







A geometric series 
20180313 

From nathi: Hi I am really struggling with this question please help !!!!
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.
The maximum height part is not answered. Answered by Penny Nom. 





Triakis 
20160627 

From Gordon: Some authorities treat "triakis" (and related terms "dyakis", "tetrakis", etc.) as attached prefixes; others treat them as separate adjectives. Thus I see one of the Catalan solids described as both "triakistetrahedron" and "triakis tetrahedron". Which usage is correct? Answered by Chris Fisher. 





An open ball is an open set? 
20160623 

From Aqeel: Theorem: The open ball is an open set? Answered by Harley Weston. 





sin 2x  sin x = 0 
20160424 

From lilly: sin 2x  sin x = 0 0 Answered by Penny Nom. 





A geometric progression 
20160303 

From Pauline: A woman measures the height of her child at birth and at monthly intervals afterwards.The child's height increases by 5% per month. Find the number of measurements she has made before the child's height is twice what it was at birth Answered by Penny Nom. 





A geometric sequence 
20150419 

From Delfina: In a geometric sequence the second term is 15 and the fifth term is 405. Find the sum of the first eight terms Answered by Penny Nom. 





1 + cot x divided by sin x + cos x 
20150115 

From Torrie: I need to solve this problem in terms of Sin, but I'm having trouble.
1 + cot x divided by sin x + cos x Answered by Robert Dawson and Penny Nom. 





Find the nth term 
20141026 

From Kenneth: According to the pattern of the following sequence. Find it's nth term:
3,9,27,81,243,.......... Answered by Penny Nom. 





67 cubic yards in cubic metres 
20140709 

From gavin: Convert 67 cu yards into cu metres Answered by Penny Nom. 





The parameterisation of of a curve 
20140401 

From Eunice: Let C be the path along the curve given by y−80=−5x2 that moves from the point (5,−45) to the point (0,80).
Find r(t) the parameterisation of C in that direction as t∈[0,5]. How am I suppose to find the parametric of both x and y?
can I let x=t, then y=5t^2+80? thanks Answered by Penny Nom. 





9,4,6,8,3,... 
20140331 

From Alynna: You are given the following pattern: 9,4,6,8,3,...
Create a formula for the nth figure.
I have trouble finding the formula, I need help trying to find it. Answered by Penny Nom. 





An infinite geometric series 
20131224 

From Muhammad: The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Answered by Penny Nom. 





How many cubic centimetres are there is a cubic meter? 
20131010 

From Larry: Change 1meter(to 3rd power) to centimetre(to 3rd power).
This is a metric conversion problem Answered by Penny Nom. 





How we convert cm to mm? 
20130908 

From Génesis: How we convert cm to mm? Answered by Penny Nom. 





A geometric sequence 
20130716 

From Relebohile: Find the n^th term of 3,6,9,12,24,48... Answered by Penny Nom. 





A curve in 3space 
20130214 

From pardeep: we have to show that the curve r(t)=(cos t)i+(sin t)j+(1cos 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. Answered by Harley Weston. 





Dropping supplies from an airplane 
20130214 

From Claire: An airplane flying at an altitude of 3500 feet is dropping supplies to researchers on an island. The path of the plane is parallel to the ground at the time the supplies are released and the plane is traveling at a speed of 300 mph.
a) write the parametric equations that represent the path of the supplies
c)How long will it take for the supplies to reach the ground?
d) how far will the supplies travel horizontally before they land? Answered by Penny Nom. 





A relation on a collection of sets 
20130204 

From raji: suppose R be a non empty relation on a collection of sets defined by ARB if and only if A intersection B is nullset.then.....the correct answer is R is symmetric and not transitive...my doubt is how it is symmetric Answered by Penny Nom. 





A geometric sequence 
20120610 

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 fortyfive. What is the first term of the sequence? Answered by Penny Nom. 





Parametric equations 2 
20120225 

From Kathy: If the angle at time 0 is not 45 degrees how can you find the initial velocity? Ball thrown from height of 7 feet. Caught by receiver at height of 4 feet after traveling 90 feet down the field. Find initial velocity. You had a similar problem answered but the angle was 45 degrees so the cos and sin were equal and the equations were simpler to work with. Thank you! Answered by Harley Weston. 





A geometric sequence 
20120224 

From Camille: Find x if the sequence 5,10,x+2 is geometric. Answered by Penny Nom. 





A tree growth modelled by a geometric series 
20120208 

From Steph: Hi I am really struggling with this question please help !!!!
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 Answered by Penny Nom. 





1 + 3 + 3^2 ...+3^(n1) = 3^n  1/2 
20120127 

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^(n1) = 3^n  1/2
This equation was used to find the number of white triangles in the Sierpinski Triangle Answered by Walter Whiteley. 





Mean and Average 
20120103 

From john: what is the difference between average and mean Answered by Robert Dawson. 





sin A/1+cos A + 1+cos A/sin A = 2cosec A 
20111020 

From Neeraj: sin A/1+cos A + 1+cos A/sin A = 2cosec A Answered by Penny Nom. 





The dimension of the box in centimetres 
20110827 

From Eliza: Find the dimension of the box in centimetres. Then find its volume in cubic centimeters.
The box is 0.7m (l) 0.4 (h) 0.2 (w) Answered by Penny Nom. 





An imaginary infinite geometric tree 
20110218 

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 rightangled 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. Answered by Robert Dawson. 





A geometric progression 
20101215 

From Abeth: find the value of x so that 2(x1), x+3, x will be a geometric progression. Answered by Penny Nom. 





The value after 30 years 
20101215 

From Abeth: At the end of every year, the owners of a building which costs 2, 500, 000 pesos deducts 15% from its carrying value as estimated at the beginning of the year. find the estimated value at the end of 30 years. Answered by Penny Nom. 





A geometric progression 
20100430 

From Kalyani: sum of infinite geometric progression is 9 and common ratio is 1/10
then sum up to 8 terms is? Answered by Chris Fisher. 





A geometric sequence 
20100413 

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. Answered by Penny Nom. 





Metric prefixes 
20100316 

From ali: How do you convert zectometres to yoctometres Answered by Robert Dawson. 





The integral of X^3/the square root of 1x^2 dx 
20100307 

From William: The integral of X^3/the square root of 1x^2 dx. Answered by Harley Weston. 





A geometric sequence 
20100222 

From Kelsey: _, 2, _, _, 250, _
i don't know how to fill in the missing terms Answered by Penny Nom. 





An infinite geometric series 
20090518 

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 Answered by Stephen La Rocque. 





A geometric progression 
20090516 

From sweta: find the ratio of GP if the first term is 1 and the sum of third and fifth term is 90. Answered by Penny Nom. 





Milliliters of oxygen in your lungs 
20090320 

From Leandrea: if you have 3 liters of air in your lungs and 2/10 of that is oxygen, how many milliliters of oxygen are in your lungs? Answered by Penny Nom. 





A trig limit 
20090205 

From Kathy: Hi! I was just wondering how to do this question:
lim 1cos2x/xsinx as x approaches 0
Thanks,
Kathy Answered by Penny Nom. 





Trig identities 
20090105 

From Michael: 1) Determine if the following is an identity. If it is, prove it, If it isn't state it.
tan x + cot x = sec x * csc x
and
1  (cos^2) x = 1+ (cot^2) x Answered by Robert Dawson and Harley Weston. 





The volume of a pipe 
20081210 

From Walter: What is the volume of a pipe 7.92 inches inside diameter and 22 km. long in cubic feet of water Answered by Robert Dawson and Harley Weston. 





A wine decanter 
20081210 

From Suzanne: I am trying to buy a wine decanter for my dad for Christmas. One big
problem I am having shopping online is finding the right size. Wine is sold
by metric ml, with a standard bottle holding 750ml of wine. Decanters are
measured by oz, and the sizes are all over the place, with one site alone
having sizes 25oz, 26 1/2oz, 50oz, 59 1/8oz, and 68oz.
Can you help me with metric conversions so I can figure out how much wine
these decanters hold? Like everybody else, I need this as soon as possible
so I can get it shipped in time for Christmas. (I'm disabled & don't drive, so
online shopping is my only way to get gifts.)
Thanks for your help!
Suzanne Answered by Chris Fisher and Robert Dawson. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





0.151515...=15/99 
20080908 

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 Answered by Penny Nom. 





How many litres of rain is this? 
20080901 

From Todd: If i have 10mls of rain over one square metre how many litres would I
and how do I do the maths for this? Answered by Penny Nom. 





Converting centimetres to metres 
20080821 

From walter: how do you convert the smaller unit to a decimal of the larger unit and then solve
17 m  130 cm Answered by Penny Nom. 





How many decimeters are in a meter? 
20080811 

From Julia: How many decimeters are in a meter? Answered by Penny Nom. 





Proofs 
20080726 

From Taylor: when doing a proof, how do i figure out the steps in which i find the statements? i find the reasons pretty easily but i do not understand how to get the proving part. that would be great if you can help me! Thanks Answered by Victoria West. 





Demographics 
20080725 

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 ?? Answered by Penny Nom. 





Geometric shapes that are the same 
20080609 

From tia: what is the name used for shapes that are exactly the same? Answered by Harley Weston. 





Geometric sequences 
20080608 

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)} Answered by Penny Nom. 





How much seed do I need per plot? 
20080513 

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. Answered by Penny Nom. 





Converting metric density 
20080428 

From Hilary: 10g/100ml=?g/?l
52g/100ml=?g/?l
65g/100ml=?g/?l
100g/100ml=?g/?l
137g/100ml=?g/?l
0.15g/100ml=?g/?l Answered by Penny Nom. 





The isoperimetric inequality 
20080421 

From Dutch: I'm searching for the proof that the sphere has the smallest volume of any figure and maximizes the volume of any figure. Answered by Chris Fisher. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





The integral of dx / (4x^2  25)^3/2 
20080401 

From Meghan: I have a question from the trigonometric substitution of my calculus course.
integral of dx / (4x^2  25)^3/2 Answered by Harley Weston. 





Parametric equations 
20080305 

From kumi: I have made a picture of a football pass 45 degrees with 30yds and height of 7ft and 4ft. But I am just stuck there. I have stared at the worksheet for soo long. I have no idea how to solve this, and I don't even know where this is going (I don't understand how parametric equations work). Can you help me with this problem?
1.The quarterback of a football team releases a pass at a height, h, of 7ft above the playing field, and the football is caught by a reciever at a height of 4ft, 30yds directly downfield. The pass is released at an angle of 45 degrees with the horizontal with an initial velocity of vo. The parametric equations for the position of the football at time t are given, in general, by x(t)=(vo cosθ)t and y=h+(vo sinθ)t16t^2.
a. find the initial velocity of the football when it is released
b. write the specific set of parametric equations for the path of the football
c.use a graphing calculator to graph the path of the football and approximate its maximum height
d. find the time the reciever has to position himself after the quarterback releases the football Answered by Harley Weston. 





150 decimeters is how many centimeters 
20080229 

From gayle: 150 decimeters is how many centimeters Answered by Penny Nom. 





How many meters/kilometers/millimeters would that be? 
20080117 

From chantal: if a ocean/lake/river is 250meters from where you are, how long would it take to get to shore? how many meters/kilometers/millimeters would that be? Answered by Penny Nom. 





x=sint, y=cos2t 
20080114 

From Art: How do i transform x=sint y=cos2t into a function in terms of x and y Answered by Harley Weston. 





How many centimeters equal one meter? 
20071115 

From Sherrie: How many centimeters equal one meter? Answered by Penny Nom. 





A particle moves in the xyplane 
20071112 

From Russell: A particle moves in the xyplane with
X = 2t^3  12t^2 + 18t
Y = 3t^4  28t^3 + 72t^2
find an equation of the line tangent to the given curve at t_0_ = 1
note: t_0_ is t subscript 0 Answered by Harley Weston. 





Converting millimeteres to inches 
20071027 

From Alison: I am hoping to buy a cabinet, the measurements are 1120mm x 560mm, what is that in feet & inches. Answered by Penny Nom. 





The nth term 
20071018 

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. Answered by Penny Nom. 





Finding a geometric mean and taking its antilog 
20070827 

From Jack: Would like to know the basic geometric mean calculation. Also how would I take the antilog from this number? Answered by Stephen La Rocque. 





Applications of sequences and series 
20070827 

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 nonmathematical areas use sequences and series
and how.
Areas such as engineering or science. Answered by Penny Nom. 





Parametric equations 
20070822 

From will: Graph and make a sketch of x = ysquared  6y + 11 in parametric mode (hint: you need to come up with 2 parametric equations).
i have already figured out that the cartesian form of the parametrics will be y = +/ sqroot(x2) + 3, but i do not know how to produce 2 parametric equations from this. Answered by Penny Nom. 





Which is more, 1.25 grams or 4.7 ml? 
20070822 

From jenni: Which is more? 1.25 grams or 4.7 ml Answered by Penny Nom. 





Isoperimetric area comparison 
20070617 

From michael: An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle 10, what is the area of the hexagon? Answered by Stephen La Rocque. 





A sequence of circles 
20070611 

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. 





Converting mass and volume of water 
20070510 

From Shian: Hello please help, I just can't seem to get the convertion thing and my mom tried to help but I still don't get it. How many grams does 1 milliliter of water weight? I was told 1g. How many grams does 0.1 liter of water weight? I was told 0.1g. Can you tell me if the answers given are correct with an explaination that I can understand? Thank you. Answered by Stephen La Rocque. 





Converting from mm to cm 
20070508 

From Amanda: How do you convert mm into centimeters? Answered by Gabriel Potter and Steve La Rocque. 





Arithmetic means and geometric means 
20070404 

From Dani: Hi!
I was just wondering why the arithmetic mean of sets of numbers is larger than the mean proportional of the same numbers?
Thanks!
Dani Answered by Haley Ess. 





A geometric series 
20070403 

From jessica: If a geometric series includes 5418+62 as its fifteenth through eighteenth terms, find the sum of the second through the fifth term, inclusive. Answered by Stephen La Rocque. 





The nth term 
20070213 

From Sarah: I am having difficulty in finding the nth term for 7,49,343,2401. Could you please help me in finding the correct answer? Answered by Stephen La Rocque. 





Find the total distance the swing traveled before it stopped. 
20061217 

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. Answered by Penny Nom. 





A geometric sequence 
20061128 

From Jillian: Find x so that 2x, x + 5, x  7 are consecutive terms of a geometric sequence. Answered by Stephen La Rocque. 





The history of the meter 
20061023 

From Caitlyn: i'm an 8th grade student and i have a lab report due and i really need to find out more about the history of the meter. Answered by Stephen La Rocque. 





how many ounces are in 750 cc's. 
20061014 

From Not a teacher: how many ounces are in 750 cc's. Answered by Stephen La Rocque. 





Metric conversion 
20061008 

From Eve: 45.6 microliter to megaliter? Answered by Stephen La Rocque. 





Metric Conversions 
20060902 

From Patricia: I have a new difficulty, metric conversion when it involves the prefixes. Some problems I need help with are: Answered by Stephen La Rocque. 





Converting sq ft to sq meters 
20060803 

From JB: I would like to convert 2700 square feet into square meters. Answered by Penny Nom. 





Volume of rainfall 
20060718 

From Randy: Calculate the amount (in gallons)of rainfall .98 inches will put over an area of 3.76 acres. Answered by Stephen La Rocque. 





Ounces of water to grams 
20060716 

From Liza: How many grams is in 10 ounces? I'm asking this question because i just bought a sea monkey and it says add 10 ounces of water and I don't know what that means. I have asked my parents but neither of them know. Answered by Stephen La Rocque. 





Isoperimetric quotients 
20060707 

From Jessica: How do you work out an algebraic equation for the IQ of an isosceles triangle. Answered by Penny Nom. 





Geometric sequence and basic functions (graphs) 
20060420 

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? Answered by Stephen La Rocque. 





Arithmetic and Geometric Sequences 
20060419 

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. Answered by Stephen La Rocque. 





Sum of a Geometric Sequence 
20060411 

From Andre: In a particular geometric sequence, U3=3.6 and U10=12.9. Find S16 and S17. Answered by Stephen La Rocque. 





A trig identity 
20060328 

From Iqbal: Could you please prove,
[tan(x)sin(x)]/sin^{3}(x)=sec(x)/[1+cos(x)]
Answered by Stephen La Rocque. 





What is the height of the pot? 
20060310 

From Michelle: If a pot is 11 inches in diameter and holds 5.8 litres what is the height of the pot?  assuming it is a cylinder. Answered by Stephen La Rocque. 





the size of a lot is 300 sqm, what is the square feet conversion? 
20060211 

From JC: the size of a lot is 300 sqm, what is the square feet conversion? Answered by Penny Nom. 





The Isoperimetric Quotient 
20060207 

From Ceri: I am studying Isoperimetric Quotient as part of my mathematics course and have been told that the only shape with an I.Q of 1 is the circle but when I work out the I.Q of a million sided regular polygon, the answer always comes out as 1. My teacher insists it is the just the calculator rounding things up, but I have tried loads of calculators and it always comes out as 1. Can you solve my conundrum? Answered by Penny Nom. 





A trigonometric identity 
20060122 

From Sarfaraz: Prove the following trigonometric identity.
sin^{2}x = tan^{2}x/(1+tan^{2}x) Answered by Penny Nom. 





How many millimeters are in 12 feet? 
20060106 

From Hunter: How many millimeters are in 12 feet? Answered by Penny Nom. 





Milliliters to grams 
20051229 

From Kaitlyn: If I'm using baking soda, how do I convert milliliters to grams? Answered by Harley Weston. 





how do you convert ml to oz? 
20051205 

From Sara: how do you convert ml to oz? Answered by Penny Nom. 





what is 5'7 
20051126 

From A student: what is 5'7" inches in cm? Answered by Harley Weston. 





An isosceles triangle 
20051114 

From Chris: PX and QY are attitudes of acute triangle PQR, and Z is the midpoint of PQ. Can you write a proof that triangle XYZ is isosceles? Answered by Chri Fisher. 





Inches and millimeters 
20050930 

From A student: how many inches are there in mm? For example 30x40 mm = how many inches. Answered by Penny Nom. 





Metric conversion 
20050901 

From Donna: I know there is an equation to figuring out, for example. .5526 km = _______ mm Answered by Penny Nom. 





A geometric sequence 
20050621 

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. Answered by Penny Nom. 





Centimeters, millimeters and milliliters 
20050419 

From A student: How many milliliters in a centimeter? Answered by Penny Nom. 





Biodiesel 
20050308 

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. Answered by Penny Nom. 





Conversion of a recipe 
20050206 

From Peg:
A Hungarian friend gave me an old, old family recipe and it calls for:
20 dg. sugar
15 dg. filbert
I can't find a conversion table anywhere that explains how to get ounces from "dg." Do you know what the equivalent would be in ounces of dry measurement?
Answered by Harley Weston. 





A geometric proof 
20041211 

From Hanna: Given: ABCD is a quadrilateral;
Prove: ABCD is a parallelogram Answered by Penny Nom. 





Geometric sequence 
20041204 

From Lesa: Find a formula for the geometric sequence: (√3  √2), (4  √6), (6√3  2√2), … Answered by Penny Nom. 





Cubic meters 
20040831 

From Brad: I have a 10' x 10' x 12" area & need to find the cubic meters, how do I do this? Answered by Penny Nom. 





A geometric sequence 
20040413 

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. Answered by Penny Nom. 





A metric prefix table 
20040307 

From April: Can you tell me what the scale is for nano, micro, mega, kilo, etc.... I know that mega is 10 to the sixth power but I can't remember the other ones. Answered by Penny Nom. 





A worm crawling home 
20040218 

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? Answered by Penny Nom. 





Geometric sequences 
20040203 

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. Answered by Chris Fisher. 





Liters in a pool 
20030805 

From A parent: I need to know how many litres in a 12 foot diameter, 3 foot deep pool? Any help much appreciated as I need to add the correct amount of chemicals Answered by Penny Nom. 





Volume of water in a pool 
20030706 

From An other: How many litres of water are in a pool that is 16 feet in diameter and 35 inches deep? Answered by Penny Nom. 





An inch and a millimeter 
20030621 

From Greg: The conversion factor for inches to millimeters 25.4 It strikes me as very odd that it's not some infinite decimal. I could understand this if one system was derived from the other but as I understand it they were derived independently. Is the conversion 25.4 or 25.4000XXXXXXX? If it's just 25.4 then how did that happen? Answered by Harley Weston. 





The metric and Imperial systems 
20030608 

From Ashlee: i am a year 8 student, and i am doing my Maths talent quest on the Metric and Imperial number system.
i was wondering, where did the 2 systems orginate and if possible, a little bit or information.
I also need to know the conversions of ounce, foot, mile..etc..from imperial to metric. Answered by Penny Nom. 





Millimeters to inches 
20030528 

From Brian: I am a music instructor just trying to get a horn repaired. I have been trying to get replacement pearls for a keyboard of a horn. The mechanic needs the measurement in inches. The calibers say that the size is .115 mm can you tell me what that is in inches, I tried your formula of 2.54 mm per inch but this is a smaller size and I cannot seem to figure it out. Answered by Penny Nom. 





8 faces, 12 vertices, and 18 edges 
20030422 

From Thomas: I would like to know the proper name for this geometrical solid. It has 8 faces, 12 vertices, and 18 edges? Answered by Penny Nom. 





______cm=0.048km 
20030227 

From Antonette: ______cm=0.048km Answered by Penny Nom. 





Millilitres and millimeters 
20030209 

From Iwan: I was just wondering whether a millilitre was equal to a millimetre, if not, what is there difference. Answered by Penny Nom. 





Milliliters 
20030204 

From James: What is a milliliter? Answered by Penny Nom. 





A bouncing ball 
20021214 

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





A geometric sequence 
20021202 

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. Answered by Penny Nom. 





Kilometers to miles 
20021009 

From A student: how many miles are in 16 kilometers? Answered by Leeanne Boehm. 





A million sheets of 30 cm long paper 
20020915 

From Jennifer: if you put a million sheets of 30 cm long paper end to end, how many kilometer long would the paper be from begining to end? Answered by Penny Nom. 





Ounces and cubic centimeters 
20020530 

From Martin: How many ounces are in 600cc of liquid? Answered by Penny Nom. 





A trigonometric identity 
20020322 

From Debby: I am stuck on a problem and wondering if you can help?? It is: Prove the following: sec^{2}(X)+csc^{2}(X) = sec^{2}(X)csc^{2}(X) Answered by Harley Weston. 





My 1978 Chevy has a 350 cubic inch engine 
20020311 

From Sharon: If my 1978 Chevy has a 350 cubic inch engine, about what size engine would that be in liter? Answered by Penny Nom. 





Miles and kilometers 
20020122 

From Dennis: I'm in the middle of purchasng a vehicle and it was built in Canada. Therefore it is in kilometers and not in miles. I forgot how many kilometers are in a mile. It registers as 183,049 kilometers. Answered by Penny Nom and Judi McDonald. 





My salary is doubled everyday for 30 days 
20020117 

From Kanishk: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Answered by Penny Nom. 





Isoperimetric quotients 
20020102 

From A student: I'm stuck on my GCSE Maths coursework, what do isoperimetric quotients measure? Answered by Penny Nom. 





Metric units 
20011025 

From Kelly: i am helping my kids out with school work and don't remember meters,centimeters decimeters and all those. We have to change meters into cm.....and so on..........is there a place on the web to look for some kind of help in these questions Answered by Penny Nom. 





A geometric series 
20011024 

From Tashalee: The sum of the first 3 terms of a geometric series is 13. The sum of their reciprocal is 13/9. how do you find the first three terms? Answered by Penny Nom. 





The average of two polygons 
20011023 

From Irene: How can I prove that the average of two polygons will give me another one? Answered by Walter Whiteley. 





Milliters and grams 
20010920 

From Bettyjo: 500 ml is what in grams Answered by Pnny Nom. 





Symmetry 
20010215 

From Sonam: What is symmetry? Who invented symmetry? what are the different kinds of symmetry? Answered by Penny Nom. 





An order relation 
20010212 

From Amy: What is an order relation? Answered by Claude Tardif. 





Geometric and arithmetic sequences 
20010126 

From Garry: what are the equations for geometric and arithmetic sequences? also, what are the equations for finding the sums of those series? Answered by Leeanne Boehm and Penny Nom. 





cot(arcsin 3/5) 
20010107 

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





Power series representations 
20001127 

From Grace: Is there a systematic way of finding a power series representation of a function? I understand that you have to manipulate the function so that it is of the form 1/(1x), but beyond that I am lost. Answered by Harley Weston. 





Comparing an integral and a sum 
20001121 

From Douglas Norberg: A fellow teacher asked me about a problem she wanted to give to her students. It involved whether to take a million dollars or a penny doubled a number of times. I was able to determine the number must have been .01 * 2^{30} which is about $10 million and a lot more than $1 million. To check that I was right I used a spreadsheet and did a Riemann sum. When I finished I reasoned that I had done the task in several steps and I could have done it in 1 step. Thus I integrated .01 * 2^{x} from 0 through 30 but the number I got was $15,490,820.0324. Why the difference? Answered by Harley Weston. 





Infinite Geometric Series 
20001110 

From Sam Carter: I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and r, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Answered by Harley Weston. 





A cycloid in Cartesian form 
20000920 

From Billy: The parametric equation of cycloid is given: x=r(tsint) y=r(1cost) How to eliminate t? Answered by Harley Weston. 





Euclidean distance 
20000906 

From Velma ZahirovicHerbert: If d(x,y) is euclidean distance between x and y Prove that d(x,y)>=0 if d(x,y)=0 than x=y and d(x,y)=d(y,x) Answered by Paul Betts. 





Geometric sequences 
20000411 

From Jodie: I am in a grade ten principles class and was taught how to do geometric sequences and series but no one in my class understood what we were taught. Our teacher is one of few to use the new curriculum which used to be the grade twelve curriculum. Could you please explain to me how to do geometric sequences and how to find the different terms and sums. Thank you very much! Answered by Harley Weston. 





History of a meter 
20000407 

From Jarod Fischer: The length of a meter has been determined in three different ways. The first and original way was determined in 1798. The second way was determined in 1960. The third and current way was determined in 1983. What were the three ways and why were the first two abandoned? Answered by Harley Weston. 





How many grams are in 1 ounce? 
20000404 

From Kathy G: How many grams are in 1 ounce? Answered by Penny Nom. 





Symmetric Primes 
20000401 

From Marlene Moore: Hi...Im in 9th grade and am having a hard time figuring out symmetric primes. Heres the problem: Find two pairs of symmetric primes of 20. Symmetric primes of 15? Answered by Claude Tardif. 





Geometrical solids 
20000315 

From Sarah:
 What geometrical solid has 8 edges and 5 vertices?
 What geometrical solid has 12 edges that are all the same length?
Answered by Walter Whiteley. 





The isoperimetric theorem 
20000224 

From Raj Bobal: How can you prove Mathematically that the maximum area enclosed by a given length is a circle? Answered by Chris Fisher. 





Pyramids and prisms 
20000118 

From Tyler: What's the definition of a Triangular Prism and a Triangular pyramid. Answered by Penny Nom. 





Proving a trigonometric identitiy 
19991217 

From Ryan: I need to figure out how to prove that sec^{2}x + csc^{2}x = sec^{2}x csc^{2}x. I am not sure where to start out with it and whether I should use reciprocal, quotient, or pythagorean. Answered by Penny Nom. 





Cubic meters to gallons 
19991209 

From Chris Compton: I am trying to convert cubic meters to gallons. Do you have the conversion formula? The problem I am trying to solve is: 59.62 cubic meters to gallons. Answered by Harley Weston.






sin x = x/10 
19991007 

From Amandeep Grover: Solve the equation sin x = x/10 Answered by Harley Weston. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





Parametric Equations 
19990806 

From Nicholas Lawton: Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is : yc/p=xp^2cp^3 Answered by Harley Weston. 





Unit conversions 
19990420 

From Deanna: My question has to do with unit conversions with English and metric systems. I need to know how to use conversion factors with powers of 10. Which way do i move my decimal point. ex. .48kl to liters. Thank you. Answered by Jack LeSage. 





Ounces and milliliters 
19990417 

From Tony Rizzi: I'm mixing a formula of: 48 oz distilled water. 15 grams of Hydroxy Ethyl Cellulose GR (powder) 30 grams of Hydroxy Ethyl Cellulose MR (powder) 200 grams of Barium Sulfate (powder) 1000 grams of Calcium Hydroxide (powder) After mixing, I need to estimate the amount of each ingredient that fits in a 3ml syringe. And how many syringes I can fill? Answered by Harley weston. 





Dotted graph paper 
19990408 

From Bridget Winward: A teacher at our school is trying to locate dotted graph paper online or in print. His class would like to make three dimensional, geometerical drawings. Please let us know if you have a good source. Answered by Jack LeSage. 





Converting Metric Measurements 
19990408 

From Rick: Do you have any simple explanations for converting Metric measurements to other Metric measurements?? What helpful hints do you also have for a 5th Grader... Answered by Penny Nom. 





Metric Conversion 
19990307 

From TDestra: Please help to answer this question: Is a cubic centimeter equivalent to milligrams or milliliters, and how many? Also, is it a liquid measure? Answered by Penny Nom. 





Converting mm's to inches 
19990222 

From Paul White: It has been a long time since high school and I do not remember how to convert mm to inches. Could you please tell me what this would convert to in inches? 210 X 254 mm. Answered by Chris Fisher. 





A trig limit 
19981114 

From Amy Atwell: what is the limit of of tanx / x + sin x as x approaches 0 Answered by Harley Weston. 





Two sides and a bisectrix. 
19981111 

From Victor Grinshtein: I am looking for someone who can tell me how to construct a triangle by 2 sides and a bisectrix using a compass and a ruler. Answered by Chris Fisher. 





Centimetres 
19981111 

From Vicky Caldwell: I work in Carpet Manufacturing and I need to know how to figure the calculation for a roll of carpet in centimeters. For example: a 12 x 100 roll of carpet equals 133.34 square yards, which is 100 linear ft. and 1,200 square foot. Can you please tell me how I would figure to get CENTIMETERS??????? Answered by Jack LeSage. 





The Left Side of a Parabola. 
19981020 

From Shay: Find the parametrized equation for the left half of the parabola with the equation: Y=x^24x+3 Answered by Chris Fisher. 





Nickles on the Highway 
19980922 

From Ronnie Mac Donald: How many nickels would it take to cover 226km of highway,each nickel is 2cm in diameter? Answered by Penny Nom. 





A Pattern 
19980914 

From Krystin: Question: 1=1x1 1+2+1=2x2 1+2+3+2+1=3x3 draw a series of diagrams to illustrate the above pattern Answered by Penny Nom. 





Sequences and series 
19980527 

From Michael Le Francois: The sum of the first ten terms of an arithmetic series is 100 and the first term is 1. Find the 10th term. The common ratio in a certain geometric sequence is r=0.2 and the sum of the first four terms is 1248 find the first term. Answered by Penny Nom. 





A Trigonometric Limit 
19970918 

From Brian Ray: What is the limit, as x approaches 0, or tan^23x/x^2? (read, tan squared 3x over...)? Answered by Harley Weston. 





Les tableaux de conversions 
20010503 

From JeanJacques: Sur quel site est il possible de trouver tous les tableaux de conversions de mètres,kg,litre,m2,m3 Quelle est la relation entre les m^{3} et les litres 1 m^{3} = 1000 litres = 1000 kg? Answered by Claude Tardif. 

