







5 mm of water over 1 hectare 
20180810 

From Joyce: Please help me with this question.
How many tonnes of water fell on 1 hectare of land during a rainfall of 5mm? 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. 





Solve sinX=0.703X for X 
20180313 

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





2^x= 2x  11 
20161127 

From Kathy: I don't know how to start this problem:
2^x= 2x  11 Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

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





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

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





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. 





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. 





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. 





x  2 Sin[x] = 0 
20140508 

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





Converting cost per cubic yard to cost per ton 
20140205 

From Mayra: If 18 cubic yards= 25 tons and it's $28.00 per yard how much is it a ton. I need help please a refresher on my algebra. Thank you Answered by Penny Nom. 





n log n = 36 * 10 ^ 12 
20131112 

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





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. 





Sinx=logx+x^2 
20121128 

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





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. 





Using Newton's Method to find a root 
20120409 

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





How many gallons of water will it take to fill a classroom? 
20101201 

From deena: How many gallons of water will it take to fill a classroom that is 26 feet long by 19 feet wide and 9 feet high? How many tons of water will that be? Answered by Stephen La Rocque. 





A logarithmic equation 
20100908 

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





The tonnage of some gravel 
20100722 

From Gregory: i have a road that is 8 miles long 20 feet wide and 4 inches deep what is the tonnage for gravel i would need Answered by Penny Nom. 





Arc length and Chord length 
20100313 

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





Cooling 
20100307 

From Lori: If a house is always at 20 degrees celsius.
Water (tea) boils at 100 degrees celsius.
5 minutes later the tea was 70 degrees celsius.
Use an equation to predict the temperature after 20 minutes. Answered by Tyler Wood. 





A pushbutton padlock 
20100117 

From Vince: Hi,
I have a pushbutton padlock using ten buttons (1234567890).
Five digits must be pushed in order to open the lock.
Each digit can only be used once.
Order is not supposed to matter.
How many different possible combinations? And what are they? Answered by Harley Weston. 





541.39(1 + i)^15 = 784.09 
20091014 

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





Find the central angle 
20090818 

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





Cubic meters of gravel in a 7 ton lorry 
20090621 

From Jackie: I have to transport gravel in a 7 ton lorry and I know how many cubic meters of gravel I need, but I need to know how many cubic meters of gravel a 7 ton lorry can hold.
Thanks, Jackie Answered by Penny Nom. 





1 cubic yard of dirt = how many tons 
20090426 

From jesse: 1 cubic yard of dirt = how many tons give the formula Answered by Harley Weston. 





What is so important about quadratics? 
20081129 

From zoe: what is so important about quadratics? Answered by Harley Weston. 





How much sand do I order? 
20080715 

From jackson: We would like to put 2 inches of sand down. The pool is 24 feet.
How much sand will we need?
The person we spoke to yesterday was talking in tons, but on these sites it is
talking cubic yards or feet.
Please help. We would like to get the sand ordered so we can get the pool up! Answered by Harley Weston. 





Filling a hole with sand 
20080605 

From greg: I have a 18 ft. diameter circle and need to put 2 in. of sand in it i need to know how much sand in cubic yards and tons Answered by Harley Weston. 





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. 





The capacity of a silo 
20080412 

From Candonn: I have a cement silo that is 30 ft. high and has a diameter of 12 ft.
I was wondering what the capacity of the silo is in tons of dry material.
The silo is flat on the bottom also. Answered by Penny Nom. 





Estimate the cube root of 270 
20080311 

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





A ton of carbon dioxide 
20080311 

From claire: I want to know the size of a box if it contained a ton of Co2? Answered by Stephen La Rocque. 





A three dimensional object 
20080304 

From Briana: what is the 3d term for pentagon? like a circle is a shhere? Answered by Penny Nom. 





Some solid figures 
20080228 

From tiffany: What solid figure could have? It has 4 more edges than vertices, Answered by Penny Nom. 





How would one find the radius? 
20071229 

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





Solve sin(x)=x^2x 
20071211 

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





0 = (1/t)  [ln(1+r) ln(t)] 
20071018 

From Brandi: Objective: solve for t, where r = 0.05
0 = (1/t)  [ln(1+r) ln(t)] Answered by Penny Nom. 





How do I determine how many tons, 15 yards of top soil is? 
20070918 

From Terry: One company is selling topsoil by the yard and another by the ton,
how do I determine how many tons, 15 yards of top soil is? Answered by Penny Nom. 





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. 





Tons of concrete 
20070703 

From Trey: I have 300,000 square feet of concrete and want to know how to convert this to tons? Answered by Harley Weston. 





How many tons of sand? 
20070619 

From Richard: I need to know how many tons of sand it would take to fill a container 20 feet
long, 20 feet wide, and 6 inches deep. I am not sure of the makeup of the sand as
far as dry, loose, wet, etc. If you could give me calculations of all the variants it
would be appreciated. Answered by Stephen La Rocque and Penny Nom. 





How many tons of dirt is this? 
20070523 

From Deb: I need to know how many tons of dirt(6 inches deep)would it take to cover 8 acres? Answered by Stephen La Rocque. 





Principia Mathematica 
20070412 

From victoria: i need help making a poster on emilie du chatelet a great mathematician can you describe
the newton principia because i know that she worked on it
thanks,
victoria Answered by Stephen La Rocque and Penny Nom. 





How many tons it will take to fill in this area 
20070329 

From Amy: I have to fill an area with millings (crushed stone). The measurements are 14 foot long, 14 foot wide, and a depth of 6 inches. How do I find the square footage and how do I convert that into tons?
I need to know how many tons it will take to fill in this area. Answered by Penny Nom. 





The volume of a hopper 
20070323 

From amitesh: Let me know how to calculate the tonnage of hopper / bins / chutes of different sizes and dimensions. Answered by Penny Nom. 





x^x = 2x 
20070222 

From ramsay: This has been bugging me for ages. How do find both real solutions to x^x = 2x? Obviously I have x=2, and there's another at about 0.35, but I can't work it out properly. Any help? Answered by Penny Nom. 





Newton meters and ftlbs 
20061104 

From Michael: What is the correlation between Newton meters and ftlbs of torque? If an engine has 100ftlbs of torque,what would that equate to in Newton meters? Answered by Stephen La Rocque. 





Computing gravity 
20060927 

From Patricia: What is the gravity of planet z in inch/hr squared if the weight of an element with mass of 45000 oz on planet z is 2N? Answered by Stephen La Rocque. 





A hamiltonian circuit 
20060724 

From Tom:
1)Prove that every simple not directed graph with 21 vertices and 208 edges has
a hamiltonian circuit but not an Euler circuit.
(I have proved that if we give the 2 edges for each vertices then after a few
steps I have 21 vertices of odd degree and 19 edges.So in the end I have 2
vertices of odd degree.So I have not an Euler circuit.But how can I prove that
there is a Hamiltonian one?)
2)If G is a tree and has a virtex k degree,prove that it also has at least k
vertices degree 1.
Answered by Penny Nom. 





I have a ditch how many tons of dirt will it take 
20060625 

From Scott: I have a ditch 200 feet long 10 feet wide and 5 feet deep.How many tons of dirt will it take to fill it? Answered by Stephen La Rocque. 





The area of a sector and a triangle 
20060623 

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





The interior angles of a right triangle 
20060520 

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





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. 





Square roots and inequalities 
20041025 

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





Newton's binomial theorem 
20030830 

From William: According to page 126 of Murtha & Willard's "Statistics and Calculus" (PrenticeHall, 1973), Newton's binomial theorem can proved inductively. I suppose that was his method, which I would like to see. Answered by Penny Nom. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





Solving x  sin(x) = constant 
20001229 

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





Conversions 
20000423 

From Tara: 750 lbs = ___ tons How do I figure this out!? I know that 1 ton is 2000 lbs, how do I figure out this answer? Answered by Penny Nom. 





Platonic Solids Surface Area 
19981202 

From Rachel Bidwell: How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch Answered by Harley Weston. 





Rowing on the Charles River. 
19970917 

From Fawwaz Muraisi: On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.How fast is the river flowing? Answered by Harley Weston. 





Un polyedre ayant comme face 20 triangles 
20000802 

From Sonia: J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux. Answered by Chris Fisher. 

