







A pattern for a truncated cone 
20131220 

From Josh: I need to know how to layout a truncated cone with a base diameter of 18" a top
Diameter 15.25 and a height of 20". Your help will be greatly appreciated. Answered by Penny Nom with a spreadsheet by Don. 





Solving a cone 
20080129 

From Marija: [Note: this problem shows how to solve anything about a cone if you are given two measurements.]
Is there a formula for finding the diameter of the base of the cone? Answered by Stephen La Rocque. 





Pattern for a truncated cone 
20070511 

From Mike: I have been trying to get this cone flat so I can build this column. Can you please help me so I can figure this out? Thanks for your help. Answered by Stephen La Rocque. 





A sand castle in the shape of a truncated cone 
20200523 

From Summer: A sand castle is in the shape of a truncated cone as shown. Calculate the length of the diameter of the base.
The diameter of the top of the truncated cone is 20cm
The height is 30cm
The slopes are 32cm Answered by Penny Nom. 





Maximizing the volume of a cone 
20200518 

From Ella: Hello, this is question  'If you take a circle with a radius of 42cm and cut a sector from it,
the remaining shape can be curled around to form a cone. Find the sector
angle that produces the maximum volume for the cone made from your circle.' Answered by Penny Nom. 





The volume of a stone 
20200502 

From KHOSI: A rectangular container is 9cm wide,17cm long and contains water to a depth of 11cm. A stone is placed in the water and the water rises 2,2cm .Find the volume of the stone Answered by Penny Nom. 





Power notation 
20200426 

From Aditi: The power notation of 1 / 128 Answered by Penny Nom. 





The missing diameter of a truncated cone 
20200417 

From Brandon: Need a formula to find missing large Dia of a truncated cone where the small dia =.19" Height= 2" and taper =16deg Answered by Harley Weston. 





Sixdigit telephone numbers 
20200312 

From Lulamile: What is the probability that a sixdigit telephone number has no repeated digits? The telephone number cannot begin with a zero Answered by Penny Nom. 





The volume of a coffee cup 
20200125 

From Amirah: What is the volume of a polystyrene cup with a height of 8cm, diameter of 5cm at the top and 4cm at the bottom when it is filled with water? Answered by Penny Nom. 





81^5 as a power of 3 
20191229 

From NA: How do we turn 81^5 into the power of 3? Answered by Harley Weston. 





Volume of a tree 
20191219 

From Maria: I have trees for sale. I need to calculate the volume of a tree from base which is wider than the stem.The base will be used for the making of hurleys, similar to hockey sticks so the wider base is crucial. Answered by Penny Nom. 





Vectors 
20190906 

From Kayla: Hi!
Due to time constraint issues, we skipped vectors in PreCalc last year. However, I'm attempting to complete my AP Physics summer homework and there are 3 problems with vectors. As I explained, I have no idea even where to begin and as such I need some help.
Problem 1:
A plane flying at 90° at 45 m/s is blown toward 0° at 62 m/s by a strong wind. Find the plane's resultant velocity.
I have tried all sorts of online calculators but none are providing me with a formula I can use to solve this problem on my own.
Problem 2:
If you walk 367 m North and 785 m West what is your total displacement from your original location?
What is the problem asking for when it says displacement?
Problem 3:
A plane travels on a heading of 127.0° at a velocity of 25 km/hr. What are the horizontal and vertical components of the plane's velocity?
As you know already, I have never done vectors so I don't know what horizontal and vertical components of velocity are.
Thank you So Much for your help!! I am struggling!!
 Kayla Answered by Penny Nom. 





Using the Laws of Exponents 
20190906 

From Samiya: i have been struggling with the laws of exponents so im having trouble with this question. the
question is to write (b*exponent2*c)(b*exponent5*c*exponent4*) Answered by Penny Nom. 





Can one equation with two variables be solved algebraically? 
20190830 

From Don: Can one equation with two variables be solved algebraically? Answered by Penny Nom. 





A flat top cone 
20190825 

From Mary: I want to make a paper model of a flat top cone with the radius of the base is 12.5 cm and the radius of the apex is 7 cm.The height is 15 cm and the radius of the apex is 5 cm. The height is 15 cm.
Can you help me with the angle and construction, please?
Thanks. Answered by Penny Nom. 





A cone of maximum volume 
20190814 

From Refilwe: The slant height of a cone is 10cm. Determine the radius of the base so that the volume of the cone is a maximum Answered by Penny Nom. 





The maximum volume of a cone 
20190714 

From A student: find the maximum volume of a cone if the sum of it height and volume is 10 cm. Answered by Penny Nom. 





One part in 10^x 
20190626 

From Jim: What is the meaning of the phrase ‘one part in 10x” where the x is an exponent? I have seen these examples: “...better than one part in 10x” and “...to within one part in 10x.” Answered by Penny Nom. 





4^x=2^x+6 
20190405 

From Olivia: How do you find the (b,n) if the solution of the equation 4^x=2^x+6 can be expressed at logb(n) where b and n are both prime numbers? Answered by Penny Nom. 





A dice game 
20190317 

From Remo: So, little game my kid came up with.
Dice are standard d6.
I roll a die, he rolls a die. If he gets the same number as me OR a bigger number he wins.
So far so good. Used the opportunity to get him to calculate the probabilities of him winning, see if I could get him interested into looking at this game from a more academic perspective. He did fine.
Then we upped the ante.
He rolls one die, I roll two dice. I his die has a number that is equal or greater than both of mine, he wins.
We had a bit of trouble solving that one, and had to resort to a table with all the results ( 6x36) to figure out where we stood.
Then again we upped.
He rolls two dice, I roll two dice.
If any one of his dice has a number equal to or greater than both of mine he wins. I only win if one of my dice is greater than both of his.
And we got stuck. Figured I would need to find a formula to resolve this one, as our earlier solution ( table everything ) suddenly is 36x36, giving well over a thousand possible results. And if we ever go bigger than that then we *really* are going to need another way to calculate it. Answered by Harley Weston. 





The top half of a cone 
20190227 

From danica: What portion of the height from top that the cone be cut into two equal volume? Answered by Penny Nom. 





The exponential form of sqrt(13) 
20190210 

From isaebl: what is the exponential form of sqrt(13) Answered by Penny Nom. 





An ice cream cone 
20190205 

From Eyuel: a scoop of ice cream has a 3inch radius how tall should the ice cream cone at the same radius be in order to contain all of the ice creams inside the cone Answered by Penny Nom. 





A cylinder with a cone on top 
20190116 

From Berania: A water tower in New York City has the shape of a cylinder with a cone on top. The cylinder has a diameter of 12 feet and a height of 15 feet. The roof has an inclination angle of 25 degrees.
(a) Determine the height of the cone to the nearest tenth of a foot.
(b) Determine the overall volume of the tower to the nearest cubic foot. Answered by Penny Nom. 





The top of a truncated cone 
20181202 

From Sameer: Bottom cone radius 1124.height is 200. Top radius 15degree decree to bottom radius. Top radius how much ? Answered by Penny Nom. 





Two cones formed from two circular sectors 
20181130 

From APARNA: The central angles of two sector of a circle are 60° and 120° . Using these sectors two cones are made. If the radius of the smaller cone is 5 cm, find the radius and base area of the larger cone. Answered by Penny Nom. 





Why 1/3 in the volume of a cone? 
20181020 

From Keith: In the formula for the volume of a pyramid, Volume = 1/3 * base * height, where does the 1/3 come from, intuitively? Answered by Penny Nom. 





Exponential form 
20180914 

From Saquanna: What is 25 in exponential form Answered by Penny Nom. 





Exponential form 
20180912 

From Grace: hi, I can't figure out how to do 735 in exponential form. note that im only in 5th grade and its not supposed to be in the scientific notation or whatever. okay, thanks! Answered by Penny Nom. 





Exponents 
20180813 

From Ella: What is the radical form of 3xy raised to 5 quantity three fifths? Answered by Penny Nom. 





Form a cone from a circle sector 
20180812 

From Tinashe: A 216 sector of a circle of radius 5cm is bent to form a cone. Find the radius of the base of the cone and its vertical angle. Answered by Penny Nom. 





Truncated cones 
20180808 

From Belgacem: Hello, I have a truncated cone: height 500mm , Base radius=147mm and I want to calculate the Top surface radius. How to do that? thank you Answered by Penny Nom. 





Paving stones area 
20180808 

From Declan: I am thinking of buying some reclaimed block paving stones. There are 750 pieces in total.
60% are L 140mm x W 140mm x H50mm
40% are L170mm x W140mm x H50mm
How much area will this cover? Answered by Penny Nom. 





The area, radius and slant height of a cone 
20180518 

From joette: If you have a cone how to find the slant height when given the area and radius? Answered by Penny Nom. 





The square root 3 in exponential form 
20180509 

From Paige: how do you write the square root 3 in exponential form Answered by Penny Nom. 





A volume expression for a pyramid 
20180423 

From Shaheer: Do a three sided pyramid and a square pyramid have the same formula if you want to calculate the volume? Answered by Penny Nom. 





A cone formed from a circular sector 
20180418 

From Jessica: A circle has a radius of 7.5cm. A sector with an angle of 240 degrees is cut out from the sector. If the sector is folded to form a cone. Find the length of the cone. Answered by Penny Nom. 





Graham's money box 
20180412 

From Tasnim: Graham's money box consists of sh.10 and sh.5 coins. There are 24 coins and it's total value is 150. Find how many of each coins are there in the box Answered by Penny Nom. 





The volume of a tent with a hexagonal base 
20180327 

From shohel: A tent has its base in the shape of a regular hexagon whose sides are 10m . If the height of the tent is 12m , then find its volume. Answered by Penny Nom. 





1/4 acre of land 
20180315 

From Jean: I have 1/4 acre of land.it is square.what should the measurement be for each side be in feet Answered by Penny Nom. 





Water in a cone 
20180210 

From Shuvo: The diagram shows a vertical crosssection of a container in the form
of an inverted cone of height 60 cm and base radius 20 cm. The circular
base is held horizontal and uppermost. Water is pursed into the
container at a constant rate of 40 cm3/s.
Show that, when the depth of water in the container is x cm, the
volume of the water in the container is (πx^3)/27 cm3.
Find the rate of increase of "x" at the instant when "x" = 2. Answered by Penny Nom. 





The code on a new phone 
20180202 

From Maria: Hi 
My husband gave me a new Samsung Galaxy mobile for out anniversaire gift. He set me a challenge which I have to solve before I can use the Phone. He has set the pin code with numbers 4, 7 and 0 and created a four digit code with the said numbers. Is there a way I can somehow list all possible combinations and try them all? Thanks! Answered by Penny Nom. 





A fraction of a mile 
20180106 

From Sierra: There are 5280 feet in a mile. what fraction of a mile is represented by 660 feet? Answered by Penny Nom. 





4444^4444 
20171210 

From Sashi: 4444 to power of 4444=?
Please share the result with simplification. Answered by Penny Nom. 





Exponential form 
20171125 

From Sherry: What is the exponential form of 3sqrt 15? Answered by Penny Nom. 





The volume of a cone without calculus 
20171002 

From Akash: How to find the volume of a cone without the knowledge of calculus? Answered by Penny Nom. 





Exponential form 
20170706 

From estela: what is exponential form of 9×1000 Answered by Penny Nom. 





A lost iPhone pass code 
20170417 

From Sam: I have a locked iPhone and it has all my of my holiday photos on it. I changed the password and then I think I did a incorrect number pattern but anyway I know it ends with 99 and the first 4 digits are 235 and 6 could you please send all of the combinations for this password (without the 99) Thx and plz get back ASAP I need it for school Answered by Penny Nom. 





A function which is onto but not onetoone 
20170416 

From Avinash: Define a function f(x):N>N which is onto but not oneone.Where N is set of natural numbers. Answered by Penny Nom. 





Forming a cone from a circle 
20170415 

From Tasha: A sector of a circle subtends an angle of 216 degrees at the centre, If this sector is used to form a cone of vertical height ,8cm, calculate the base radius of the cone Answered by Penny Nom. 





How to find last two or three digits of a large exponent like 17^256? 
20170330 

From Raginee: How to find last two or three digits of a large exponent like 17^256? Answered by Penny Nom. 





2^a, 2^b, 1^1 and 1^0 
20170317 

From Émile: If you had 2^a = 4 and 2^b = 4 you could assume that a = b right? Yet we can observe that 1^1 and 1^0 both equal 1, yet 1 = 0 isn't true. So if given a log base 1 number 1 the would the answer be 1 AND 0? Answered by Penny Nom. 





Exponential form 
20170304 

From michael: I was teaching my student about exponent when we stumbled across this problem.
"write (125)^3 in exponent form"
The problem is with the number "125". I think 125 = (5)^3. But one of my student thought that it is 125= 5^3.
Both of them is equal to 125 but they totally different in structure. I wonder which one is correct and why it is. I am worried if they get this wrong, it might spell problem in the future when we start substituting the numbers with variable.
Thank you very much for reading my question and answering it. Answered by Penny Nom. 





One millionth of one percent of 90,000,000,000 
20170116 

From Gene: What absolute number is one millionth of one percent of 90,000,000,000 Answered by Penny Nom. 





Acres and miles 
20161130 

From Carolyn: If I am running a pipeline of 1,100 miles, how many one acre plots will it take to cover this distance?
Carolyn Answered by Penny Nom. 





Exponential form 
20160831 

From Lily: Hi! I was wondering, I was having a little issue understanding this one problem. It was "write 81 in exponential 2 different ways" and I already got 9(2) but I was wondering what the second one could be! Thanks! Lily Answered by Penny Nom. 





A cone inscribed in a hemisphere 
20160807 

From anonymous: A cone is inscribed in a hemisphere. the slant height of the cone is 20cm. When cut along its slant height, the cone forms a sector of a circle.
find the angle of the sector, to the nearest 1 decimal place. Answered by Penny Nom. 





The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





600(1+0.05)^7 
20160421 

From chelsey: I am unsure on how to solve this problem, 600(1+0.05) 7 ? Answered by Penny Nom. 





A stained glass cone lamp 
20160409 

From Edwin: In making a 16" dia. cone lamp (stained glass), how many square feet of glass do I need. Answered by Penny Nom. 





The last two digits of a phone number 
20160403 

From Joshua: I want to find the last two digits of a phone number whose first eight numbers of a ten digit phone numbers are known. Answered by Penny Nom. 





The volume of a cone 
20160331 

From Odum: Find the volume of a cone with radius 6.5cm and height 12.6cm Answered by Penny Nom. 





Exponential form 
20160126 

From Jufe: What is the exponential form of ³√11x² Answered by Penny Nom. 





Exponential growth 
20160126 

From Paul: The value of a stamp was 0.03 in 1851. The value in 2011 is $50,000. If the value increased exponentially, what is the annual growth rate? Answered by Penny Nom. 





The diameter of the top of a truncated cone 
20160124 

From Peter: I am trying to calculate the diameter of a truncated cone given
one diameter the height of the cone and a 10% taper from one end
to the other. For example a butter churn is 18" tall and 9" in
diameter at the base. the sides need to slope inward at 10%
What is the diameter at 9" and 18" Answered by Penny Nom. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





The height of a truncated cone 
20151204 

From Jack: I need to build a truncated cone that has a top of30 inches and a base of 64 inches . The sides need to be at a 64.5 degree angle. This will determine the height. Can this be calculated? Answered by Penny Nom. 





Pouring a foundation 
20151127 

From Lisa: Hi im building a house 30ft long 18 ft wide I would like to pour a foundation of 6 inches
deep. How much sand, cement , 1/2" gravel do i need. Answered by Penny Nom. 





Exponential form 
20151017 

From Will: What is exponential form of 8? Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





A stone walkway around a pool 
20150529 

From Jerri: I have a rectangular pool 15x30 and it will require stone placed around it 4 feet out and 4 inches deep how much will I need? Thanks, jerri Answered by Penny Nom. 





The intersection of a plane and a cone 
20150516 

From Tom: Is there a way to derive an equation that describes the perimeter of the intersection of a plane and a cone regardless of the angle of the plane to the cone. Assume that the plane does not cut through the base of the cone, the x, y, z location of the vertex is known, the distance from the vertex to the plane through the axis is know., and that the angle of the cone is known. Answered by Chris Fisher. 





A fraction with a negative exponent in the denominator 
20150430 

From ellen: 7/ab to the 4 power Answered by Penny Nom. 





A wireless fence 
20150418 

From Dave: I'm buying a wireless fence to keep my pet in my yard. It has a half acre range. In a straight line how far would that be? Answered by Penny Nom. 





A cone of maximum volume 
20150316 

From Mary: I have to use a 8 1/2 inch by 11 inch piece of paper to make a cone that will hold the maximum amount of ice cream possible by only filling it to the top of the cone. I am then supposed to write a function for the volume of my cone and use my graphing calculator to determine the radius and height of the circle. I am so confused, and other than being able to cut the paper into the circle, I do not know where to start. Thank you for your help! Mary Answered by Robert Dawson. 





Constructing a cone 
20150312 

From Levi: While the mathematics at the welding shop page was very helpful there is one vital part missing. If I have never built a cone how do I figure out how much bigger the diameter of my
circle has to be when laying flat on the floor verses the diameter when it has been pulled into a cone. Answered by Harley Weston. 





The volume of a cone 
20150205 

From Linda: How do you calculate the volume of a cone that is 25cm high and has an angle of 20 degrees? Answered by Penny Nom. 





Largest cone in a sphere 
20150115 

From Alfredo: What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm? Answered by Penny Nom. 





Missing digits in a phone number 
20150107 

From Janelle: I had a friend try and play a game on me, regarding phone numbers, so I only know the area code , and the last four digits of the phone number. Which means, there are 3 digits that I need to figure out all the possibilities to. Answered by Penny Nom. 





A cone is 2/3 full of sand 
20141214 

From Janice: A cone with a radius of 3.5 cm and a height of 12 cm is 2/3 full of sand.
What is the volume of the sand inside? Answered by Penny Nom. 





Planar curves 
20141213 

From ann: what does planar curve mean in your definition of a cone? Answered by Penny Nom. 





Exponential notation 
20141127 

From Jaqui: May sound super easy, but how would you SHOW that you simplified
3x3 to the power of 2 (the little 2)?
thank you!
Jaqui Answered by Penny Nom. 





Doubling the dimensions of a cone 
20141121 

From Hannah: If the volume of a cone of height 10 cm is 261.8 cm3, show that this
volume is increased by a factor of 8 if the dimensions of the cone are doubled. Answered by Penny Nom. 





Prime factorization in exponent form 
20141031 

From Emma: I need to find out how to make a prime factorization of 120 in exponential form. Answered by Penny Nom. 





One zero to a quadratic expression 
20141006 

From Kevin: Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question? Answered by Penny Nom. 





Filling three holes with stones 
20140820 

From mark: how many tonnes of hardcore/crushed stone would it take to fill
1 hole 9ft diameter 5ft deep
and 2 holes both 3ft diameter and 5ft deep Answered by Penny Nom. 





1/3 of $320 
20140813 

From Student: Grade:5
Please help I got tutor for selective and this question is really
bugging me a lot what is 1/3 of $320?
plez answer quick before I fail :( Answered by Tyler Wood. 





An oval pool 
20140621 

From steve: I have a 16' x 28' oval pool that is buried 24" deep inground. The dig site is dug
2' wider all the way around the pool. I need to back fill this area with stone. I want to fill this area with 6 to 8"
of stone. How many tons of stone will this take?
Thanks you
Steve Answered by Penny Nom. 





A cone of vision 
20140429 

From David: It is known that a fish in water looking up has a 97 degree "cone" of vision that sees "through" the surface of the water. If a fish lies 4 inches below the surface, the cone forms a window (circle) smaller than if a fish lies 8 inches below the surface. What is the ratio of inches of depth to the radius of the circle on the surface that is its visual window? Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





Ms. Werenich's nickels, dimes and quarters 
20140319 

From London: Ms. Werenich has twice as many dimes as nickels and 4 more quarters than nickels. If she has $4.50, how many of each coin does she have? What would the let statements be of this problem and can you solve it? Answered by Penny Nom. 





Determine the selling price 
20140308 

From augustine: knowing an auctioneer charges a 7% fee and I know I want $74,400 what is the formula to determine selling price. Answered by Penny Nom. 





A cone inscribed in a sphere 
20140228 

From joel: how can I find the radius and the height of a cone INSCRIBED in a sphere, given the sphere having a radius of 6? ( note: the diameter of the cone is equal to its slanted height). Answered by Penny Nom. 





Four digit phone numbers 
20140225 

From Tom: Hi, I'm an online math teacher, working on lessons for my students.
This question is in their book and I can't do it...! Help!
It has to do with phone numbers, and in this problem,
we are only dealing with
the last 4 digits of the number.
It asks how many possible numbers we have
if at least one digit repeats in the last 4 digits of the number. Answered by Penny Nom. 





The diameter of the base of a cone 
20140223 

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. Answered by Harley Weston. 





What is the exponential form of 1/square root of 6v? 
20140216 

From Prince: What is the exponential form of 1/square root of 6v Answered by Penny Nom. 





The volume of a cone 
20140208 

From hibba: why is the volume of right circular cone divided by 3? Answered by Penny Nom. 





Prime factorization 
20140206 

From Kadeejah: Write the prime factorization of 37 in exponential form Answered by Penny Nom. 





Fractions and exponents 
20140111 

From john: what is the exponent form of 9^4/7^2 and 6^3/10^5 Answered by Penny Nom. 





A boxandwhisker plot with one whisker 
20140109 

From Susan:
Question from Susan, a teacher:
I read your answer to the question about could a box & whisker have NO whiskers.
It made sense to me. However I am preparing for my advanced class and I have a sample graph comparing box plots of data.
Several of the box have only 1 whisker. There is no explanation for this. Can you help me out. I cannot think of a data set that would produce this. Thanks! Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

From Natasha: Would one flip the inequality symbol in this equation: (explain why)
(9a)/(9) > 81
And please explain in what circumstances one would flip the inequality sign
THANKS! Answered by Penny Nom. 





7 digit phone numbers 
20131208 

From Sean: Hi I was wondering how you would calculate how may 7 digit phone numbers there are with only odd digits? Answered by Penny Nom. 





Exponential form 
20131201 

From Alina: My question says to express each number in exponent form in as many different ways as I can; 16, 81 and 64. How do I do this? Answered by Penny Nom. 





A frustum 
20131012 

From Lily: A cone of height 6in. and radius of base 4in. has its top cut off by a plane parallel to its base and 4in from it.
Find the volume of the remaining frustum.
I have worked out the volume of the entire cone but I don't know how to work out the radius of the top of the frustum.
Thanks Answered by Penny Nom. 





Maximize the volume of a cone 
20131009 

From Conlan: Hi I am dong calculus at school and I'm stumped by this question:
A cone has a slant length of 30cm. Calculate the height, h, of the cone
if the volume is to be a maximum.
If anyone can help me it would be greatly appreciated.
thanks. Answered by Penny Nom. 





A Holeinone on all four par 3's 
20130904 

From Robert: There are four (4) par 3's at a specific 18 hole course.
One member has the honor of making a Holeinone on all four par 3's.
It has taken him 8 years to do it!
How does one go about computing the odds of this TREMENDOUS accomplishment?
Respectfully,
Robert laffal Answered by Victoria West. 





Ordering crushed stone 
20130903 

From Prakash: Dear Sirs,
I am working in a Soft Landscaping contracting company. If I need to purchase crushed stone with the size 5070mm for $53,429 m^2$ area, how many 20feet containers should I need to order to my suppliers? The 20foot container has internal dimensions 5,897 mm by 2,348 mm by 2,285 mm and the $53,429 m^2$ area is to be covered by 10 cm of stone. Answered by Harley Weston. 





Differentiate x^x  2^sinx 
20130809 

From tarun: derivative of x^x  2^sinx Answered by Penny Nom. 





Slicing through a cone to form an ellipse 
20130806 

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? Answered by Chris Fisher. 





A one acre plot of land 
20130619 

From Carol: If I have a one acre plot of land, what is the measurement in feet on each of the four sides? Answered by Penny Nom. 





650*(1+0.005)^96 
20130417 

From joAnn: i am trying to figure out how to solve a question like this for example:
650(1+.005)96
I have been doing it this way but takes forever and wanted to know a shorter way
650 x 1.005 x 1.005 x 1.005 x 1.005 96 times
HELP Answered by Penny Nom. 





A cone problem 
20130414 

From Courtney: Hello,
I am having difficulty solving this cone problem. The biggest challenge I have is figuring out what angle they are talking about:
The angle at the base of a cone is 34.5 degrees. Find the diameter of the cone at point on the edge of the cone 26cm from the tip. Answered by Penny Nom. 





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

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





An equation with exponents 
20130224 

From Chelsea: (81 to the power of 3n+2 over 243 to the power of n) is equal to 3 to the power of 4
Find the value of n.
The answer I got was n is equal to negative (4 over 7).
The answer in my text was n is equal to negative (4 over 17) Answered by Penny. 





The height of a sheet metal cone 
20130209 

From Charles: Sheet metal cone.
I need a cone with a finished base of 38.19719 diameter
The cone is to be from a 48 diameter round with the wedge cut out.
The best calculation I have is the arc is 286.479. (correct?)
Could you verify this arc angle but more so what is the cone height? Answered by Harley Weston. 





Exponential form 
20130205 

From Sandra: What is 37,008 in exponential form? Help me please!!! Answered by Penny Nom. 





How many edges does cone have? 
20130128 

From Meriem: how many edges does cone have pls? Answered by Lorraine Dame, Chris Fisher and Walter Whiteley. 





A triangular island 
20121229 

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? Answered by Penny Nom. 





A 4 digit phone lock using the digits 4, 2, 3 and 0 
20121224 

From Ragu: I would like to know formula for searching a combination of 4 digit. eg.
I knew my Phone Lock combination is my car plate number 4230. But
this time, i used another way around instead of 4230.
But I am sure, there is only this 4 digits only. 4 & 2 & 3 & 0 Answered by Penny Nom. 





What's your secret? 
20121111 

From ryan: Tuscan school has a fair. At the fair, Pia plays "what's your secret?
The game starts with 3 players who are told the same secret.
Each of those 3 players tells another 3 player, and so on.
At the end of the 3rd round, everyone who knows the secret
will compare what they have heard. What number in exponent form
represents the number of people who know the secret after 3 rounds?
How many people is that?
Thank you very much.
P.S. I got 3 cube. which is 27
But when i map it out I end up with 39. Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





Functions 
20120918 

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 show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Functions 
20120918 

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 show me the work
Please give me the trick of finding such functions Answered by Robert Dawson and Harley Weston. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





Exponential form 
20120904 

From angie: How do i write 9^5 in exponential form? Answered by Penny Nom. 





Exponntial form 
20120830 

From Robin: My math teacher has asked the question:
"Write mmmxxjmyy2 in exponential form"
How would you solve this problem? Answered by Penny Nom. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John Answered by Penny Nom. 





The exponential function form f(x)=a^x 
20120813 

From Lucy: Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative? Answered by Penny Nom. 





A pile of topsoil 
20120723 

From Perry: I have a pile of topsoil that is 42ft long and 16ft tall shaped like a cone how many yards of topsoil do I have. Answered by Penny Nom. 





Fence post holes 
20120719 

From Gerry: Hello, I'm digging 30 8" dia holes, 5 ft deep for fence posts that are 4"x 4" Can you please help me figure out how much stone dust I should order for all 30 holes. Thanks Answered by Penny Nom. 





A truncated cone: the central angle 
20120717 

From Tom: I have researched several sites, including this one and am fairly confident I can do the calculations required to produce the two radii and the slant height for a truncated cone.
I a somewhat confused by the central angle. Some sites indicate that it should never exceed 180 degrees while others do not. Different examples on your site seem to use this in two different ways in constructing a truncated cone.
Sometimes the angle seems to indicate the section to be removed, while in other examples the angle seems to indicate the section to be saved. Since the two angles will always total 360 I am confused about how to use the info to
calculate the minimum rectangle required to contain the pattern. I'm guessing that in some cases I may need to use the chord or sagitta to determine the desired height and width of the material. Any help is greatly appreciated.
Thank you.
Tom Answered by Penny Nom. 





Expanded exponential form? 
20120612 

From Ramon: express the numbers 990 614 000 005 in expanded exponential form. Answered by Harley Weston. 





A lamp shade 
20120515 

From Fleur: I am helping my child make a cone lampshade, the measurements are as follows in "cm's"
21 cm = height
8 cm = top diametre
40 cm = bottom diametre
Please could you give the pattern (cut out) dimensions for final cut. Answered by Penny Nom. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





Radioactive decay 
20120402 

From Christy: Hello, how do I go about answering this question?
Should I be using the formula Ce^(kt)?
Given that the decay constant for Radium is .000428/year, how long, to the nearest year, does it take a sample to decay to 15% of its present mass? Answered by Penny Nom. 





A water tank is in the shape of a truncated cone 
20120308 

From Victoria: Suppose you have a water tank in the shape of a truncated cone. The larger diameter is K, the smaller diameter is K/2, and the height is also K (all measured in meters). The force of gravity on an object of mass, m, is F=9.8m (measured in Newtons). The density of the water is 1000 kilograms per cubic meter. What is the volume of the tank and how much mass will the tank have when it is full? Answered by Penny Nom. 





81+8 to the 3 power 
20120308 

From KiMesha: 81+8 to the 3 power Answered by Penny Nom. 





2x^3*2x^2/3x^2 
20120306 

From hope: 2x^3*2x^2/3x^2 Answered by Penny Nom. 





The dimensions of a conical tent 
20120304 

From yash: a conical tent is to accommodate 11 people.Each person must have 4m square of space on the ground and 20m cube at air to breathe.Find the height and radius of the conical tent.26202 Answered by Penny Nom. 





Building a tipi 
20120129 

From Lacy: Hi there!
We are building a tipi for our children. We want to build a large one about 15ft tall with a base of about 15 feet diameter. I am trying to figure out how much canvas we need to accomplish this. I graduated about 20 years ago and am struggling. Please help if you can. Answered by Penny Nom. 





Exponential form 
20120115 

From Helen: How do you write (1/x) in exponential form? Answered by Penny Nom. 





The volume of a frustum of a cone 
20111224 

From CV: If I know the height, taper, and volume of a frustum cone,
what are its Radii?
Calculating frustum cone volume is straight forward.
v=Pi/3*h*(R*R+r*r+R*r) where;
v=volume;
h=frustum height;
R=major radius;
r=minor radius;
Pi=3.1415926;
t=taper, ('slant angle' where t=0 is a disk)
Here is the tricky part.
Knowing 'h', 't', & 'v';
Calculate one or both of 'R' & 'r'.
Specifically, what is the formula for 'R=' or 'r='? Answered by Penny Nom. 





Water is flowing into a cup 
20111219 

From Tim: A cup has a radius of 2" at the bottom and 6" on the top. It is 10" high. 4 Minutes ago, water started pouring at 10 cubic " per minute. How fast was the water level rising 4 minutes ago? How fast is the water level rising now? What will the rate be when the glass is full? Answered by Penny Nom. 





Exponential form 
20111212 

From Zoey: What is the exponential form of 1/8?? Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





A log equation in exponential form 
20111111 

From Sarah: Express the equation in Exponential form
log2 to the 16th power=4 Answered by Penny Nom. 





Exponential form? 
20110830 

From Emily: I have a 6th grader that needs to find out what is the exponential form of 461,885,811 Answered by Penny Nom. 





A pattern for a cone 
20110830 

From Izzy: I need to create a cone as a prop and my math is not good enough to create the pattern.
Here are my instructions :
The diameter is 2'5" and it has to be 4 feet tall. It is a giant cone. I want it to be pointy at the end, not truncated. Answered by Penny Nom. 





Exponential form 
20110823 

From kiara: The African bush elephant is the largest land animal and
weighs about 8 tons . Write the amount in exponential form . Answered by Robert Dawson. 





A cone with an oval as a base 
20110803 

From Emily: Hi, I was wondering how to calculate the surface area of a cone with an oval as a base (which I think is referred to as an elliptic cone or something like that). I have the both the maximum and minimum radius as well as the height, but I don't have a slant height and I'm not sure how to calculate it and then calculate surface area. I would really appreciate some help. Thanks! Answered by Robert Dawson. 





Exponential form 
20110518 

From Kara: How do I write this in exponential form?
log 1/8 = 3 Answered by Penny Nom. 





An exclusion zone around a triangle II 
20110503 

From Aishwarya: A long time ago Mr gibson found an island shaped as a triangle with three straight shores of length 3km, 4km and 5km. He declared an exclusion zone around his island and forbade anyone to come within 1km of his shore. What was the area of his exclusion zone?
This question was answered but did not understand the explanation. Answered by Robert Dawson. 





(27^r^1)^2/3 
20110424 

From YungJu: (27^r^1)^2/3 Answered by Penny Nom. 





Cone story problem 
20110416 

From Chelsea: There is a cone with a story problem that states only that the radius is the same as the altitude and that the slant height of the cone is 6cm. I have no idea how to figure this problem out. Answered by Penny Nom. 





The volume of a flower pot 
20110407 

From kp: I have 2 flower pots with the following dimensions that I am trying to calculate the
volume of Soil I will need to fill them. pot #1 29"tall, top of pot 31.5 inches across( radius of 15.5") the bottom of the pot is 21"across (radius 10.5)
Pot #2 29"tall, top of pot 26 across (radius 13") the bottom of the pot 17'"a cross (radius 8.5")
thank you
KP Answered by Penny Nom. 





A conical container and a spherical balloon 
20110406 

From Steven: Water is running out of a conical container 12 feet in diameter and 8 feet deep (vertex down) and filling a spherical balloon.
At the instant the depth of the water in the cone is 4 feet, the radius of the sphere is approximately 4 feet.
The rate of change of the depth of the water in the cone at the instant is approximately ______________ times the rate of change of the radius of the balloon. Answered by Penny Nom. 





The number of points on a line is equivalent to that of a surface 
20110324 

From Gary: I I was reading about how the number of points on a line is equivalent to that of a surface. This was done by taking any point on a line then taking alternating digits and making them as points on an x and y axis therefore points on a surface.The problem is as i see it if you just take a line then hold it over a surface you have just put the points on the line in a one to one correspondence with the points directly under it on the surface.Now you have all the rest of the surface which cannot be mapped onto the line since it is already used up.What am i missing? Answered by Penny Nom. 





What is x to the power of 0? 
20110323 

From Jason: What is x to the power of 0? Answered by Robert Dawson. 





At what rate is the grain pouring from the chute? 
20110226 

From MJ: Suppose that grain pouring from a chute forms a conical heap in such a way that the height is always 2/3 the radius of the base. At the moment when the conical heap is 3 m high, its height is rising at the rate of 1/2 m/min. At what rate (in m^3/min) is the grain pouring from the chute? Answered by Penny Nom. 





Cutting the top off a conical tent 
20110222 

From tom: how far from the top must you cut a conical tent in order to cut the
cloth in half... Answered by Penny Nom. 





Making a truncated cone 
20110218 

From lisa: We need to make a cone that has the following dimensions.
143/8" diameter on large end
133/8" diameter on small end
4" tall
What are the dimensions I need to cut in order to make a cone with one seam? Answered by Stephen La Rocque. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





A cone with a specific angle 
20110201 

From John: Hi my daughter came with a seemingly easy question (which to me it was not)
How to make/calculate a cone of a specific angle from top to bottom radius. Answered by Penny Nom. 





(7cubed * 8(exponent6))exponent 6 
20110129 

From Shalaine: What is the exponential form of (7cubed•8(exponent6))exponent 6? Answered by Penny Nom. 





Flipping a cone over 
20110117 

From Fionna: The height of your cone is "x".
Holding the cone so that the vertex is at the bottom, fill it half full with water. The depth of the water is "1/2x".
Put a lid over the top, and flip it over.
What is the new depth of the water, now that the cone is flipped? Answered by Penny Nom. 





Exponential form 
20110102 

From jumana: find any five examples of exponential form from real life situation Answered by Penny Nom. 





A truncated cone 
20101231 

From jagjeet: dear suppose i have cone of 50cm radius at base and 100cm radius at top at a height of 80cm. now keeping base radius of 50cm and height of 80cm i want to increase top radius to 150cm how will i do that. plz height m talking abt is vertical height not slant height Answered by Penny Nom. 





A water tank has the shape of a right circular cone 
20101207 

From mike: A water tank has the shape of a right circular cone with height 12 feet and radius 8 feet. Water is running into the tank so that the radius r (in feet) of the surface of the water is given by r=0.75t where t is the time (in minutes) that the water has been running. the volume V of the water is given by V=1/3 pi r^2h. Find V(t) and use it to determine the volume of the water when t=5 minutes. Answered by Penny Nom. 





How long will you and your friend be able to talk? 
20101123 

From beket: you and your friend leave your home town at the same time your friend travels by train 45 mph directly east while you travel by train 50 mph going directly south you are talking on cell phone but you plan charges extra if the phones are 100 miles apart. How long will you and your friend be able to talk before the charges increase? Answered by Penny Nom. 





Two algebraic expressions 
20101029 

From chaptay: what is the difference between x(n^2) and x(n)^2 Answered by Penny Nom. 





Powers 
20101020 

From dylan: how do you write 20736 in exponential form .same for 1728 and 50625.
is there a formula to figure out how to express large know numbers in exponential form. Answered by Penny Nom. 





An exponential equation 
20101019 

From Sandi:
Question from sandi, a student:
I have several questions similar to this one and was wondering if you could walk me through this one. I'm totally lost on how to do it.
Paramecia reproduce by splitting in two. In a laboratory flask, a colony of paramecia had an initial population of 500. Each day, the population of the paramecia was counted. The results are as listed.
Time (in days)Population
0500
1600
2720
3864
41037
51244
61493
71792
82150
1.)Using graphing calculator make a scatter plot of the data in table.
I think I did this part right I set my window at Xmin=0 Xmax=10 Xscl=1 Ymin=0 Ymax=2500 Yscl=100 Xres=1
2.) Determine an exponential equation to represent the population as a function of time without using a graphing calculator.I have no clue how to do this.
3.)Suppose the flask and food supply is large enough to support the trend of the population growth. Estimate the population of the colony when the time is 10 days. Answered by Penny Nom. 





Can a function be both even and one to one? 
20101009 

From Tracy: Can a function be both even and one to one? Answered by Harley Weston. 





Exponential form 
20101006 

From celina: what is the exponential form of 4x*4x Answered by Penny Nom. 





(5xy)^5 
20100910 

From ana: (5xy)^5 Answered by Penny Nom. 





Exponential form 
20100824 

From Courtney: What the Exponential form? For Ex. X2*X5*X4?? Answered by Penny Nom. 





A play tent 
20100628 

From Susan: Hi!!!
I am making a play tent as seen at the link below and need to figure out how to get the dimensions for the cone shape. The one shown has 4 different seams, but I guess I can get away with just one seam to sew it together (?) I need it to go over a hula hoop as that is what I am using for the round support at the top. My hula hoop is
35" in diameter from outside edge to outside edge. I would like the height of the teepee to be around 30" from the center to the peak.
Thanks so much, oh my gosh, I have been fretting for 2 days about this and my hair is about to fall out!!!!
Please contact me if you need any additional info.
~Susan
http://www.landofnod.com/family.aspx?c=52&f=4100 Answered by Penny Nom. 





Volume of a styrofoam cup 
20100623 

From Stacy: how do you find the volume of a truncated cup with height of 3, top diameter of 2.5, and a bottom diameter of 2 Answered by Penny Nom. 





Exponential form 
20100616 

From charlotte: what is the exponential form of 6x6x6x5x5x5x5= Answered by Robert Dawson. 





My phone is "sim locked" 
20100610 

From Daniel: Question from daniel:
got a phone that says sim locked, it requires 09 digit code to get in, how many combinations could there be if you could please list the possibilities, the number can be repeated. Answered by Penny Nom. 





graph y=(2x^23x)e^ax 
20100531 

From James: graph y=(2x^23x)e^ax Answered by Robert Dawson. 





More on a truncated cone 
20100528 

From Mike:
Question from Mike, a parent:
I was reviewing this question and answer:
http://mathcentral.uregina.ca/QQ/database/QQ.02.06/phil1.html
But I have trouble with this part:
Now if we express the radius of the inside circle as r and the outside circle's radius is R, then this means r/R is 911/1728. But earlier we said that the outside radius R is simply w more than the inside radius r, so R = r + 282. That means that r/R = r/(r + 282). Now we can simply solve the equation for r:
r/(r+282) = 911/1728
This means r = 314 mm (with rounding).
Can I get more detail on the method to solve for r?
Thank you,
Mike Answered by Penny Nom. 





The "vertex" of a cone 
20100427 

From Tom: By definition a vertex is a point where three edges meet in a 3 dimensional object.
My ten year old son argues that the point at the top of a cone is not a vertex since it does not fit the definition. He got the answer wrong on a test recently but insists that he is right. I need a mathematician to answer this for him. Answered by Robert Dawson and Chris Fisher. 





A conical pile of gravel 
20100413 

From Chassity: The gravel pile is 120' around at the base and goes up 20' high at the peak. How many tons or yards of gravel in that pile? Answered by Penny Nom. 





If a third is a fourth of a number, what is the number? 
20100408 

From larry: If a third is a fourth of a number, what is the number? Answered by Penny Nom. 





A max min problem 
20100406 

From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





A 4digit phone code 
20100121 

From pat: my daughter can`t remember her 4digit code to unlock her phone. she is pretty sure it starts with a 4. can you help us? my brain is locked up Answered by Robert Dawson. 





The cube of an integer 
20100120 

From Shankar: Can the cube of an integer end with 1985 ones ? Answered by Robert Dawson. 





A cone circumscribed about a given hemisphere 
20100119 

From Neven: The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base?
(G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives) Answered by Chris Fisher. 





The volume of a frustum 
20091229 

From dave: I have a frustum top 1.7r bottom .55r and 2.14 h
I have to calculate cement in a silo every week.
I am not very good at maths but i have been adding the top and bottom
to get an average so as to turn it into a cylinder and i come up with
8.5m3 I know that the correct volume is 9.24 m3. Can you tell me why
getting an average width on the top and bottom of a frustum doesn't work.
Thank you. Answered by Chris Fisher. 





A pile of sand 
20091216 

From Malik: Sand is leaking out of a hole at the bottom of a container at a rate of 90cm3/min. As it leaks out, it forms a pile in the shape of a right circular cone whose base is 30cm below the bottom of the container. The base radius is increasing at a rate of 6mm/min. If, at the instant that 600cm3 have leaked out, the radius is 12cm, find the amount of leakage when the pile touches the bottom of the container. Answered by Harley Weston. 





Oneeighth of one million dollars 
20091116 

From Jarrett: what is 1/8 equal to out of a million dollars. Answered by Penny Nom. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





Evaluating x^2 + (yz  3)^2 
20090928 

From Kathy: My daughter and I are having trouble solving this equation:
x²+ (yz – 3)²
if x=4,y=2 and z=0
We are having difficulty with the x² part of the equation. Thanks Answered by Penny Nom. 





Exponential form 
20090918 

From karen: Q: Write the following in exponent from: a * a * a * a * * * a, where there are n 1 a's
note: *asterisk means times. Answered by Penny Nom. 





how many ones are in 1 million 
20090917 

From djuan: how many ones are in 1 million Answered by Harley Weston. 





Exponential form 
20090908 

From hanna: hi,
well i am really bad in math and i have a math paper and i was just
wondering what 3x3x3x3x3 was in exponential form and what is
exponential in a way a person like me would understand? Answered by Penny Nom. 





What is 8 tons in exponential form? 
20090901 

From Tyler: what is 8 tons in exponential form Answered by Penny Nom. 





Exponential form 
20090831 

From cecil: what is the exponent form 564000? Answered by Stephen La Rocque and Harley Weston. 





Making a cone 
20090819 

From angela: how can i make a cone with a 6cm of heigth and has 2cm radius in the opening?? Answered by Stephen La Rocque. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





The volume of a telephone pole 
20090811 

From robert: 12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions? Answered by Harley Weston. 





Exponential form 
20090805 

From motaz: Let x = log_2 1/8 Write the exponential form of the equation and solve the equation for x Answered by Stephen La Rocque. 





A cone with the top cut off 
20090802 

From Paul: I am making a cone with a diameter of 1300, a base of 500, a side length
800. I need to workout so I can draw it out flat, cut it out, and make into
a cone. Answered by Harley Weston. 





The lateral area of a cone 
20090715 

From ashley: What is the radius of a cone with the lateral area being 443.3 mm^2 and the slant height being 14.7 mm. Answered by Penny Nom. 





Fractional Exponents 
20090707 

From bob: 2^5/2  2^3/2 Answered by Janice Cotcher. 





Find out the length of a cup when its volume is halved 
20090525 

From Thomas: I'm having trouble with a question.
What kind of formula would i use to find out the length of a cup when its volume is halved? Answered by Stephen La Rocque. 





Nickels, dimes and quarters 
20090525 

From Amy: Coming from South Africa I find working with nickels, dimes and quarters confusing.
How many dimes are in a nickel and how many quarters are in a dime? Answered by Penny Nom. 





The dimensions of a larger cup 
20090523 

From Elizabeth: Hey
If i have a cup that holds a volume of 477mL and the bottom radius is 2.8cm and the top radius is 4.9cm and the height is 10cm. If i increase the volume by one and a half times what is the new measurements if the cup is directly proportional to the first one.
Thank you Answered by Stephen La Rocque and Penny Nom. 





The volume of a cone 
20090520 

From Lillian: okay! so my math question is about the volume of a cone! my work sheet gave me the volume and base of the cone and asked me for the height! please help me discover the height of a cone when the volume is 78.54 cm (cubed obviously) and the base is 6 centimeters. thanks so much :) Answered by Penny Nom. 





Rewriting an Expression with Positive Exponents 
20090513 

From lynda: (4x)to the 0 power times x squared over 3to the 3 power i have to rewrite the expression with pos exponents Answered by Janice Cotcher. 





1/(square root 16) 
20090421 

From Conor: Hi Guys!
I dont have a square root sign so im just gonna use the ^ symbol :)
I am just wondering if
1/(16^a)
when rewritten can it be
1/16 to the power 1/2
Thanks :) Answered by Penny Nom. 





12 oz. cup 
20090419 

From Tom: I am a ceramic teacher and wanted my students to make a 12 oz. cup, what formula should we use? Answered by Chris Fisher. 





Exponential form 
20090416 

From Pete: Hi,
How do you express ³√h^4 in exponential form. I am having a lot of
trouble with this one.
thanks
Pete Answered by Stephen La Rocque. 





A large, hollow, ice cream cone 
20090403 

From Darah: A manufacturer is making a large, hollow, ice cream cone to serve as an ad for a local BaskinRobbins. The ice cream cone is made up of a cone with height 8 feet, topped by a hemisphere with radius 6 feet. How much ice cream could the hollow object hold? If a gallon is 0.13368 cubic feet, how many gallons does it hold? If 3 gallons of BaskinRobbins heavy cream chocolate blend weighs 24 pounds, how much would the ice cream cone weigh, excluding the weight of the construction material? Answered by Stephen La Rocque. 





Grain of rice on a chess board 
20090330 

From andy: Is there an easy way for my students to find out 8 to the power of 21 to solve the grains of rice doubling investigation on a chessboard? Any suggestions welcome. Thanks very much Answered by Robert Dawson and Claude Tardif. 





How many ball bearings can you make from a cone? 
20090314 

From Vatsal: there is a sum in my maths book which states the following:
how many ball bearings of diameter 2.5 cm. can you get by
melting a solid metalic cone of radi. 20cm and a Hight of 5 meters?
how do i do this please tell me even the minute things like cancellatoins and where to
use = , ; or any such thing because Im a bit weak in maths Answered by Harley Weston. 





Express 13 mills as a decimal part of $1.00. 
20090313 

From Kenneth: Hello:
I read the following in an old business mathematics textbook:
"Express 13 mills as a decimal part of $1.00."
I can determine the answer as follows: There are 1000 mills in or per
$1.00. 13 mills divided by 1000 mills/$1.00 equals $0.013, the answer.
My question is as follows: What does "...as a decimal part of $1.00"
indicate or represent from "Express 13 mills as a decimal part of
$1.00."?
Is (a decimal part of $1.00) any decimal less than $1.00 with the decimal having a dollar sign
before it.
I thank you for your reply. Answered by Harley Weston. 





If 5 to the power of y = 625, what is y? 
20090302 

From Charlene: If 5 to the power of y = 625, what is y? Answered by Penny Nom. 





Comparing 2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 etc. 
20090301 

From JIM: WHICH WOULD BE LARGEST USING THE NUMBERS 2,3,4,5 :
2^3^4^5 ; 2^5^4^3 ; 5^4^3^2 : ETC. OF ALL THE POSSIBLE
COMBINATIONS ? IS THERE A GENERAL FORMULA ? I AM
UNABLE TO FIND A COMPUTER THAT CAN HANDLE SUCH LARGE
CALCULATIONS . I ALSO DO NOT THINK IT IS AS STRAIGHT
FORWARD AS FIRST APPEARS . THANKYOU , JIM Answered by Stephen La Rocque, Robert Dawson and Harley Weston. 





A conical sleeve 
20090217 

From Jonathan: I'm having a hard time making a design pattern for a cone sleeve, the thing is the cone sleeve is 22 degrees, how can i know the angle of this when it is flat on paper, based on my calculations, it should be around 66  69, but i want it to be exact can anybody help? Answered by Penny Nom. 





A fraction with negative exponents 
20090214 

From Gabriel: What does the line seperating the top from the bottom mean? what does it tell you to do and what is the answer to the question?
Question 3
Simplify. Write the answer using only positive exponents. Assume all variables represent nonzero numbers.
(x^5)^4(x^1y)^3
________________
(xy^4)^3 Answered by Penny Nom. 





Large exponents 
20090212 

From Dan: I would like to know how to calculate a whole number as the base that
has a large exponent;Such as 7 to the 23rd.power=. Otherwise if I use a calculator
it goes off the scale. Answered by Stephen La Rocque. 





6^x = y 
20090212 

From Jamie: Find x:
6^x=y Answered by Harley Weston. 





A sphere in a cone 
20090210 

From Shubham: An upturned conical vessel of radius 6cm and height 8cm is completely
filled with water. A sphere is lowered in the conical vessel filled with
water and the size of sphere is such that it just touches the sides of
cone and is just immersed. What fraction of water overflows? Answered by Harley Weston. 





Fertilizer in a bin 
20090203 

From Todd: Hello I am looking for a formula to figure out the fertilizer volume in a hopper bottom bin not only when it is full but part full as well. When you are filling it is heaped up in the middle to make a cone and when you are emptying the bin the cone is inverted so it would be nice to be able to quickly figure out the tonnes partly filled and when full.
Lets say the bin is 32 feet high from top of bin where you fill to the bottom where the product goes out and it is 16 feet in diameter. I know how to calculate the cylinder it is the cones on the top and bottom of the bin I have the main question on. Answered by Harley Weston. 





Missing three digits in a phone number 
20090130 

From Elmer: I have part of a phone number. the first 3 digits are 212, the last digit is four, and the three missing digits are all odd, how many numbers will I have to call to get the right number?
212 _ _ _ 4? Answered by Stephen La Rocque and Penny Nom. 





Water flowing from a cone to a cylinder 
20090123 

From Ray: Water is passing through a conical filter 24 cm deep and 16 cm across the top into a cylindrical container of radius 6 cm. At what rate is the level of water in the cylinder rising when the depth of the water in the filter is 12 cm its level and is falling at the rate of 1 cm/min? Answered by Harley Weston. 





The volume of a cone 
20090113 

From ab: the area of the base of the cone shown is 314 cm and it's height is 12 cam what is the volume? Answered by Penny Nom. 





The top half of a cone vs. the bottom half of the same cone 
20090108 

From Tammy: What is the ratio of the volume of the top half of a cone vs. the bottom half of the same cone? Is it seven times larger, or four times larger? and is the ratio consistent regardless of the size of the cone opening? Answered by Penny Nom. 





50 coins with a value of $1.00 
20090108 

From Ana: you have 50 coins which have a total value of 1.00. What are the coins and how many of each do you have? Answered by Robert Dawson. 





The radius of a cone 
20090102 

From kalpaj: A conical funnel holds 100ml. If the height of the funnel is 10 cm, determine
its radius, to the nearest tenth of a centimeter. Answered by Penny Nom. 





What is i^i? 
20081227 

From randomness: i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Answered by Robert Dawson and Penny Nom. 





Solving an equation for D 
20081218 

From Darrin: In his finance class, my son is being asked to take the following equation and solve for "D":
1 / [1  (1 + D/12)^T] = (1 / D) * [((12*B) / (P*T)) + Y + ((12N * Z) / (360T))]  [(12Z) / (360T)] * F Answered by Robert Dawson. 





The 2 rightmost digits 
20081218 

From Peter: Is there a pattern for the 2 rightmost digits of a power? For example, one problem for a math competition was what are the 2 rightmost digits of 3^1993? Answered by Robert Dawson and Victoria West. 





The nth power 
20081212 

From Kellie: I am taking a 9th grade course yet im in 7th grade. I do not understand the nth power
and i have no clue what it is. could you explain to me what it is? Answered by Robert Dawson. 





Ratio of Volumes of a Cylinder and a Cone 
20081206 

From rohan: A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES. Answered by Janice Cotcher. 





Three onedigit numbers 
20081206 

From JOANNA: Could you please tell me what Adding Three OneDigit Numbers += 15 19 without using any number twice Answered by Penny Nom. 





The volume of a cone 
20081203 

From Tamriko: Hi! Help me, please to solve the following problem: The diameter of an icecream cone is 6 cm and the slant height is 10 cm. What volume of icecream would fit inside the cone? Thanks! Answered by Penny. 





Related rates 
20081126 

From Lyudmyla: How fast is the volume of a cone increasing when the radius of its base is 2 cm and growing at a rate of 0.4 cm/s, and its height is 5 cm and growing at a rate of 0.1 cm/s? Answered by Harley Weston. 





How do you solve " (x4)^3/2 = 6 "? 
20081117 

From Jim: How do you solve " (x4)^3/2 = 6 " ? Answered by Penny Nom. 





The volume of a cyclone 
20081113 

From Dianna: I need to figure the cubic yards of a cyclone. 144" down to 48" 60" high Answered by Penny Nom. 





A conical funnel 
20081112 

From Rachael: Hello, I am a 10th grader in AP Calc, and can not figure out this question:
Water is running out of a conical funnel at the rate of 1 inch^3/sec. If the radius of the base of the funnel is 4 in. and the altitude is 8 in., find the rate at which the water level is dropping when it is 2 in. from the top. Answered by Harley Weston. 





The prime factorization of one billion 
20081102 

From Alta: The prime factorization of 1000 is 2 cubed times 5 cubed. How do you write the prime factorization of one billion using exponents? Answered by Penny Nom. 





Equations with the variable in the exponent 
20081028 

From fari: Solve for x
5 * 4^x3=40
5^x=25^(x+8) Answered by Penny Nom. 





Water is leaking from a conical tank 
20081024 

From Kimberly: Water is leaking out of an inverted conical tank at a rate of 12000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank. Answered by Stephen La Rocque. 





Put in lowest terms 6a^2c/8ab 
20081024 

From hana: put in lowest terms 6a^2c/8ab Answered by Stephen La Rocque. 





Exponential form 
20081021 

From layla: how we wite 256 in exponential form Answered by Harley Weston. 





The volume of a slice from a wedge 
20081016 

From Jeff: If I have a wedge shaped object (ie, a triangle of nonspecific type
extruded along a length) and it is sliced from the twocorner base at
one end to the onepoint tip at the other, what is the volume of the
upper (smaller) part as a percentage of the whole? I hope I have
explained it clearly enough. Thanks. Answered by Harley Weston. 





The rate of change of the volume of a cone 
20081015 

From Barbara: Suppose that both the radius r and height h of a circular cone change at a rate of 2 cm/s.
How fast is the volume of the cone increasing when r = 10 and h = 20? Answered by Harley Weston. 





A cone shaped pile 
20081010 

From Nadine: I have a pile of wheat in the shape of a cone. I would like to know how much
wheat I have. I have found the equation "V=1/3 pie r squared h" , but it dosn't
work! The pile is 7 feet high, diameter is 50 feet, circumference is 185 feet.
I also measured the slope 19feet. (Probably not needed) You need to know that
wheat weighs 60 pounds per bushel, and I would like to know how many bushels
I have. Even if I could receive the # of Volume Bushels, I could convert that.
Can you help me?? Answered by Stephen La Rocque. 





Logs and exponentials 
20081006 

From Charles: I seem to remember you could solve exponential problems using natural logs quite simply without calculators, such as the fifth root of 400 or 33 to the 4th power. All you did was convert the number to its natural log and then just divide by 5 or multiply by 4 and then convert it back. I just remember how to do this. Thanks. Answered by Harley Weston. 





4^x = 2^x + 12 solve for x 
20081002 

From Dave: 4^x = 2^x + 12 solve for x. Answered by Harley Weston. 





Exponential form 
20080925 

From Pat: The African bush elephant is the largest land animal and weighs about 8 tons. Write this amount in exponential form. Answered by Penny Nom. 





Exponential form 
20080916 

From shawn: Write the product in exponential form: 5.5.5.2 Answered by Penny Nom. 





What is the derivative of (2^sinx)/(logbase4(2x+1))? 
20080916 

From Jesse: What is the derivative of (2^sinx)/(logbase4(2x+1)) Answered by Harley Weston. 





Solving Exponential Equations Using Logarithms 
20080915 

From Todd: 7(6^x)=6e^2x Answered by Janice Cotcher. 





An ice cream cone 
20080909 

From olivia: Judy has a sugar cone and wants to know how many cubic inches of ice cream it will hold if it is filled completely to the top of the cone and no more. The cone has a height of 4.5 inches and a radius of 1.5 inches. Answered by Penny Nom. 





The biggest right circular cone that can be inscribed in a sphere 
20080908 

From astrogirl: find the volume of the biggest right circular cone that can be inscribed in a sphere of radius a=3 Answered by Harley Weston. 





An exclusion zone around a triangle 
20080907 

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. 





2^x = 1,000,000 
20080906 

From Peter: How do I solve for "x" in the following equation: "2 to the power of x = 1,000,000" ? Answered by Penny Nom. 





The square root of 2 the the X power 
20080905 

From Peter: How can I rewrite the expression: The square root of 2 the the X power? Answered by Penny Nom. 





1,679,616 as a power of 6 
20080903 

From Denise: express 1,679,616 in exponential form as a power of 6. Answered by Penny Nom. 





A cardboard spaceship 
20080831 

From Lee: I am building a "cardboard" spaceship for my 4 year old grandson.
The cabin is a dishwasher box with a cool control panel and elipse shaped
windows.
I really need help designing the cone or"nosecone".
The diameter of the base is 26", 24" tall, with a 6" diameter opening
at the top.
Thank you for the help!
Lee Answered by Penny Nom. 





Solve e^x + e^(x+1) = 250 
20080825 

From Laura: "solve this equation correct to three decimals"
e^x + e^x+1= 250 Answered by Penny Nom. 





BEDMAS 
20080812 

From Rebecca: I have 3 questions.
1) I don't really understand BEDMAS.Im going in to the 6th grade and im
kind of nervis about it.?
2)When you're doing BEDMAS what does the small 3 or 2 above the
other numerals mean?
3)How would you answer this:5+2 x 9  9 x 12= ?? Answered by Janice Cotcher. 





A cone on the end of a cylider 
20080805 

From Jerry: Hi.
I need to make a plastic cone to fit on the end of a cylinder. The only dimension i have is the diameter of the cylinder.
This 553 mm.
I need to find the formulae required and how much material will be required. Answered by Penny Nom. 





Find the product of 2^35 and 5^38 in sci. notation. 
20080803 

From Peter: I am preparing for a competition and a lot of the noncalculator problems are like find the product of 2^35 and 5^38 in sci. notation. How would you do that? Answered by Penny Nom. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





The number of digits in a really big exponent 
20080721 

From Pete: how would you find the number of digits in a really big exponent without a calculator? Answered by Penny Nom. 





A cube inscribed in a right cone 
20080716 

From Steven: A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone? Answered by Victoria West and Harley Weston. 





Making Change 
20080709 

From Peter: In how many ways can you make 30 cents with quarters, nickels, and pennies? Answered by Penny. 





Exponential form 
20080703 

From Kent: How to write 8 365 005 106 in expanded and exponential form? May I request you also to explane how does it solve. Answered by Stephen La Rocque. 





Units digit 
20080702 

From seemachauhan: How to find unit digit of various numbers and what are unit digits? Answered by Penny Nom. 





Some phone numbers 
20080630 

From star: What do you think the probability of finding the last 3 digits of a telephone number if the 1st digit begins with 7? Answered by Janice Cotcher and Harley Weston. 





Write log_2 (1/8) = 3 in exponential form 
20080627 

From Jaime: how do you write log2 (1/8) = 3 in exponential form?
the 1/8 is a fraction and the 2 is a base of 2 Answered by Penny Nom. 





How many face does a cone have? 
20080621 

From Vanessa: How many face does a cone have? Answered by Harley Weston. 





(2b^1c^3)^3 (b^4c^2)^0 
20080605 

From ashley: Simplify this expression
(2b^1c^3)^3 (b^4c^2)^0
Please help me. I not sure about the zero on the outside of parentheses. Answered by Penny Nom. 





Liquid is being pored into the top of a funnel 
20080525 

From Stella: Liquid is being pored into the top of a funnel at a steady rate of 200cm^3/s. The funnel is in the shape of an inverted right circular cone with a radius equal to its height. It has a small hole in the bottom where the liquid is flowing out at a rate of 20cm^3/s. How fast is the height of the liquid changing when the liquid in the funnel is 15cm deep?
At the instance when the height of the liquid is 25cm, the funnel becomes clogged at the bottom and no mo re liquid flows out. How fast does the height of the liquid change just after this occurs? Answered by Stephen La Rocque. 





The cube of 2y in exponential form 
20080519 

From Xiu: I dont get this question..
Write "the cube of 2y" in exponential form. I know the answer is (2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me? Answered by Leeanne Boehm. 





The inverse of a function 
20080503 

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





The volume of a stone 
20080417 

From sara: a rectangular tank 30 cm long and 20 cm wide is filled with water to a depth of 8 cm. When a stone was put in, the water level rose to 11 cm. Find the volume of the stone. (Assume that the stone is completely under water.) Answered by Penny Nom. 





A truncated cone 
20080411 

From jason: i need to know how to figure the cubic feet of a cone that the top is 72" wide the bottom is 25" wide and it is 48" tall.
is there a specific formula for this? Answered by Penny Nom. 





1(1P)^75=0.05 
20080405 

From Amy: 1(1P)^75=0.05 Answered by Stephen La Rocque and Penny Nom. 





The exponential form of x radical y to the third power 
20080330 

From Jennifer: what is the exponential for of x radical y to the third power Answered by Penny Nom. 





Exponential form 
20080216 

From annna: i already got the answer for what is the prime factorization of 648 which is 2x2x2x3x3x3x3
but how do i write that answer in exponential form? Answered by Penny Nom. 





Growth factor and growth rate 
20080213 

From william: what is the difference between growth factor and growth rate? Answered by Stephen La Rocque and Harley Weston. 





Why is the number 1 neither prime nor composite? 
20080207 

From ronni: why is the number 1 neither prime nor composite? Answered by Harley Weston. 





Negative Exponents 
20080129 

From Bill: t to the negative fourth power inside parenthesis to the ninth power
OVER
t to the negative fourth power inside parenthesis to the third power
I am confused on how to start the problem. What I did was invert the Ts to make them positive and I then multiplied the powers. I am not sure if this is the correct process. Answered by Harley Weston. 





Belledout pier 
20080128 

From Gina: I need to know how to find the total yards needed to fill a concrete pier that is 54"/ 108" and 26' deep.
That is...54" @ the top of the pier belled to 108" @ the bottom...26' deep. Answered by Stephen La Rocque. 





x^3 y^(6) 
20080124 

From Bill: I need help completing this negative exponents problem:
x to the power of 3 multiplied by y to the power of negative 6.
What would the process to solving this problem be? Answered by Penny Nom. 





How do I write the following in exponential form? 
20080109 

From Mandy: How do I write the following in exponential form?
( square root of a^2 b)^5 Answered by Penny Nom. 





Exponential form 
20080108 

From liam: i was wondering if anyone could help me with this question and tell me how and what the did; exponetial form of 4 326 180 501 Answered by Stephen La Rocque. 





Multiplying exponentials 
20080102 

From jessie: Can you please explain how to put x^3 y^2 times x^1 y^3 in simplest exponential form? Answered by Penny Nom. 





Radicals in exponential form 
20080102 

From Andre: The title of the section in my textbook is to write each of the following
radicals in exponential form.
My question is how do u write the squareroot of 10 in exponential form? Answered by Penny Nom. 





Smallest cone containing a 4cm radius inscribed sphere 
20071219 

From Eva: A sphere with a radius of 4cm is inscribed into a cone. Find the minimum volume of the cone. Answered by Stephen La Rocque. 





Exponential form 
20071130 

From Sasha: How do I write the number 127398 in exponential for? Answered by Penny Nom. 





Exponential Growth 
20071119 

From lisa: Hi i am a 8th grader who is learning about algebra
and we are having test on exponent and i don't really get it
i asked my teacher and she told me i should pay more attention
so i want to know what exponential Growth means Answered by Penny Nom. 





The vertex of a cone 
20071118 

From miriam: how many verticies does a cone have Answered by Penny Nom. 





Exponential form 
20071116 

From ashley: write a sentence for exponential form. Answered by Penny Nom. 





Cones and pyramids 
20071110 

From Eric: I have a question regrading the differences between a cone and a pyramid.
In my son's Maths workbook, a cone is always referred to as a pyramid,
which confuses me very much. I understand that a pyramid is a special case of a
cone and therefore you can refer a pyramid as a cone but not the other way around.
Am I correct? Answered by Harley Weston. 





Distributing prize money 
20071108 

From Barbara: Question from Barbara, a student:
In writing competition, the first place winner receives 1/2 of the prize money. The second runner up receives 1/4 of what the winner won.
what was the total amount of prize mone distributed if the winner receives $6,000? Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20071108 

From amarilis: why is the number 1 neither prime nor composite? Answered by Penny Nom. 





The sum of the ones 
20071029 

From Hangsun: When 2 two digit numbers are added what is the greatest possible sum of the ones? Answered by Penny Nom. 





A graph with 100 vertices 
20071024 

From amarjeet: let g be a graph with 100 vertices numbered 1 to 100. Two vertices i and j are adjacent only if ij=8 or ij=12. The number of connected components
in g are:
1. 8
2. 12
3. 4
4. 25 Answered by Penny Nom and Victoria West. 





Stanley Cup costume (truncated cone pattern) 
20071019 

From Janet: You hockey fans will love this question. I am making a Stanley Cup halloween costume and need a flat pattern for the bowl portion. I believe a truncated cone will work nicely. Base circumference needs to be 32" (10.19 diameter). Top circumference needs to be 44" (14 diameter). It needs to be 8" high. Thanks for your help. Answered by Stephen La Rocque. 





Surface area of an openended cone 
20071016 

From Lorne: What is the surface area of an open ended cone? Measured at 10' high,
16' diameter on the bottom and 2' diameter at the top. Answered by Stephen La Rocque. 





Doubling every day 
20071007 

From Jerrie: Patti saved pennies for 10 days. The first day she saved 1 cent. Every day after that she saved twice as much as the day before. How much money did Patti save altogether? Answered by Stephen La Rocque. 





how do you get 9^59^4/8 to equal 9^4 
20071001 

From nathen: how do you get 9^59^4/8 to equal 9^4 Answered by Stephen La Rocque. 





Two power expressions 
20070929 

From James: find the values for a and b
(a*x to the power of 1*y)(1/2*x*y to the power of b)=6*y to the power of 6
please show me how to do this. Can I begin by taking out the powers? Answered by Leeanne Boehm. 





Size of a sphere fitting inside a cone 
20070927 

From Juan: I am supposed to find the largest sphere that
will fit into a cone. I am assuming is a maximizing problem, but I am not sure
of what relation (between a cone and a sphere) to use. Answered by Penny Nom and Stephen La Rocque. 





Exponents 
20070926 

From Calvin: Exponential form
5 3exponent x 5 4exponent divide 5 2exponent Answered by Stephen La Rocque. 





Exponential regression 
20070924 

From Anonymous: I need help in finding this. Find a formula for exponential regression.
Determine how to calculate a and b in the formula.
Y = ba^x
where y is as a function of x. Answered by Penny Nom. 





Large exponents 
20070924 

From Kira: Is there an easy way to calculate a number with a large exponent? For example, 2(10)^35. Answered by Stephen La Rocque and Victoria West. 





12 men can complete a work in 8 days 
20070923 

From farah: 12 men can complete a work in 8 days. 3 days after they started working, 3 more men joined. In how many days will all of them together complete the remaining work. Answered by Stephen La Rocque. 





Solving an equation with fractions 
20070920 

From Len: I am having a brain cramp or maybe I just forgot some basic math,
but I am having trouble solving for "r" in your truncated cone example
where r/(r+w)=r/R or r/(r+282)=911/1728. Could you refresh my memory
by showing the steps to solve for "r"? Answered by Harley Weston. 





Tens and ones 
20070916 

From julia: My son has come home with a math question "what i know about 10s and 1s" we're totally stumped any information you can provide would be greatly appreciated Answered by Harley Weston. 





The contents of a silo 
20070914 

From Steven: I need to know how to find the weight of the contents of a silo that is 4 feet across and is funnel shaped at 60 degrees Answered by Penny Nom. 





Exponential form 
20070912 

From Ericha: How do I express 1,679,616 in exponential form as a power of 6 using a calculator? Answered by Stepehe La Rocque and Penny Nom. 





Prime factors in exponential form 
20070906 

From Michelle: how would you write this: factor 48 as a product of primes written in exponential form Answered by Stephen La Rocque. 





Exponential form 
20070905 

From jeanette: the African bush elephant is the largest animal and weighs 8 tons. write this amount in exponential form. Answered by Stephen la Rocque and Penny Nom. 





X^3 = 3/10 
20070905 

From ioana: If we have X at power 3 that result equally with 3/10 haw much X is ?? Answered by Penny Nom. 





Exponential form 
20070831 

From Victoria: The cost of each space shuttle is about $10,000,000.
Write this amount in exponential form. Answered by Stephen La Rocque. 





Exponential form 
20070829 

From Emily: Write the Exponential Form of 125 x 25 and 81 x 27. Answered by Stephen La Rocque. 





A truncated cone 
20070824 

From JUAN: i need to create a template for a cone that has a 4 " opening at top, a 14" base and 12" tall.Can u tell me how to achieve this ?
u have similar problems but when i try to do it , is not coming up right , please help.. Answered by Harley Weston. 





How much would 3 yards of stone cost? 
20070821 

From Sue: If it costs $13.50 a ton of 3/4" stone, how much would 3 yards of stone cost? Answered by Steve La Rocque. 





Logs and exponentials 
20070731 

From Marsia: Explain how the functions of exponents and logarithms relate to each other. Answered by Penny Nom. 





A cone with two fruits 
20070726 

From Meg: You have a cone shaped bag. At the bottom of the bag is an orange with
radius r. On top of the orange is a melon with radius R. It touches the
orange and fits snugly in the bag, touching it in a ring around the orange.
Its top is at the same level as the top of the bag. What is the radius of the
cone? Answered by Stephen La Rocque. 





A one to one function 
20070724 

From Marsia: Explain what it means for a function to be one to one. Answered by Harley Weston. 





Calculating sales taxes 
20070711 

From Tonya: Hi, Im having trouble calculating GST and PST
I know that in this province, GST is 6% and PST is 7%, I have a total of $275, and GST is 0.06, and PST is 0.07, so do I add those two and multiply them by the total, $275? Answered by Stephen La Rocque. 





The lock code for my phone 
20070630 

From Amanda: okay so i forgot my lock code for my phone its four digits but i know it doesn't have a 1 or a 0 in it so it has to be from numbers 2 to 9 i need to know all the four digit combinations asap cause i cant use my phone till can someone please help me Amanda Answered by Penny Nom. 





If A is 1 and Z is 26 
20070629 

From Sue: If A is 1 and Z is 26 is there a word that when you multiply all the numbers instead of letters adds up to a million? Answered by Chris Fisher and Harley Weston. 





Exponential form: x^y 
20070622 

From Kishor: whats the easy way to calculate X raised to Y where y is much greater than x. Answered by Stephen La Rocque. 





Volumes of cones and cylinders 
20070529 

From George: 1. The volume of a cylinder is 1353cm3
A) What is the volume of a cone with the same radius as the cylinder
but double the hieght of cylinder?
B) What is the volume of a cone with the same height as the cylinder
but with three times its radius? Answered by Steve La Rocque and Walter Whiteley. 





Solve for I 
20070523 

From Mark: A=4.9(B)*C^(.00925(D.542))* E^(.015(D))*E^(.013(F))* (G/B)^(.00825(D.225))* H^.877*(I/B)^.511*(J/B)^.319 Answered by Stephen La Rocque. 





Constant rate of sand falling in a cone 
20070520 

From Nhi: Sand is falling into a conical pile . After 5 min. the pile has radius 24 and height 26 . After 7 min. tell how far the point c. is from the top of the cone (A). Answered by Stephen La Rocque. 





Lateral area of a right cone 
20070517 

From Crystal: In my homework the question says the lateral area of a right cone is 226.08 cm cubed.
the slant hieght is 12 cm. Find the total surface area. How do I do that? Answered by Stephen La Rocque. 





Maximizing the volume of a cone given the slant length 
20070514 

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. 





Prisoners 
20070512 

From Ryan: Last monday, the county jail had 200 prisoners. Of these, 130 were accused of felonies, and 121 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? Answered by Stephen La Rocque. 





Exponents and geometry 
20070512 

From Cynthia: Hi is (x^6)(x^4)1/2 = 5
And
How does 1/2(3.14)(4.1) =26.3917 Answered by Penny Nom and Stephen La Rocque. 





Understanding log equations 
20070510 

From Sean: The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by N (t) = a / 1+ be^ kt. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b. If the rumour is initially spreading at the rate of 500 people per day, find k. Answered by Penny Nom. 





Is the point on a cone called a vertex? 
20070509 

From Felicia: Does a cone have a vertice? My teacher says that a vertice can only be
made if two or more edges join up at an angle, so what do you call a point on a cone? Answered by Walter Whiteley. 





Slicing a doublenapped cone with a plane 
20070507 

From Andrew: I am writing a paper about creating parallel lines by slicing a doublenapped cone with a plane. I have found out how it can be shown by algebra that the equations for parallel lines are generated from the degenerate case of a second degree polynomial in two variables, but I have yet to find a source with a visual representation of this case. Do you know if it exists? Answered by Chris Fisher. 





The radius of a cone 
20070507 

From Braden: i need to find the surface area but i only have the slant height and the height i need the radius how do i find it? Answered by Penny Nom. 





Maximize the volume of a cone 
20070427 

From ashley: hello,
I've been stumped for hours on this problem and can't quite figure it out.
The question is: A tepee is a coneshaped shelter with no bottom. Suppose you have 200
square feet of canvas (shaped however you like) to make a tepee. Use
calculus to find the height and radius of such a tepee that encloses the
biggest volume.
Can you help?? Answered by Stephen La Rocque and Penny Nom. 





What is the square root of 729 to the third power? 
20070425 

From Tori: What is the square root of 729 to the third power? Answered by Penny Nom. 





Exponential form 
20070416 

From Cassia: I was just wondering, how do you write the squared root of 7x(to the 5th) in
exponential form? If you could help explain that I'd be grateful. Thanks Answered by Brennan Yaremko. 





How do i form a paper cone 
20070414 

From Sash: How do i form a paper cone with the height of 25 cm, the slant height
of 25.8 cm, and the radius of 6.2 cm? Answered by Stephen La Rocque. 





3 divided by 3 to it's fifth root 
20070406 

From Annie: How do I transform the equation 3 divided by 3 to it's fifth root to simple radical form
(getting the radical out of the denominator)? Answered by Penny Nom. 





A "claw setting" for a gemstone 
20070330 

From Stephanie: I'm trying to make a cone out of a flat sheet of metal for a "claw setting" for a gemstone.
The cone must be 8mm wide at the top and 11mm long tapering to a point. But because the prongs must be cut out of the top the cone should not start to taper for a length of 3mm from that top 8mm. The 3mm prong is then bent over the 8mm stone. That probably doesn't make enough sense. But I don't know how to explain it. If it helps a claw setting is the very common prong setting for engagement rings or earrings. Please help as soon as possible as this is a commissioned piece for someone and I'm running out of time. I don't remember any math really from high school so please make the instructions really easy to follow. Thank You!! Answered by Penny Nom. 





A one pass calculation of standard deviation 
20070319 

From Murtaza: Hi
I searched the listings but couldn't find what i am looking for. I have a dataset and i am allowed only 1 pass through it. At the end of this pass i must have the mean and standard deviation. Calculating the mean is easy as also demonstrated in your listings. I think the same can be done for standard deviation as well. But the doubt that i have is this : Will the calculated standard deviation be sequence dependent ? i.e. if i change the order in which the data items enter the system, will the std deviation also change ??
Thanks in advance
Murtaza Answered by Penny Nom. 





Negative exponents 
20070314 

From cookie: (2.50x^3)  (3.0x^1)
please show me how to do this. The answer in the book is 7.5 x ^4 Answered by Penny Nom. 





exponential decay of Carbon14 
20070312 

From Christine: How do I set up the exponential decay formula for Carbon 14 with an initial amount of 1500 grams. Answered by Stephen La Rocque. 





A truncated cone 
20070310 

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 Answered by Penny Nom. 





The volume of a styrofoam cup 
20070308 

From leanna: find the volume of a styrofoam cup if the diameter of the top is three inches, the diameter of the base is 2 inches, and the height is 4 inches. Answered by Penny Nom. 





A metal shroud for a outdoor fireplace 
20070306 

From Arnold: I am making a metal shroud for a outdoor fireplace, it is basically a lampshade type pattern,like the bottom of a cone.The top has to be 6 inches to fit the 6 inch stovepipe,and the bottom will be a 24 inch circle. the sides will be 18 inches in length.With the cost of the sheet metal,I can only afford to cut this out once,can you help me with the pattern ? Answered by Penny Nom. 





A long narrow cone 
20070304 

From Amy: I am an art student making a piece of jewelry out of a flat metal sheet. I'm trying to make a long narrow cone that's roughly 3 1/4" long and just slightly under 1" wide at the base. Since I'm no math wiz, I'm having a really hard time. Please help. Answered by Penny Nom. 





The lateral area of a cone 
20070227 

From Michael: Ive seen the other question about surface areas. I still don't understand the lateral area. In my math book, it has (pi * r * L) as the equation, r = radius and L = height of the cone. This is 8th grade math. Thanks. Answered by Penny Nom. 





The radius of a cone 
20070226 

From lee: hi i have a cone to calculate, the height and radius are equal and the slant height is 0.5m
the total surface area is 15m sq i need to calculate the radius of the cone Note : this will lead to a quadratic equation could somebody have a look please Thanks Lee Answered by Penny Nom. 





The volume of a cone 
20070224 

From SAFDAR: How to derive the formula for volume of cone? Answered by Penny Nom. 





Surface Area of a cone 
20070219 

From Cari: I am doing a math project. I am very confused on how to find the surface area of a cone. I have looked at other equtions but i still don't understand. How do you find the surface area of a cone that has a 15cm length and a 3.5cm radius? Answered by Penny Nom. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





Large exponents 
20070209 

From Nick: I am trying to figure out an extremely large number. It relates to the estimated number of bacterial divisions in 12775 generations of bacteria. The problem I need to solve is: 2^12775 or 2 to the power of 12,775. Answered by Stephen La Rocque and Penny Nom. 





Dividing money unequally 
20070206 

From Linda: I have a total of $13,826.48. It is to be divided by 15 kids  2 of the kids only get half of what the other 13 do  how much do the 13 get and how much does the 2 get? Thanks Answered by Haley Ess and Steve La Rocque. 





The volume of a cone 
20070131 

From ajay: WHY VOLUME OF CONE IS ONE THIRD OF THE VOLUME OF CYLINDER? Answered by Penny Nom. 





Take $.01 and double it every day for 30 days. 
20070126 

From Pat: Take $.01 and double it every day for 30 days. How many dollars would you have? Answered by Stephen La Rocque. 





Is 2^2 = 4 or 4? 
20070123 

From Joan: Is 2 squared, when written without parentheses around the 2, 4 or could this correctly be solved by squaring 2 (2 x 2) for an answer of 4? Or, to correctly get an answer of 4, would the problem have to read (2) squared? Answered by Stephen La Rocque. 





Simplify (2x)^4 (1/2x^3)^2 
20070121 

From Sarah: Simplify (2x)^4 (1/2x^3)^2 Answered by Penny Nom. 





Negative exponents 
20070111 

From Bob: I have to write this "Y7" (but the 7 is an exponent) as a positive exponent. How? Answered by Penny Nom. 





Phone number combinations 
20070104 

From Efrain: i want to know the different combinations for numbers 7 digits the number are 09 its basically the different phone number combinations example: 5556689 or 5654896 i just want to know for many different combinations are there.... Answered by Penny Nom. 





Two cones 
20061230 

From Cassie: A cone of radius 6 and height 12 and a different cone of radius 8 and height 12 intersect as shown in the figure below, where the vertex of one matches with the center of the base of the other. Find the volume of the intersection of the two cones (in exact form). Answered by Penny Nom. 





Place value, coins and money 
20061212 

From Emily: I was wondering what the best way would be to teach place value using coins and money. I have used base ten blocks already and am looking for a way to integrate money, perhaps on a place value chart and perhaps using decimals. Answered by Diane Hanson. 





Wheat is poured on a conical pile 
20061117 

From Rachel: wheat is poured through a chute at the rate of 10 cubic feet per minute and falls in a conical pile whose bottom radius is always half the altitude. how fast will the circumference of the base be increasing when the pile is 8 feet high? Answered by Penny Nom. 





Motorcycle expansion chamber design 
20061114 

From David: I'm interested in calculating cone information regarding motorcycle expansion chamber design for example. I guess it's called a truncated cone, from what I've read so far. If I know the center line height, small radius, and large radius of a truncated cone then, how can I calculate the angle (included angle?) the cone forms? I'd like to know the variations of the formula so I can calculate for angle, or length, or one of the diameters if I know the other two measurements. Answered by Stephen La Rocque. 





After how many hours will the class have been notified? 
20061110 

From Brittany: A college math class consists of 32 students. On Monday at 9:00 a.m., the teacher tells one student to notify other students that the test scheduled for Wednesday at 9:00 a.m. has been cancelled. The model for the number of students in the class who will have heard this information after t hours is N=3232e^0.02t. After how many hours will the class have been notified? Answered by Stephen La Rocque. 





Zero as an exponent 
20061028 

From Don: Any real number (except zero) to the zero power equals 1 correct? Question: If for example x to the zero power equals 1 What is x to the zero power equal to? What is (x) to the zero power equal to? Answered by Penny Nom. 





Putting things in exponent form 
20061018 

From Sheila: Write in exponential form 2 sq. root a with an exponent 5. I do not understand on how to do it. Answered by Stephen La Rocque. 





A specific 8 digit number in a 11 digit mobile phone number 
20061013 

From James: I need to know the chance of finding a specific 8 digit number in a 11 digit mobile phone number.
the number must be 29571596 and the 11 digit phone number must end in this.
All numbers 09 are used in a mobile number but the first 2 digits will always be 07.
Is there a way to work this out?? Answered by Stephen La Rocque. 





Constructing a cone 
20060920 

From Suresh: i want to know the required size of plate for cone rolling,sizes are 2950mm is bottom dia,894 is top dia and 600 is height.I have already read u r answers but i little bit confused ,harely and sue have given useful answers but when i worked both method the required plate size is different. so i like to know which method is easy and correct.and also i like know whether it can be rolled without segment my rolling machine width is 1500. Answered by Penny Nom. 





The radius of a cone 
20060908 

From Hermanson: I know the cone is 20 degrees at the top and 80 degrees at the bottom. What is the formula for finding the radius? Answered by Stephen La Rocque. 





A base number raised to the power of 0 
20060824 

From Sheila: I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out. Answered by Penny Nom. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





A problem with exponents 
20060809 

From A student: (8a to the negative 2 b cube c to the negative 4/4a squared b to the negative 3 c squared) to the negative 2 Answered by Stephen La Rocque. 





2 to the 5th power 
20060619 

From Murray: Is 2 to the 5th power = 32? Answered by Penny Nom. 





Pyramids and cones 
20060606 

From Melissa: I was wondering if a cone can be considered a pyramid. Looking at many definitions of pyramids I have read that pyramids come to a common vertex. A cone comes to a vertex. But I also read that pyramids all have triangular faces. In this case a cone would not be considered a pyramid. Am I correct? Answered by Chris Fisher. 





A truncated cone 
20060528 

From Phil: Hi, I am an art student and I am trying to make a "truncated cone" (ie: a cone with the top cut off) out of sheet metal. I need to design a template first and am having problems working out the angles. The truncated cone is 250mm high, 550mm wide at the bottom and 290mm wide at the top. Can you help? Answered by Stephen La Rocque. 





I want to calculate 0.00353 to the power 1.3 
20060514 

From Richard: I want to calculate 0.00353 to the power 1.3 How do I do it? Answered by Stephen La Rocque. 





Pythagorus and cone dimensions 
20060426 

From Glynnis: How do you find the measure of a side that is not the hypotenuse using the Pythagorean Theorem? Also, how do you figure the surface area and volume of a cone when the radius is 5 yards and the height is 8 yards? Answered by Stephen La Rocque. 





What is the surface area of a cone with a hemisphere on top? 
20060420 

From Jordan: How do you find the surface area of a cone with a hemisphere on top? The only information I have is the radius of the hemisphere, which is 4, and the total height, which is 7. Answered by Stephen La Rocque. 





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. 





Cubic yards of landscape stone 
20060419 

From Janet: I need to spread landscape stone around my pool. A landscaper said I need 16 yards. What is the area of a cubic yard if I want the stone 3" deep? Answered by Stephen La Rocque. 





Cone dimensions 
20060412 

From Mirnela: The height of a cone is 40 and the radius is 9. How
do I find the slant height of this?
Also, how do I find the area of the base of a cone if the radius is 7?
Answered by Stephen La Rocque. 





An exponential function 
20060403 

From Meadow: The graph of an exponential function passes through the points (0,1) and (4,10) find the constant of growth or decay. State the function. Answered by Stephen La Rocque. 





Exponential decay 
20060329 

From Casey: Fifty milligrams of a drug was injected into a patient at 6am. The drug is known to be eliminated according to the law of exponential decay. At 8.30am it was determined that 60% of the drug remained in the body. How many milligrams will remain in the body at midday? Answered by Penny Nom. 





The volume of water in a cone 
20060321 

From Ghulam: A vessel has the shape of an inverted cone.The radius of the top is 8 cm and the height is 20 cm. Water is poured in to a height of x cm.Show that if the volume of the water is V cubic cm,then V=(4/75)pi x3. Answered by Penny Nom. 





A cone with an oval as base 
20060301 

From Richard: I am trying to find the volume of a cone that is not round but oval. Answered by Penn Nom. 





A lampshade shape 
20060211 

From Rose: Is there a solid shaped like a lampshade? Or do you just call it the bottom portion of a cone? Answered by Penny Nom. 





3^4 and (3)^4 
20051217 

From Brad: What is the answer to
3^{4} = ?
(3)^{4} = ?
(3)^{4} = ? Answered by Penny Nom. 





A sheet metal cone 
20051205 

From Laura: I am an art student and in the process of making a cone out of sheet metal. I am unable to work out the template I need to produce my final cone. The dimensions I have are that the final cone will be 58mm high and will have a diameter of 102mm. Answered by Penny Nom. 





A long distance call 
20051205 

From A student: The Small World long distance phone company charges 55cents for the first minute of a long distance call and 23cents for each additional minute.
1. How much would a 10 minute longdistance call cost?
2. If a call costs $4.55. how long did the call last?
3. Write an equation for the total cost, C, of an mminute longdistance call. Answered by Penny Nom. 





A pattern for a truncated cone 
20051204 

From Nick: I need to make a large cone segment. The large end has ID of 57 inches and the small end has ID of 23 inches. The cone is essentially a 45 degree cone (90 degrees at the tip). The sides of the segment are 2 feet long. How do I lay out a flat pattern that will fold into this segment? I need to know radius 1 and radius 2 and the angle the piece must be. Answered by Penny Nom. 





A truncated cone 
20051203 

From Sonny: I need to create a template for a cone that has a 2" opening at the top, a
4" base and stands 6" tall. Can you tell me how to achieve this? Answered by Penny Nom. 





Express t as a function of d 
20051130 

From Matthew:
I have a problem on my homework I cant seem to figure out. Basically it gives me this Linear Regression Equation:
ln t=1.5 ln d0.8954
and it wants be to transform the equation expressing t as a function of d. For some reason I keep getting it wrong. Anyone got an idea of how to do this?
Answered by Penny Nom. 





Volumes 
20051031 

From Diane: My name is Diane and I am a returning student to a vocational technical school.
As a reference point to see what I did/didn't remember from my HS math days, I was sent home with a 75 problem math packet. I was fine until I got to computing:
1. the volume of a cylinderis it pi r^{2} h?
2. the volume of a cone is it pi/3 r^{2} h?
3. the volume of a sphere I can't even hazard a guess.
Help my last classroom was 23 years ago, and I've forgotten far too much! Answered by Penny Nom. 





(2^6) = ? 
20051029 

From Amy: My teacher gave me the problem (2^{6}) on our homework. She marked it wrong when I wrote down 64 for an answer. She said the correct answer was 64. Can you explain why it is 64? Answered by Penny Nom and Leeanne Boehm. 





A slump cone 
20051027 

From Wendy: we are trying to make a slump cone (used to measure the slump in concrete). It has dimensions of 8" diameter on the bottom, 4" diameter hole on the top and a height of 12".
Please help, it is getting frustrating. Answered by Penny Nom. 





A conical hat 
20051022 

From Manish: I need to make a conical hat for my daughter's upcoming fancy dress, the circumference of the base(hollow) is 50 cms,the height of the cone is 30 cms,what should be the dimensions of the paper which will make a cone of the beforementioned dimensions? Answered by Penny Nom. 





A cone with vertex (1,1,2) 
20050926 

From Brandon: Find the equation of a double cone with vertex (1,1,2) and which intersects the xy plane in a circle of radius 4. Answered by Penny Nom. 





The volume of a pool 
20050709 

From Douglas: I have a pond that I need to treat with an anti algae solution which needs to applied based on the volume of water in the pond (in gallons).
The rough diameter of the surface of the pond = 25 ft
The depth of the pond = 8 ft
The pond shape is conical
How many gallons of water are in my pond? Answered by Penny Nom. 





Surface areas 
20050511 

From Jessica: How can I demonstrate to my high school students the reason for the formulas for the surface area of a prism, right cylinder, and regular pyramid, and right cone? Answered by Penny Nom. 





How much sand is in a pile? 
20050416 

From Larry: I was wondering if there is a formula for determining how much sand would be in a pile. I am a student in medical school, and this is a bonus question for a test. I hope you can help me. Answered by Harley Weston. 





Some liquid in a cone 
20050403 

From Vasuki: There are 2 right cones, height is X. one of them is filled from the bottom up (round side) = x/2, when you invert the cone and add the same amount of liquid inside the second cone, what is the HEIGHT of the liquid? Answered by Penny Nom. 





2^10 = 1/2^x  1 
20041213 

From Randy: Could you explain to me how the following equation is solved please.
2^10 = 1/2^x  1 Answered by Harley Weston. 





e = ln(b/a) solve for a 
20041201 

From Daniel: I am trying to make "a" the subject of this equation "e = ln(b/a)" but am not sure if i'm doing it right. Any help would be appriciated, Answered by Claude Tardif. 





Construction of a cone 
20041120 

From John: I am a builder working on a project where I need to make a cone. It's a right circular cone with 15" base radius and slant angle of 30 degrees. I want to cut it out of flat sheet metal then bring the edges together to form the cone. Is this enough information? Answered by Penny Nom. 





The force of a 5000 tonne lorry 
20041027 

From Aaron: A 50 tonne lorry is parked on a slope with a gradient of 4%.
Due to the self weight of the lorry, what is the force
* acting down the slope
* acting normal (at right angles) to the slope Answered by Penny Nom. 





The last digit of a large exponent 
20041020 

From Landon: How can one determine the last digit of a large exponent by hand. I have seen several examples of how to do this by breaking it up into smaller exponents, but is there a formula or some common things to look for? Answered by Penny Nom. 





Manipulating exponents 
20041017 

From A student: I was wondering if you can describe the steps in getting the solution to the problem below. I have the solution of 5/3 in the back of a book, but I have no idea how that answer was reached.
2raised to the 100th power + 2raised to the 98th power divided by 2raised to the 100th power  2raised to the 98th power Answered by Penny Nom. 





The volume of a pile of mulch 
20040922 

From Sam: Is there a formula to determine the cubic feet of something in a pile. IE I need to determine the cubic feet of a pile of mulch. The pile comes to a peak, so the length and width decrease as the pile increases. Answered by Penny Nom. 





Zero to the zero 
20040918 

From Greta: My name is Greta, and I am a 7th grader and my test is coming up. The question I would like to ask you is why 0 elevated to 0 is unidentified. Answered by Penny. 





Constructing a cone 
20040907 

From Steve: I am trying to build crayfish traps; one of the components is a cone shaped entry section.
The cone I want to make would be 12" in diameter at the base and 12" in height, from base to peak.
I need a formula to calculate the dimensions and a method of transferring the shape onto a flat piece of material.
Answered by Harley Weston. 





Water in a cone 
20040728 

From A student: A vertically inverted cone( i.e. vertex down) has a radius 7
inches and height 24 inches. Water is filled to one third of its
height .Find the ht of water when cone is turned upside down Answered by Penny Nom. 





x = 2^x 
20040712 

From A student: If the graphs of y=x and y=2^{x} are drawn on the same set of axes, they will intersect when x is equal to what?
(1)1
(2)2
(3)0
(4)They won't intersect.
I know the answer is number 4 by graphing which is permitted; however, I would like to know if there is any algebraic way to do this type of problem.If yes, please show me how.Thanks. Answered by Penny Nom. 





Algebraic simplification 
20040331 

From Chris: Simplifying Exponents
Question
b^5d^2/b^3d^8 Answered by Penny Nom. 





Large exponents 
20040326 

From John: I
have encountered problem with the lack of memory every calculator
seems to have. No calculator, on or off the computer, I've found
has the amount of memory or writing space to calculate the sums I want
to solve. The sums are in great importance for my continued progress.
The sums are following:
16777216^1310270, 16777215^995328, 16777215^786432 and 16777215^480000 Answered by Claude Tardif. 





Equivalent sets 
20040306 

From A student: If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Answered by Penny Nom. 





An elliptic cone 
20040224 

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.
Answered by Penny Nom. 





The vertex of a cone 
20040129 

From Richard: Please help me explain to my fourth graders as to why a cone has a vertex even though it does not have any straight edges. Answered by Chris Fisher. 





x^x^x^x^... 
20040123 

From Ryan: you have a number say x and it is to the power of x which is to the power of x and so on infinite times like x^x^x^x^x^x^x^... i have to figure out what x is so that the answer is always 2 Answered by Penny Nom. 





Making a cone 
20031222 

From Tracie:
I am working on a craft project at home and I have been given the following information: 16" tall and 13" diameter at base, with 1 and 1/2 " opening at top.
Is there a basic formula for creating a cone with this info?
Answered by Claude Tardif and Penny Nom. 





Noneuclidean geometry 
20031208 

From Geoffrey: How can you use noneuclidean geometry to navigate on a sphere? What geometers did work in this area? Answered by Chris Fisher. 





NonEuclidean geometry 
20031203 

From Geoffrey: What are the applications of NonEuclidean geometry (especially hyperbolic and spherical)? Answered by Walter Whiteley. 





Notation 
20030915 

From Kim:
Question: i have a couple of questions 1. write in standard form a)4x2x8 b) 5 to the power of 4 . . . Answered by Penny Nom. 





One million seconds 
20030904 

From Vince: If you can write a number each second for one million seconds, how many hours would it take? Answered by Penny Nom. 





One percent of a billion 
20030904 

From Charles: What is one percent of one billion? Answered by Penny Nom. 





Why is 5 to the 0 power always 1? 
20030824 

From Crystal: Why is 5 to the 0 power always 1? Answered by Penny Nom. 





Water in a cone 
20030812 

From Adrienne:
Water is poured into a tank in the shape of an inverted right circular cone.ð The height of the tank is 8 m and its radius at the top is 4 m. a. Draw and label a picture to represent this situation.ð (I know how to do this) b. Identify all variable quantities. (h = 8m, r = 4m) c. Find an equation that relates the variable quantities, and reduce the number of variable quantities to two. I was thinking about the equation V = 1/3 pi r^{2} h, which is the Volume of a cone, but I am stumped as to how I am supposed to "reduce the number of variable quantities to two." Can you point me in the right direction? Answered by Penny Nom. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





Solve x = y^z for z 
20030628 

From Nathan: If x = y^z is there a way to solve for z, if x and y are given, without guessing or already knowing the answer?
ie: 64 = 2^z 6 is the obvious value for z. Is there a way I could solve for this variable using a formula, which would also apply when more complex values were substituted for x and y? Answered by Penny Nom. 





5 to the power n 
20030528 

From Sam: What is the integer n for which
5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power + 5 to the n power = 5 to the 25th power? Answered by Penny Nom. 





Rules of exponents 
20030505 

From Carl: Hi, I am a student who would like to recall how to multiply exponents. Here is such an equation: 6.02569 X 10^{25} X 5.25^{4} =?
Also, adding exponents. Don't I just add subtract the exponents separately? Such as 5^{23} +15^{12} =?? Answered by Penny Nom. 





Manipulating exponents 
20030421 

From Denita: Rewrite using only positive exponents:
(4a^4b^2)^4 * (4a^ 3 bc^2)^ 3 Answered by Harley Weston. 





The vertex of a cone 
20030327 

From Holly: I read your response to Callie about whether a cone has a vertex or not. Is it ONLY a vertex if both halves of the cone are together or can one half of the illustration have a vertex? Answered by Walter Whiteley. 





A sequence that converges to e 
20030316 

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 1.1^{11} = 2.8531167... 1.01^{101} = 2.731861... 1.001^{1001} = 2.71964085... 1.0001^{10001} = 2.71841774... 1.00001^{100001} = 2.7182954... 1.000001^{1000001}1 = 2.178231875... 1.0000001^{10000001} = 2.178219643... There apears to be a pattern. My conjecture is: 1.'infinite number of zeros'1^{1'infinite number of zeros'1} = e. Answered by Penny Nom. 





Arithmitic sequence 
20030201 

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. Answered by Claude Tardif. 





A function that is onto but not onetoone where f:N>N 
20021206 

From Lisa: A function that is onto but not onetoone where f:N>N Answered by Penny Nom. 





A lampshade from a cone 
20021126 

From Ellsie: I need to make a pattern to cover an old lampshade. This is actually the bottom portion of a cone. Please help me figure out how to draw this pattern, so that we can complete our project. Answered by Penny Nom. 





Exponential notation 
20021019 

From Ivy: I understand how to figure out for example 4 to the power of 3,what I don't understand is how to figure it out using both negative numbers and negative exponents,as an exaple 4 to the power of 6 and what makes this different that (5) to the power of 7,please help me if you can.I am an adult taking correspondence and finding it quite frustrating. Answered by Penny Nom. 





Exponent 0 
20021002 

From Debbi: can you please tell me what the exponent 0 is (i.e. 7^{0}) Answered by Penny Nom. 





The interrelations of the propositions in Euclid I 
20021001 

From Rob: I'm a student at St. John's College in Santa Fe New Mexico, are school is devoted to the great books and we're now reading Euclid's Elements in english and Attic Greek. We have an assignment to show a frequency or flow chart of how all the propositions of book one are interrelated. Answered by Chris Fisher. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





Fractional exponents 
20020920 

From Jill: The problem is with fractional exponants: 10 1/3 mult. by 10,000 The 1/3 is an exponant of 10. Answered by Penny Nom. 





A paper model of a cone 
20020814 

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. 





Future value 
20020627 

From Susan: If one were to invest $115 a month for 20 years and expect a 4% annual return, what is the value of this money in 20 years? Answered by Leeanne Boehm. 





Conics 
20020529 

From Brooke: Which conic cannot be generated by an intersection of a plane and a double napped cone? Answered by Chris Fisher. 





Telephone banking 
20020522 

From Fiza: To use telephone banking to pay bills, the customer has to enter the last three digits of each bill. the numbers 0 to 9 can be used. if the number happened to be the same on more tan one bill, the customer has to enter the first three digits as well. (a) what is the probability that a person has 2 bills to register with the same last three digits? ANSWER:P(2 bills to register)=1/10P3 1/(10!/7!), 1/(10*9*8)=.001389 (b) what is the probability that a person with 10 bills to register has at least 2 bills with the same last three digits? ANSWER:P=1/(10*10*10) =0.001 Answered by Andrei Volodin. 





oneths 
20020430 

From Logan: why are there tenstenths hundredshudreths, but not oneths if that made no sense then how about this why does everything have two ways of saying things like tens and tenths but not a oneths Answered by Claude Tardif. 





The vertex of a cone 
20020413 

From Callie: Does a cone have a vertex? Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 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 . . . Answered by Walter Whiteley. 





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. 





Negative exponents 
20020116 

From Julie: If z to the power of 4= 1/z4 then how would you solve 1/t2? Answered by Penny Nom. 





Exponential form 
20011211 

From Crystal: Hi, I am asking a question on behalf of a homeschooling grade 11 student. She is having trouble with changing something like (3^{4})^{2} into a exponential form. First of all she needs to know what the term means "exponential form" and then the process of it. Answered by Penny Nom. 





Water in a conical tank 
20011020 

From Sarah: The problem: Water flows into a conical funnel at a continuous rate of one gallon per minute (One gallon = 231 Cu.In.). The height of the funnel is 5" and the diameter is 8". The 1st formula: I need to develop a formula that will give the volume, in cubic inches, of the water in the funnel at any time t (in seconds). V = f(t). The 2nd formula: I need to develop a formula that will give the height of the water in the funnel at any time t (in seconds). h = f(t). Answered by Penny Nom. 





Rules of exponents 
20011014 

From Carissa: how do you work this out? Investigate the relationship between a,b,c and d if 2^{a}*2^{b}=4^{c}/4^{d}? Answered by Leeanne Boehm. 





Zero as an exponent 
20011004 

From Wendy: How do I explain to kids that i.e. 5 exponent 0 = 1? Does 0 exponent 0 = 1? Answered by Leeanne Boehm and Penny Nom. 





1:5 
20010927 

From Sandy: A colleague and I have a disagreement about dilutions. I seem to remember that I was taught (although it was a long time ago) that a RATIO was written thusly: 1:5 , and read " one part to five parts", for a total of 6 parts. On the other hand, a fraction is written: 1/5 and is read" one part in five" for a total of 5 parts. My colleague says that the ratio reads "one part in five" and is essentially the same as a fraction. Which is right? Have I been doing dilutions wrong all this time? I teach Animal Nursing and need to know where I can find a consise answer to such questions for making up medicated fluids, etc. Answered by Penny Nom. 





Earthquake warning 
20010903 

From Dillon: In the city of Skangai there are 6 million people.Each person has to tell 2 more people that theres going to be an earthquake. After they do they leave the city. There will be no duplications.It takes 3 minutes to tell each person. How long will it take for the whole city to know about the earthquake? Answered by Penny Nom. 





A phone bill 
20010618 

From Janet: What is the formuala to calculate cost per minute? Here is the data below # of calls  238 # of minutes  443 cost  $70.06 Answered by Penny Nom. 





Exponential form 
20010606 

From A student: Hello can u please answer my question what is the exponent form of 8x8x8x8 Answered by Penny Nom. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





A pile of sand 
20010514 

From Gul:
 Sand for use on icy roads is stored in a conical pile 14.2 m high and with a base diameter of 34.4 m
 calculate the volume of the pile
 if one sander can take 6.9 m of sand, how many sanders can be filled from the pile?
Answered by Penny Nom. 





Powers 
20010304 

From A student: Hey, can you show me how you do .. (2xy)to the 3rd power (x) to the 2nd power? Answered by Penny Nom. 





Faces 
20010221 

From Sandy: How many faces are there on a sphere? What are the faces of a cone? What is the definition of a "face" of a 3D object? Answered by Walter Whiteley. 





Multiplying one and two digit numbers 
20010211 

From Marty: When multiplying do you put the number you are multiplying by on the top or the bottom. Example if you are multiplying by 6's would you write the problem 6 x 2 or 2 x 6 Maybe it just doesn't matter. But when you get to double digits, the double digit always goes on the top? Answered by Penny Nom. 





Bicycles and phone calls 
20010208 

From Sarah:
 A bicycle has a diameter of 66 centimeters. How many times must the tire rotate to travel 1 kilometer?explain answer.
 Becky want to make a long distance call to her friend Sarah from a pay telephone.She has $5.00 in change.The call costs $0.90 for the first three minutes and $0.24 for each additional minute.How long can Becky talk to Sarah?
Answered by Leeanne Boehm. 





(2b+3)(b1) 
20010206 

From Melissa: Alright, lets say you are multiplying (2b+3)(b1) and you are using "FOIL" first you would get : 2b^{2}+2b3b3 then you add liketerms. when multiplying,if the bases are the same, add the exponents...does the same thing apply when you are adding the results of the multiplication even though it's addition? would the answer be 2b^{3}3b3 or would it be 2b^{2}b3? Answered by Penny Nom. 





1 + 1 = 1 
20010123 

From Stephanie: My friend has this as a bonus question the other day and I want to figure it out. I don't know how 1+1 in any form could equal 1. Please let me know how you come about geting that. Answered by Claude Tardif. 





Polynomials and exponents 
20010115 

From A student: I am duing a project in math on polynomials and exponents. I need a real life usage of polynomials and exponents for my project. Answered by Penny Nom. 





Exponents 
20010114 

From A student: I am wondering if a number raised to the second power is "squared" and a number raised to the third power is "cubed" is there a name for any number raised to any other power. Answered by Harley Weston. 





Calculating the tax 
20001222 

From A grocer: I have a small grocery store. I have a bag of money containing $325. This represents the mornings receipts and a tax of 5.75% is included in the total. How can I separate the gross take from the tax take so that I'll know how much is mine and how much is the state's? Answered by Penny Nom. 





Graphing F(x) = 3^{x} 
20001106 

From Jose: graph the exponential problem F(x)=3^{x} Answered by Harley Weston. 





Isolating an exponent 
20000924 

From C. Scott: Suppose you invest $500.00 in an account that pays 10% interest compounded annually. How long will it take for this value to triple? A=p(1 + i)^{a} A=1500 i=0.1 1500=500(1.1)^{a} p=500 a=unknown How do you solve this problem algebraicly? How do you isolate the variable (a) when it is an exponent? Answered by Harley Weston. 





Manipulating powers 
20000913 

From Phil: 2^{1/5} x 4^{2/5} = ? Answered by Penny Nom. 





Making a paper cone 
20000730 

From John: The question of how to lay out & cut out of paper, cones came up. I would like the cone have : A base of 4 inches and height of 4 inches, 6 inches, 8 inches. Answered by Harley Weston. 





Calculator and telephones keypads phones 
20000627 

From Thomas Smith and Veronica YatesRiley: On a keyboard, why is the number "7" on the top of the keypad as opposed to the number "1" at the top a telephone keypad? Answered by Penny Nom. 





Volume of a sphere 
20000521 

From Kevin Partridge: Does anyone have a way to physically demonstrate how to explain the volume formula for a sphere? Or perhaps how to derive the formula without calculus? Answered by Harley Weston. 





Radioactive decay 
20000518 

From Catherine Sullivan: Please help me with the following: The radioactive isotope carbon14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon12 at a rate proportional to the amount of C14 present, with a half life of 5730 years. Suppose C(t) is the amount of C14 at time t.  Find the value of the constant k in the differential equation: C'=kC
 In 1988 3 teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of C14 contained in freshly made cloth of the same material. How old is the Shroud according to the data?
Answered by Harley Weston. 





A colony of bacteria 
20000422 

From Nicci Demmin: Suppose that the bacteria in a colony can grow unchecked, by the law of exponential change. The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain at the end of 50 hours? Answered by Penny Nom. 





Lining a cone 
20000406 

From Jim Campbell: I am not a student, I am trying to solve a business problem. The question. If I want to put a lining in a chute that is cone shaped, how do I calculate the size steel plate I need to do that. The cone is 10' in diameter at the top and has a 20" hole at the bottom. The total height of the chute is 8'. Answered by Harley Weston. 





y = x^x^x^x... 
20000405 

From Michael Hackman: Find the derivative of: y = x^x^x^x... on to infinity. Answered by Claude Tardif. 





Compounding continuously 
20000321 

From Gina: You deposit $1500 in an account that pays 6.5% annual interest, compounded continuously. Find the balance after 10 years. I'm not sure what to do with the "compounded continuously" part. Answered by Penny Nom. 





Functions that satisfy f' = f 
20000316 

From Kevin Palmer: Recently my calculus teacher asked his students to try and find any functions whose derivatives where the exact same as the original function. The only function then I have determined that statement to be accurate in is all the natural exponential functions. Ex. f(x) = e^{x}, f'(x) = e^{x} If possible could you please email me all the functions that you can find in which the original function and its derivative is identical. Answered by Claude Tardif. 





Saving for college 
20000301 

From Andrew Kunz: SAVING FOR COLLEGE In this project, you will forecast a friend's finances. Jane has received $75 from her grandparents on every birthday since she was one year old. She has been saving the money in an account that pays 5% interest. She is saving her money to help you pay for her college education, which she will start this fall after her 18th birthday. She also has been receiving birthday checks from her other relatives, but these didn't start until she was 12 years old. The amounts of these checks from her 12th birthday until her 18th birthday are $45, $45, $55, $50, $55, $60, $65. How much money will she have saved just from her birthdays by the time she starts college? IS this a reasonable amount to pay for a used car during her junior year in college? If she had invested her money in a different accoutn that had earned 7% interest, how much more money would she have saved? Answered by Penny Nom. 





Slant height of a cone 
20000224 

From Jocelyn Wozney: I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciatedI am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semivertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant. Answered by Harley Weston. 





More on googols 
20000223 

From Kevin Brennan: Could you please give me a couple of examples of when you MATH guys would use a google. Do youu measure, like, galaxies with it ? Or was it created to keep track of Mr Gate's bank account. Answered by Penny Nom. 





An unbelievable story 
20000117 

From Melissa: good morningi am taking a course "math for elementary teachers" and i have a take home problem that i really need help on. here is the question the million dollar problem a recent item in the newspaper described a robbery in which the robber had held up a local bank for 1 million dollars in small bills, had the tellers put the money in a briefcase which he gave them, and fled the scene on foot. is this story believable? explain your answer! Answered by Harley Weston. 





Phone Number Possibilities 
20000109 

From Hamilton Weston: How do phone companies arrive at the possible number of phone numbers that can be generated for customers? Answered by Harley Weston. 





Logarithms 
19991216 

From Pierre: Can you please answer those three question  inverse or the exponential function.
logx 81 = 4, x expo4 = 81, x = +or 4square root 81, x = +or 3 s.s = {3} Why is 3 not acceptable.  .
. . Answered by Harley Weston. 





Log Cancel 
19991203 

From Justin Murray: Ok I feel like a goof because I know this and I cant think of an answer But I want to isolate the x in the function y=2^x how do I do this? Answered by Harley Weston. 





Zero to the zero 
19991202 

From A middle school teacher: I am a middle school teacher who is looking for a precise explanation of why zero raised to the zero power is undefined. I am hoping to get an explanation using something other than the fact that diividing by zero is undefined. Answered by Penny Nom. 





Get rich quick 
19991202 

From Holly Hutson: If one cent were placed in an investment that doubles in value every day, what would be the value of the investment at the end of 30 days? Answered by Penny Nom. 





A matching quiz 
19991120 

From William J. Ricciardi: I gave a matching quiz the other day and one of my students got all 9 incorrect. That got me thinking......What is the probability that someone could get all 9 questions incorrect? Answered by Peny Nom. 





Two derivatives 
19991116 

From Gina Renicker: The derivative of: y=e^{(xlnx)} and y=x^{2arctan(x1/2)} Answered by Harley Weston. 





Nines and ones 
19991105 

From Greg Miller: Using the numbers 1, 1, 9, 9, only once each, how can I create an expression that equals 10 using only the basic functions of addition, subtraction, multiplication, division, and/or parentheses? Answered by Claude Tardif. 





(5)^2, 5^2 and (5)^2 
19991013 

From Jennifer Brown: What is the difference between the following problems: (5)^{2}, 5^{2} and (5)^{2} Our text book (Beginning Algebra, fourth edition, published by McGraw Hill, by Streeter, Huthison and Hoetzle) says the second and third problem are exactly the same. I don't see how that can be. Is there a mathematical rule that explains this? Answered by Penny Nom. 





A googol 
19991006 

From Kevin Brennan: describe to me a guegoll is that how u spell it? it sounds like that Answered by Penny Nom. 





Surface area of a cone 
19990918 

From Frothy: I don't understand how to find the surface area of a cone. The height is 12cm and the radius is 5cm. Answered by Walter Whiteley. 





2 to the x and x squared 
19990917 

From John: For what values of x is 2 to the exponent x greater than x squared? Answered by Harely Weston. 





Slopes of curved lines 
19990609 

From Stephen Ehrler: When one plots the graphs of y=2^{x}, y=3^{x}, y=x^{x} When each of these graphs pass through point (0,1) do they have the same slope? I know they are different lines but is it possable that they have the same slope at point (0,1). Answered by Harley Weston. 





The Binomial Theorem for rational exponents 
19990415 

From Angela Evans: The full question is this: Isaac Newton generalized the Binomial Theorem to rational exponents. That is, he derived series of expansions for such expressions as (x+y)^{3} (x+y)^{2/3} (x+y)^{5/6} What did Newton find? What are the first four terms of the series expansions of binomials above? How can this extended Binomial Thrm. be used to aid in calculations? Answered by Penny Nom. 





Large Numbers 
19990405 

From CK: Hello. I need a lesson plan for grades 4 to 7 dealing with the concept of large numbers. Specifically, how to teach scientific notation. The lesson plan has to deal with the following: the size of the universe is so huge that is is almost beyond the ability of the mind to comprehend. One way is to measure... Answered by Chris Fisher. 





NonEuclidean Geometry 
19990210 

From Robert Smith: Is noneuclidean geometry necessary for the college bound student? I have students that are inerested in teaching math one day. My school is restricted to Euclidean Geometry. Answered by Walter Whiteley and Jack LeSage. 





Primary Mathematics 
19990208 

From Syairul: Mr Wu earned $2365 in January. He earned $375 more in February than in January. If he spend $4250 in the two months and saved the rest, how much did he save? Answered by Jack LeSage. 





Money and Counting 
19990203 

From Deborah Goodman: I am looking for ways to tutor my daughter in money counting and handwriting skills. Answered by Jack LeSage. 





(4)^0 = ? 
19981202 

From Derek Yau: I would like to know why any number to the exponent 0 equals to 1 also, I would like you to please answer this question: (4)^0 = ? I know the answer is 1 but I am confused as to if it is a negative one or a positive one. Answered by Jack LeSage and Penny Nom. 





French Francs 
19981001 

From Richie Franklin: 1.what did one dollar equal in France francs ten years ago, twenty years ago, and fifty years ago? Answered by Chris Fisher. 





15 to the zero 
19980624 

From Mike Husken: My daughter has the problem: 15 with an exponent of zero=1. Could you help explain why? I would appreciate an answer soon as she has class tomorrow. thanks, Answered by Penny Nom and Patrick Maidorn. 





A Logic Problem 
19980607 

From Anthony Bacigalupo: My name is Anthony Bacigalupo and I take Sequential ][ Math and am taking a practice regents. When doing a logic problem, I encountered the following statements, where I am trying to prove P ( I left out steps unrelated to the question).... Answered by Chris Fisher. 





Pay Phone Problem 
19980226 

From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem) A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British). A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom. 





(50^20)(20^50) 
19980224 

From fion: 50 power of 20 X 20 power of 50? How many zero can be found in the answer and why? Answered by Penny Nom. 





Some Calculus Problems. 
19971030 

From Roger Hung:
 What real number exceeds its square by the greatest possible amount?
 The sum of two numbers is k. show that the sum of their squares is at least 1/2 k^2.
 .
. . Answered by Penny Nom. 





Diagramming Powers 
19971015 

From David Fill: I am a teacher in Massachusettes. We have been diagramming numbers such as two to the third (a 3D cube). One of my students asked me how you would diagram two to the fourth. I have searched through all of my teachers books and cannot seem to find the answer to this question. Is there a way to diagram this? If there is, how would you do this? Your help would be greatly appreciated. Answered by Penny Nom. 





Formulae for Surface Area. 
19970428 

From Gary Millward: I'm trying to help my son with his Math homework (Grade 10) and he has to find the surface area of a cone and rectangluar pyramid. We have the formulas for the volume of these solids, but can't seem to locate the formulas for surface area. Answered by Walter Whiteley. 





Natural Logarithm Functions 
19970423 

From Rickson: The following two questions are some of my son's homework that he is having trouble with......any advice or assistance would be appreciated. (eX)5=1000.............the X and 5 are exponents lnx + ln(x+3) = ln10 In each question the problem is to find x. Answered by Harley Weston. 





Smith, Rodriguez and Jones 
19961107 

From Rafayel Ambartsumyan: On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones. ..... Who is the engineer? Answered by Penny Nom. 





How do you raise a number to an imaginary/complex power? 
19960703 

From Andy Golden: How do you raise a number to an imaginary/complex power? I know how you raise "e" to a complex power, like e^(pi*i): cos pi + i * sin pi But what about numbers other than "e"? What if I want to raise 5 to the 2i power? How is that done? Answered by Chris Fisher. 





a to the power zero 
19960603 

From Beti: Why is a number to the power 0 equal to 1? Answered by Harley Weston. 





Exponents 
19960225 

From Eric Cote: I want to know why the grade six math books tell you that the little number at the top right of another number (exponent) is called the power, but the grade seven and up books tell you it's called the exponent? Answered by Harley Weston. 





A=B+C+D+F+G+H+J 
20071127 

From Boubendir: voila ma question et comme savoir les nombres additioné en etulisant le resultat
A=B+C+D+F+G+H+J
au debut ons a les B,C,D,F,G,H,J on connaissent leur valeur comment retrouver
valeur on etulisant leur resultat Answered by Claude Tardif. 





volume d'un cône 
20061129 

From Emmanuel: On peut diviser un cube en 3 pyramides et ainsi en déduire le volume d'une pyramide. Mais comment peuton déduire le volume d'un cône de celui d'un cylindre? Comment visualiseton la division d'un cylindre en trois? Answered by Claude Tardif. 





l'explication de 1  1,1 exposant 5 
20060812 

From Karin: Ma question est l'explication de 1  1,1 exposant 5 Answered by Claude Tardif. 





Volume d'un cône 
20060424 

From Christelle: Caroline décide de se servir de ses connaissances mathématiques pour "rouler" son petit frère: "Arthur, ditelle, je te propose que nous mettions chaucun un euro dans l'achat d'un cône glacé. Je mangerai la première, jusqu'à mihauteur, et toi, tu auras la seconde moitié."
Combien la part de Caroline représenteraielle par rapport à celle de son petit frère s'il acceptait ? Answered by Claude Tardif. 





Exposant 
20050906 

From Enzo: Puisje savoir combien donne 2 exposant 100 ?
et 9 exposant 3012 ? Answered by Claude Tardif. 





le système RSA 
20050219 

From Un eleve: Je suis actuellement en classe préparatoire MP au lycée Henri Poincaré de Nancy et je souhaiterais obtenir des informations sur l'exponentiation modulaire car je réalise un TIPE sur la cryptographie et plus particulièrement le système RSA. pourriezvous m'indiquez en quoi consiste l'exponentiation modulaire et comment cela fonctionne. Answered by Claude Tardif. 





Recherhce sur pi et exponentielle 
20010317 

From Cyril: étudiant a la fac de sciences de montpellier je cherche des informations concernant la demonstration suivante: "comment prouver que pi et exponentielle sont irrationnels?" Answered by Claude Tardif. 





Exposant à la 0 
20000704 

From Sylvie: J'aimerais savoir combien fait 0 exposant 0. Answered by Claude Tardif. 





Le sang humain 
19981006 

From Golden: Le sang humain contient approximativement 2,5 x globules rouges. Chaque globule a un rayon de 0,004 mm. Si on le place ces globules bout a bout, quelle est la longeur de la chaine en millimetres? En kilometres? Compare toi avec la circonference de la terre (24 000 km) (Travail avec exposants) Answered by Claude Tradif. 

