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 Topic: approximation
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The volume under an an uneven surface 2020-05-01
From Solon:
I am trying to fill an area of floor which has an uneven surface. I need to know the volume of fill. If you imagine a rectangular room (4 corners) that measures 189 inches by 240 inches and the depth at each corner is different.
Let us say corner #1 has a depth of 1", corner #2 has a depth of 0", corner #3 has a depth of 2" and corner #4 has a depth of 4".
How would i find the volume of said floor area?

Any assistance would be greatly appreciated!

Converting inches to centimeters 2018-05-25
From Jason:
Hi!
Is there a method to approximately convert inches to cm in my head without using a calculator?

Thanks! Jason

Solve sinX=0.703X for X 2018-03-13
From PARAM:
sinX=0.703X
2^x= -2x - 11 2016-11-27
From Kathy:
I don't know how to start this problem:
2^x= -2x - 11

The height of a parabolic arc 2015-12-30
From Tom:
Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known?
Using Newton's Method to find a root 2012-04-09
From Nancy:
Use Newton's method to find the real root function, accurate to five decimal places

f(x) = x^5+2x^2+3

From rachelle:
under certain condition, it is found that the cost of operating an automobile as a function of speed is approximated by a quadratic equation. use the data shown below to find the function. then use the function to determine the cost of operating the automobile at 60mph.
speed
(in miles per hour)
operating cost
per mile(in cents)
10 22
20 20
50 20

A Lagoon, free form, inground swimming pool 2009-12-22
From donna:
What is the linear footage of a 14 x 23, Lagoon, free form, inground swimming pool?
Figure out the square root of something 2009-12-20
From eric:
is there an ez equation to figure out the square root of something?
The acute angle formed by intersecting lines 2009-12-17
From Katie:
To the nearest tenth of a degree, find the size of the acute angle formed by the intersecting lines 3x + 2y = 12 and x - 2y = -2. Was is necessary to find the intersection point?
The volume of a pond 2008-11-04
From Malcolm:
I am looking for a formula to find the volume of my pond. I know the average surface diameter and the average bottom arc length.(The arc from one bank through a point in the bottom and on to the surface on the other bank. I am not able to get a good measurement of the depth at this time. Can the volume be figured with the known measurements (the cord and the arc)? Thanks: MS
The cube root of a really big number 2008-07-17
From Pete:
Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator?
The square root of 21 between what two numbers? 2008-04-03
From Danielle:
The square root of 21 between what two numbers?
The cube root of 198 2008-03-27
From bobby:
what is the cubed root of 198
Solve sin(x)=x^2-x 2007-12-11
From ming:
is there anyway you can solve
sin(x)=x^2-x without a calculator?

The normal approximation to the binomial 2007-09-30
From m.j.:
Slot Machines The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution.
The irrationality of PI 2007-08-07
From Matthew:
I have what I like to think of as a rather interesting question that I can't explain confidently for the life of me. If we take a circle with a radius of 1 and we calculate the circumference, we can use 2 pi R. Doing this calculation results in a circumference of 6.28318530717~ which goes on forever. However, if you were to take a that same circle in the real world, say with radius 1cm and wrap a string around it, and then measure the string, you don't get 6.28~, you get something like 6.2, a much more finite distance. The length of the string is not an irrational number, like the math claims it to be.
Answered by Claude Tardiff and Stephen La Rocque.
Finding square roots 2007-05-17
From Chandler:
I would like an easy way to find the square root of a number.
x^x = 2x 2007-02-22
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?
Large exponents 2007-02-09
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.
The cube root of 8000 2007-01-31
From Jacqui:
How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it?
How does knowing the sum for 2+7 help you find the sum for 6+1 2006-10-26
From Andrea:
How does knowing the sum for 2+7 help you find the sum for 6+1
An approximation 2006-10-22
From Ellen:
consider the curve -8x^2 +5xy+y^3 +149 =0 Write an equation for the line tangent to the curve at (4, -1) use this equation to approximate the value of K at the point (4.2, K)
The area of a sector and a triangle 2006-06-23
From Howard:
I thought of the following problem which is similar but much simpler than the tethered goat problem: What is the angle(it is more illustrative in degrees)of arc of a unit circle so that the area between the chord it subtends and the arc length is equal to the area of the triangle with opposite side the subtended chord.
Answered by Stephen La Rocque and Penny Nom.
The interior angles of a right triangle 2006-05-20
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.
Approximating an integral 2005-01-27
From A student:
i used excel to find the area under a graph instead of integrating the function the analytical way. These are the different answers i got with different width of the x-values, the smaller the x-increment gets the more precise the area is when compared to the answer obtained the numerical way. I have trouble seeing why the answers i get is getting bigger and bigger and not smaller can someone plz explain?
12(1.221)^t = t + 3 2004-07-14
From Jay:
This problem has me stumped since i cannot separate the t and the 3. Here it is:

12(1.221)t = t + 3

It's on a logarithm worksheet, but how do i figure it out?!

Programming without trig functions 2004-05-25
From Derek:
I am a programmer trying to calculate the following.

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

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

Rounding 27.27 2002-11-03
From A parent:
If you have a problem 27.27 and you need to round to the first 7 the answer would be 27

Would 27.0 be acceptable as well or is it completely wrong.

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

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

Cube roots 2002-03-26
From Kathy:
My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without?
Approximating 260 divided by 3 2001-04-02
From Andrew:
Choose the letter of the best estimate.

260 divided by 3

a. 60
b. 70
c. 90
d. 100

Cube roots on a calculator 2001-03-24
From Will:
Hi my name is Will.I have a question about the calculator TI-83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that?
Finding roots 2001-02-01
From A student:
My math problem is right now we are working on roots. I don't quite understand how to find the answer to the problems, i was wondering what is the easiest, and fastest way to find the answers to roots?
Answered by Penny Nom and Claude Tardif.
Solving x - sin(x) = constant 2000-12-29
From Keith Roble:
If x is in radians, how do you solve for x, where: x-sin(x) = constant?
Rounding 2000-04-15
From Tawana Brown:
I was uncertain as to whether a number such as 85.25 rounding to the nearest tenth would be 85.3 or 85.2. I thought I had heard somewhere that if 5 is the last number that you don't round up. But I have also heard that anything 5 and above you do round up. It's been awhile since I've done rounding, so I need a refresher course.
Answered by Walter Whiteley and Harley Weston.
Estimates 2000-04-11
From Sue Jordan :
I am looking for examples of estimates for underestimating and overestimating. When would you do each one. For my child age 11 6th grade.
Approximations 1999-12-20
Long-time ago I red an article about surprizing (and in a way frustrating) results in math, for example the limit of a nicely defined infinite series which was believed to be a simple rational number, but later was determined to be a transcendent number that missed the rational value by an incredibly small amount (so for example the limit proved to be 2.75000...00137.. with a lot of 0's in between). I cannot find that article anymore, so i was wondering if you have any such examples, or you can point to any relevant information source?
Two calculus problems 1999-12-13
From Alan:
I have 2 questions that are very new to me, they were included on a quiz and the material was never covered. Our teacher never explained the purpose and detailed explanation of how to solve the problem. Could you help? Thanks.

Question 1:
A ball is falling 30 feet from a light that is 50 feet high. After 1 sec. How fast is the shadow of the ball moving towards the light post. Note that a ball moves according to the formula S=16t^2

Question 2:
How many trapezoids must one use in order for the error to be less than 10^-8 if we want to find the area under the curve Y=1/X from 1 to 2. Find the exact area, Graph the function and use the trap rule for the "N" that you found.

Calculating a square root 1999-10-28
From Jonathan:
What is the formula for calculating a square root?
Square roots without a calculator 1999-09-14
From Josh Weiner:
Is there any way to find out a square root without a calculator?
The bricklayers formula 1998-11-24
From Rachel Kaplan:
I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this.
From Lana Sabo:
Question:
fifteen times the square root of twenty, divided by the square root of 2.

nine subtract the square root of forty-five, divided by 3.

the square root of 18 plus the square root of 12, divided by the square root of 3.

Approximating pi. 1996-11-04
From Ben Dixon:
How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference?
Approximating roots. 1996-11-04
From Ben Dixon:
How do you calculate a square root? eg the square root of 2.

There is obviously some sort of successive approximation type algorithm for doing it to however many decimal places is required, but what is the algorithm?