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I apologise for any offence caused; it was an inappropriate response from me. I do appreciate all the help and guidance I get from all of you.Thank you for the clarification.

Okay, well, no-one was saying Galileo was stupid - that’s why stupid was in ''. However, my point was simple (I thought): In his time, he was considered a crackhead because of their ignorance. Their...

Thanks ebaines et al. I would take issue with questioning people being termed ‘delusional’ though. Just because their perspective is against the norm, that shouldn’t condemn them to the stupid silo....

Okay, well, I’m no scientist or astronomer, but there still seems to be conspiratory theorists plugging away on the idea that the whole Apollo mission was a huge hoax. It would seem to me that one...

Yep, that’s a real big help. Thanks a bundle.
Working out the logs, then subtracting the ’n’ values, then dividing by log(0.75), I got 72.75 years which checks when I replace the values in the...

Okay, well, honestly that’s confusing. Or should I say asks more questions than it solves, ha!
1). Why would I use logarithms in a situation like this?
2). Can it be solved without the use of...

Okay. Hi and thanks again for the help.
Needless to say I have one more question that needs a bit of input.
The population of New York and LA aregrowing at 1% and 1.4% a year. Starting...

Right. I got w = -0.93 & 13.43 and when substituted back as sqrtx, the former is not possible, so there’s only one answer which is (13.43)^2 or x = 180.37. Really appreciate your input. Thanks a lot.

Oh gosh, that’s a step I forgot about. So substituting I get 100 + 100w = 8w^2
Using the quadratic formula, I got [100 +/- sqrt(100^2 + 320)]/16. So the result for w was 13.43 or -0.93....

Okay, I’m afraid I’ve hit upon another stumbling block.
The original question is: log10(8x) - log10(1+sqrtx) = 2
I got it to 10^2 = 8x/(1 +sqrtx)
Now I get confused.
If I multiply both sides by...

Wow! Okay, so I got to (9^m-1)(9^m-27)=0 and so the solutions are m = 0 or m= 3/2. Correct? When I substituted the values, they both worked in the original equation. Thanks so much.

I don’t think there is. It has been given as a question but I always understood that unlike exponents couldn’t be added.
I can re-write it as 3^2m + 3^(3-2m) = 28 but I’m not sure how that would...

Thanks so much. I have someone in Canada who can send me this book fairly quickly. Appreciate your help and assistance.

No, I'm afraid I am referring to the Irish poet, Seamus Heaney, and his collection of poems entitled 'District and Circle'. But thanks for the input. Cheers.

Hi. I am teaching Language Arts to students in Bangalore, India. I have one student that has taken up A Level Literature and has chosen Seamus Heaney's selection of poems in District and Circle as...

Thanks so much. I must have missed the reading by him. Fantastic. Appreciate the prompt response.

In Stephen Spender's poem, 'My Parents', the fourth line of the first stanza is written as 'And climbed cliffs and tripped by country streams' in the CIE approved book Songs of Ourselves. However, I...

I have this question that came up in an A level examination (12th grade) which I find difficult to answer: If arg(z - 1/2) = 1/5 pi, what is arg(2z - 1)?
Any help would be most appreciated.
Cheers....

Thanks. Very helpful. But this does then lead to another question: if all you have to do is 'zap' milk for 1-2 seconds and it stays fresh for much, much longer, can't the same principle be applied to...

I have always been curious about the actual make-up of long life milk. As a kid in the UK, I remember the milkman delivering bottles of regular or cream milk to your door daily which would be placed...

Fantastic! Thanks so much! That’s really helpful and put in terms that even I can understand. Cheers.

Here is the scenario: I recently purchased some land for $70,000 with the intention of developing a small resort. The plans and ideas are all mine and it is my intention to manage the project from...

Really helpful. Thanks so much.

Hi. Yes sorry, by mod I mean absolute value, but there isn’t an x^2 missing.
First I had to find the sum of the geometric series (1 -x ) + ( x^3 - x^4 ) + ( x^6 - x^7 ) +.. . ( 3^3n - 3^3n-1 ) which...

Excellent. Thanks so much. Very clear explanation. On the same subject, I had another question that I had difficulty with. Any help would due appreciated.
I had to show that the sum of the infinite...

Okay, thanks, that helps to clarify. I really thought I was off thinking that I would need to use the ‘numerical technique’, although I would have thought that if theta - sin theta is defined, then...

Hi. Thanks. Very helpful. The information you gave was a bit too technical for the level that is being taught (this is a AS level mathematics course - 11th grade). But I went back to my work and...

Hi. Thanks. Very helpful. Based on the information you gave, I went back to my work and found the answer, but by using a slightly different approach.
During this section of the course we have been...

I have the following question in the ‘radians’ section of my coursework:
An eclipse of the sun is said to be 10% total when 10% of the area of the sun’s disc is hidden behind the disc of the moon....

I am really stumped by this question. It’s in the AS level course (11th grade).
An infinite geometric series has first term a and sum to infinity b, where b ≠ 0. Prove that a lies between 0 and 2b....

I had to show that the sum of the infinite series 1 - x + x^3 - x^4... is equal to 1/(1 + x + x^2) and state the values of x for which this is valid. I found the first part with no difficulties, but...

Hi, I am tutoring the UK curriculum for AS (11th grade) Level Mathematics and came upon this question which has stumped me. Any help would be appreciated.

An infinite geometric series has a first...

Dear Uber, Thanks again. I'm sure the method is correct, the only problem is that this question is in a revision paper for UK AS level mathematics (equivalent to US 11th grade). As such, your...

Dear Uber, Thanks so much. Very helpful.

I have a problem which I can not seem to fathom. I am asked to differentiate [(sqrt x) + 1]^2 / x with respect to x. I tackled the problem as follows:
First I expanded the top term to become [x +...

I had this question come up in AS Level mathematics and I'm stumped.
ABC is a triangle. D is the mid-point of BC, E is the mid-point of AC, F is th amid-point of AB and G is the mid-point of EF....

Hi. I have a question that has stumped me. Any help would be appreciated.
The origin O and a point B(p,q) are opposite vertices of the square OABC. Find the coordinates of the points A and C.
I...

Hi. I have a question that has stumped me. Any help would be appreciated.
The origin O and a point B(p,q) are opposite vertices of the square OABC. Find the coordinates of the points A and C.
I...

Hi. I have a problem with an AS Level math question on differentiation.
I had to find the inverse of f(x) = 4 - x^2, where x is greater than or equal to 0, which I found to be sq rt (4 - x)....

I have a problem which I can't seem to fathom. I am asked to differentiate [(sq rt x) 1]^2 / x with respect to x. I tackled the problem as follows:
First I expanded the top term to become [x ...

Hi. I have a question that has stumped me. Any help would be appreciated.
The origin O and a point B(p,q) are opposite vertices of the square OABC. Find the coordinates of the points A and C.
I...

Sorry, I have one more question that's bugging me.
I had to find the inverse of f(x) = 4 - x^2, where x is greater than or equal to 0, which I found to be sq rt (4 - x).
However, it then goes on to...

Hi Corrigan. Well I have a problem which I can't seem to fathom. I am asked to differentiate [(sq rt x) + 1]^2 / x with respect to x. I tackled the problem as follows:
First I expanded the top term...

Hi Corrigan. Thanks once again. It had dawned on me that the graph couldn't oscillate below 0, but I hadn't realised the effect that had on the period.
Better just clear up a confusion: although we...

Hi. Back again I'm afraid. I'm stumped with this question: I have to determine the min and max values of y and the least possible values of x at which these occur. Question is: y = 8 - 3cos^2x. I...

Hi.
Well, I used option P for pi. I also use an American keyboard if that makes a difference. If you have a solution, I would appreciate the input. Thanks.

Hi Corrigan. Thanks so much. I didn't sink in to relate r to h, so with the information you gave, I worked out the right answer. Really helpful and thanks for keeping it simple! Some explanations are...

Thanks, that was the 'zagging' bit. By substituting r = (1/3)h I get the correct answer.
Btw, I don't copy-paste math formulas, but I have noticed that pi(Ï€) looks like pi on my laptop but all...

HI again. Sorry, I have another problem I can’t seem to work out:
A funnel has a circular top of diameter 20cm and a height of 30cm. When the depth of liquid in the funnel is 12cm, the liquid...

HI again. Sorry, I have another problem I can't seem to work out:
A funnel has a circular top of diameter 20cm and a height of 30cm. When the depth of liquid in the funnel is 12cm, the liquid is...