find out how much water 500 ft of 3/4 inch hose will hold. I'd also like to know how you figured the answer.
Chisanbop 2002-11-07
From Paul:
I'm trying to find the book/books that explain this system? I have one small book that explains the very beginning of the system, but covers only about 10 to 20%. I'v tried several book sellers and have had no luck.
What is nth term? 2002-11-06
From Joga:
What is nth term:

First sequence:
2, 4,7,11, 16, nth term

Second sequence:
4,10, 28, 82, nth term

A house's selling price 2002-11-05
From Tanisha:
a CERTAIN REAL-ESTATE AGENT RECEIVES \$6 FOR EVERY \$100 OF A HOUSE'S SELLING PRICE. HOW MUCH WAS A HOUSE SOLD FOR IF THE AGENT \$10,725._
Compass points 2002-11-05
From Mhairi:
I was asked this in maths but I am not sure if it is geography. Name all the compass points? We have been given 8 but he told us there is more and we have to name them.
The percentage grade of that hill 2002-11-05
From Cathy:
If there is an 80ft climb over a kilometer(about 3280ft) what is the percentage grade of that hill?
Jimmy's hits 2002-10-27
From Patty:
One seventh of Jimmy's hits were doubles
12.5% of his hits were homeruns
He did not have any triples

How many hits did Jimmy have? (Be sure to include the equation that represents the number of hits)

x 4 + x 5 = 100 2002-10-27
From Bill:
One of my students has stumped me. He asked how to solve the equation 4 x + 5 x = 100

All I can think of are graphing methods to get an approximate solution. What am I missing?

Two problems 2002-10-14
From Eva:

a) How many different equivalence relations can be defined on the set X={a,b,c,d}?

b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof.

Answered by Leeanne Boehm and Penny Nom.
Tree diagrams 2002-10-12
From Denean:
1. For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?

2. In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?

From Lisa:
The longest-lived US presidents are John Adams(age90), Herbert Hoover (also90), and Harry Truman (88). Behind them are James Madison, Thomas Jefferson, and Richard Nixon. The lattter three men lived a total of 249 years, and their ages at the time of death form consecutive odd integers. For how long did Nixon, Jefferson, and Madison live?
From Debbie:
The school newspaper is interviewing 6th grade students to see what sports they follow regularly on TV. Of the 70 students interviewed; 40 enjoyed basketball; 40 enjoyed baseball; 40 enjoyed football; 20 enjoyed basketball and football; 22 enjoyed baseball and basketball; 27 enjoyed football and baseball; and 12 enjoyed all three sports. How many students out of the 70 interviewed didn't follow any one of the three sports?
Answered by Leeanne Boehm, Penny Nom and Walter Whiteley.
Sums of evens 2002-09-14
From Rosa:
How do I find a geometric way to easily compute sums of consecutive even numbers 2 + 4 + 6 + ....
Answered by Leeanne Boehm and Harley Weston.
Base 5 numbers 2002-09-13
From Vera:
? how do you change a base 10 number to base 5
7+8+9+...+1000 2002-09-11
From Shirley:
My question is what is the formula for adding up numbers when you don't start with number 1? For example 3 + 4 + 5 + 6 = 18. But how could you arrive at the answer without adding all the numbers?
How do start from 2700 and get 35% back out? 2002-09-09
From Dennis:
2000 x 0.35 = 700 + 2000 = 2700
How do start from 2700 and get 35% back out? If I have 2700, how do I figure out that 35% of 2000 is 700 and adding the two them together will get me 2700?

Social security numbers 2002-09-06
From Chris:
How many different number combinations are there for the social security system? We know that there are only a certain ammount of combinations available and the current US population is at 281 million. The number system should include as many nine digit combinations as possible using the numbers 0-9 in multiple different spots.
8,27,64 . . . 2002-09-05
From Mike:
We have been trying with no luck all night to complete the following math pattern (next 3 entries) 8,27,64 . . . Any ideas??
1, 2, 4, 8, 16, 32, etc. 2002-09-04
From Ginger:
I've been working with finding the nth term for a few weeks, and i can't seem to figure this one out!

1, 2, 4, 8, 16, 32, etc.

Express 5120 as a sum of consecutive numbers 2002-08-25
From Todd:
Express 5120 as a sum of more than 1 consecutive number.
Sets and elements 2002-08-22
From Dianne:
I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come?
A paper model of a cone 2002-08-14
From Bruce:
I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion?
Answered by Walter Whiteley and Chris Fisher.
Percentage 2002-07-20
From Sally:
If 20% of 100 is 80, then why is the percentage difference between 80 and 100 25%.
A polygon inscribed within an ellipse - Part 2 2002-07-08
From Steven:
I recently sought your advice about a problem that I have been working on for eight years or so concerning a polygon inscribed within an ellipse. I think that I may have confused matters by the way in which I put the question and hope that the enclosed diagram will clear matters up. In the ellipse below I have drawn three chords inscribed within one quadrant ( this would pertain to a twelve sided figure within the whole ellipse). These chords are exactly the same length as each other, for example if the major axis of the ellipse was 360 and the minor axis 240 I have worked out that a twelve sided figure would have sides of 78.2487. However I worked this out empirically with a method that could only be described as gruelling I would be most grateful if you could tell me of a method that would work for any ellipse and any number of sides.
An equalateral polygon inscribed within an ellipse 2002-06-30
From Steven:
How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse?

I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero?

What is the next term? 2002-06-21
From A student:
What is the next term in the sequence:

1, 5, 14, 30.....

| n + 4 | + | 3 - 2n | = 16 2002-05-24
From Randall:
I don't seem to be able to solve this: | n + 4 | + | 3 - 2n | = 16
Sequences that agree on their first four terms 2002-05-16
From Mike:
Are there two formulas that define sequences that agree on their first four terms, but differ on the fifth term and all succeeding terms?
The law of cosines and obtuse angles 2002-05-09
From Bryant:
The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle.
What's the next term? 2002-04-29
From A student:
Find the nth term for the following:

1) 12, 30, 56, 90, 132
2) 6, 30, 84, 180, 330
3) 8, 15, 24, 35, 48
4) 10, 17, 26, 37, 50
5) 24, 40, 60, 84, 112
6) 24, 60, 120, 336, 504

Please show the FULL working out.

Conversion of units 2002-04-29
From Matt:
I am having trouble finding a workable equation for the following problem, particularly the conversion of two systems of measurement.

The question states that there are 27 grams of salt in a kilogram of seawater. And it asks how many tonnes (1 tonne = 1000 kilograms) of salt are there in one cubic kilometer of ocean. It also says that the density of seawater is 1.1 g/cm3.

What is the equation and how do I figure out how many kilograms there are in a cubic kilometre?

Ratios 2002-04-17
From A student:
1. Medication is givin at 1cc. per 20 pounds of body weight. A dog weighs 16 pounds how many ccs. of medication does the dog get?

2. Dr. Lee wants you to prepare 1000 ml. of a 10% dextrose solution in lactaed ringers for diuresis or a patient you have a 1 L bag of lactated ringers and 500 ml of 50% dextrose for injection. How would you prpare the solution?

Diagonals in a polygon 2002-04-10
From Murray:
If you have a regular polygon with n sides and you draw all (n-3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into.
Answered by Caude Tardif and Chris Fisher.
Composition of functions 2002-04-06
From Yvonne:
In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 4 and g(x) = sqrt(x)

The range of f(x), x<=-4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(-x2 - 4).

In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything?

If you conect all the vertices of a regular n-gon... 2002-04-01
From Murray:
If you conect all the vertices of a regular n-gon with lines you will have (n-3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other.
Some 5 card hands 2002-03-28
From A student:
From a standard deck of cards how many 5 card hands are possible consisting of a. exactly 4 hearts

b. two cards of one kind and three of another(like a full house).

A cone in 3 space 2002-03-20
From Matthew:
Let C in R3 be the cone defined by x2 + y2 - z2 = 0

(A) Let P be the plane described by x + 2z = 1

(i) Find a description of P in terms of two parameters s and t

.
.
.

Percentage difference 2002-03-08
From Tedd:
Can you give me the formulas for calculating percentage differences between two numbers? For example: if the first number is 10 and the second number is 15, then the second number is 50% larger than the first number. However, the formula to calculate that percentage won't work if the first number is greater than the second number as in the following example: The first number is 15 and the second number is 10, with the second number being 33.3% less than the first number. Or maybe I'm mistaken and the same formula will work in both situations.
A sequence 2002-03-07
From Caroline:
hi, here is the problem,

1
11
21
1211
111221
_ _ 2_ _ _

we can't get the sequence of the last line ,with the 3rd number being 2,thanks