







Converting inches to centimeters 
20180525 

From Jason: Hi!
Is there a method to approximately convert inches to cm in my head without using a calculator?
Thanks!
Jason 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 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. 





2^x . 5^3 = x^4 
20130905 

From Zuhdina: Hi, I got a question, 2^x . 5^3 = x^4
I want to know the value of x without using calculator, I've already done some questions in logarithm and I always stuck in the same model equationI think if someone shows me the way, I can do the other 'stuck equations' 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. 





Compatible numbers 
20080925 

From Katie: I am having trouble remembering how to find compatible numbers used to find the estimate in the foloowing problem. Can you please help me solve it and explain it to me? My son is in 5th grade and I need help. Thank you. Here is the problem: 2,752 / 28 estimate: 90 Answered by Penny Nom. 





The square root of 21 between what two numbers? 
20080403 

From Danielle: The square root of 21 between what two numbers? Answered by Penny Nom. 





The cube root of 8000 
20070131 

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? Answered by Penny Nom. 





An approximation 
20061022 

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) Answered by Penny Nom. 





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. 





As close to 841 as possible 
20060621 

From Alan: using these numbers by either add subtract division multiply come up with the answer as close to 841
100 25 10 7 6 3 Answered by Paul Betts. 





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. 





12(1.221)^t = t + 3 
20040714 

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?! Answered by Harley Weston. 





x^{ 4} + x^{ 5} = 100 
20021027 

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? Answered by Harley Weston. 





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. 





Approximations 
19991220 

From Adrian Valc: Longtime 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? Answered by Chris Fisher. 





Two calculus problems 
19991213 

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. Answered by Harley Weston.






Spreading a rumor 
19990913 

From Bornstar14: There is someone who wants to spread a rumor within 7 days to 250,000,000 people. he wants to know how many people he should tell on the first day (assuming the rumor is passed by everyone who was told to the same amount of people) so that everyone knows on the 7th day. What I did is the 7th root of 250,000,000. this answer is not possible unless rounded. is it okay for the number to be approximate? Answered by Penny Nom. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 

