∫ x^2 / √[16-9x^2] dx
∫ x^2 / √[16-9x^2] dx
(As usual please don’t help me, even if I ask myself a question. I want to do it myself.)
The last one was a bit mean (I put it there to slow down the fast finishers) but they did manage it when I gave them the right substitution. #ALevelMaths
(As usual please don’t help me, even if I ask myself a question. I want to do it myself.)
Here's this week's Monday area problem:
Find the exact value of the green area.
I have no choice but to #trymathslive with it.
(Bearing in mind that it's late and I may need to leave suddenly to go sleep)
I have no choice but to #trymathslive with it.
(Bearing in mind that it's late and I may need to leave suddenly to go sleep)
More an exercise in (trigonometry) language fluency than anything else. i.e. do you know how to interpret the terminology to be able to do it in your head.
@davidkbutler.bsky.social
#UKMathsChat #iTeachMaths
#geometrypuzzle
Consider a quadrilateral with corners at (0,0), (2,0), (a,b), and (0,2) where (a,b) is such that a, b > 0 and a + b > 2 (this is just to ensure it's convex).
What's its area, in terms of a and b?
#UKMathsChat #mathsky
(Note it’s not quite live, since we did it at One Hundred Factorial yesterday, but I have to reconstruct it from scratch so it’s nearly live.)
If you only sum EVERY OTHER term (starting at and ending on the same terms as before), you get 39.
What is the sum of EVERY THIRD term (again, starting at and ending on the same terms)?
#iTeachMath
(Note it’s not quite live, since we did it at One Hundred Factorial yesterday, but I have to reconstruct it from scratch so it’s nearly live.)
I'd do it myself, but I need to go to bed!
If you only sum EVERY OTHER term (starting at and ending on the same terms as before), you get 39.
What is the sum of EVERY THIRD term (again, starting at and ending on the same terms)?
#iTeachMath
I'd do it myself, but I need to go to bed!
Here's my reasoning... {Sorry I haven't read your intermediate posts so I didn't spoil my problem solving}
Clearly 2025 is sum of 2 consec integers 1012 + 1013 ✅
3 integers: n + n+1 + n+2 = 2025
3n + 3 = 2025
3n = 2022
n = 674
674 + 675 + 676 ✅
Here's my reasoning... {Sorry I haven't read your intermediate posts so I didn't spoil my problem solving}
Clearly 2025 is sum of 2 consec integers 1012 + 1013 ✅
3 integers: n + n+1 + n+2 = 2025
3n + 3 = 2025
3n = 2022
n = 674
674 + 675 + 676 ✅
1/(31+1/31)+31/(1+1/961)
I can multiply top and bottom of each fraction by the bottom of the fraction-within-a-fraction.
1/(31+1/31)+31/(1+1/961)
= 31/(31×31+1)+31×961/(961+1)
1/(31+1/31)+31/(1+1/961)
I can multiply top and bottom of each fraction by the bottom of the fraction-within-a-fraction.
1/(31+1/31)+31/(1+1/961)
= 31/(31×31+1)+31×961/(961+1)
I do enjoy seeing different methods.
You started with numbers adding to 41 and checked the products.
I began with factor pairs for 288. Because 41 is odd, one of the factors must be odd, and knowing that 9 is a factor of 144, I narrowed down to 9x32.
I do enjoy seeing different methods.
You started with numbers adding to 41 and checked the products.
I began with factor pairs for 288. Because 41 is odd, one of the factors must be odd, and knowing that 9 is a factor of 144, I narrowed down to 9x32.
d) What other numerators "work"?
e) Consider how this example was constructed, and see if you can make a similar one (in a base ≠ 2 or 3).
... phew! i haven't proofread and bsky has no edit button, but those are my #TryMathsLive ideas for the day
#iTeachMath ♾️ 🧮
d) What other numerators "work"?
e) Consider how this example was constructed, and see if you can make a similar one (in a base ≠ 2 or 3).
... phew! i haven't proofread and bsky has no edit button, but those are my #TryMathsLive ideas for the day
#iTeachMath ♾️ 🧮