Find the Radius
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- Опубліковано 26 сер 2024
- This was a fun question, I hope you guys love it.
Does anybody read these descriptions? I think it would be funny if everybody who read this paragraph commented their favorite color and then their favorite animal. Then so many people in the comments would be confused cause there is no prompt in the video. :-)
engineers: yeah, should be around (9+12). Put a box around it.
If we were in a situation where significant digits came into effect, we'd be ignoring the decimels anyway, and 21.25 rounds to 21.... so, close enough for engineering work :D
I was going to do this xd
Close enough
Multiply it by 3 for safety
If only I weren’t a semiconductor engineer…
i was so confused for a while why it wasnt just 9+12, i think i need to go back to basic geometry classes...
Look again
@@mikey9252 yeah 😭😭
Probably because the arc shaved off some distance of the line formed by 9 cm and 12 cm compared with the radius.
It just isn't a circle, just drawn like one, the values are somewhat wrong as well, to make the problem look more beatifull. Nobody wants to see dirty square roots on his plate.
@@user-gm1ty8vu5v It is supposed to be a quarter circle.
You can actually see that r is slightly more than 21, so the final answer is most satisfying.
Oh hell yeah my friend, same brain cell 😅😂
Wrong
@@andreaahplay6152 fym "wrong"? 21.25 IS slightly more than 21.
All this to add ".25" to the radius, i'd say that is 21.4 without thinking
Then you would be approximately correct
"how exciting" always gets me
Another way to arrive at x = 13/4: Use the intersecting chord theorem by filling out the rest of the circle and extending the 12 cm segment horizontally until it hits the circle’s left side (that will make the chord 12 + 9 + 21 long). Similarly, extend the 16 cm segment vertically to hit the circle’s bottom (chord length 16 + x + 16 + x). Then you have the relation:
(12)(30) = (16) (16+2x), giving x = 13/4.
From there you can also use another formula to find the radius! The formula is x^2 + y^2 + z^2 + t^2 = 4r^2 with each letter representing a segment of intersecting chords, that was how i managed to get the answer. (Be aware that this formula can only be used if the chords are perpendicular to each other)
Man, I struggle with this stuff but I’m going to keep trying until it makes more sense.
It's all practice bro dw. Are you in engineering class?
It is best to do it with coordinate geometry as follows
If the center of the circle is the assumed origin then the equation of the circle would be
x^2 + y^2=r^2
Point A which lies on the top end of the 16cm line has coordinates (9,16+k) where k is the clearance of the 16cm line from the ground and the point B on the circle which is the right end of the 12cm line has coordinates (21,k)
We have two equations that correlates R and k. Solve and you are done
that's a prettier way to do it
I mean, its the same solution, since the equation os the circle is literally the Pythagorean theorem with x and y 😅. But everything goes if its easier for u to get the equations this way
Point B has coordinates (21, k), no?
@@ryotoiii7945 my bad...I will correct it
hey andy i really appreciate you showing all the steps, i know how to do the rest once u do the first few steps but i wish my teachers would show ALL their work when i was learning this stuff. really helpful for those who aren’t familiar with the techniques
i actually tried to get rid of a hair on my screen
turquoise bison man i love this one
How exciting! Dont you love pink capybaras?
Blue jaguar! I like your videos, keep making them 👍
blue capybara
Red sloth! I find these videos really helpful
Put a box *inside* the quarter-circle; put a box *around* the answer. How exciting!
Great animation, If I had this description and animation in grade 2 i probably would’ve understood it!😊
green narwhal!
Love it!
Agreed.
color-grey animal-Dog
I'm partial to forest green and I love the Manta Ray.
Blue Chameleon
Im in 6th grade and this guy did it in a way i could understand. good job man!
Green octopus!
This might actually might be regarded
I been out of school too long where I feel like I shouldn't have enjoyed that as much as I did
Never stop making uploading i dont know what i'd do without these videos😞
blue and idk about animal but hey your smart.
Blue Aardvark.
Blue deer! I ALWAYS read the description box!
Black, Red Panda !
This sounded more like a yugioh duel than a math problem
my favorite colour is honestly beige
and my favorite animal is capybara😀
This is how I did it with video paused, check both triangles, mismatch, go back find my mistake, check again r=21.25 how exciting
*Oh god! It's **2:25** midnight in my country and I'm watching your videos.*
From India
Grab a pen & paper 🤓
It's always a good time when the mind seeks knowledge.
its 6am here 🗿🗿🗿🗿 I have been studyin for the past 48 hours I think? Honesly I don't even remember now
I feel like he made things excessively harder by not just using decibels and continually using fractions. It added so many more steps than if he just simplified his fractions to decimals as he went.
Pink penguin
green cat
...am i the only one that did this?
Gotta admit it did confuse me lol but I liked the part with the yellow gecko :)
Oh, that was much less convoluted than what I did. I drew the segment bisector on the chord, knowing that it goes through the center of the circle, and used similar triangles. I guess your solution is fine too.
Turquoise crab
Wow, red cat. How exciting.
Purple axolotl
Carry a ruler. Measure the lenght of a known line. Measure the lenght of the radius. Use this ratio to get the actual lenght of the radius. Problem solved. Used this shortcut plenty in school and college. Works especially well for MCQs when time is a factor.
4r² = w² + x² + y² + z²
from what is given, you can deduce, that the values needed are 30, 12, 16 and 22,5
Those values squared are 900 / 144 / 256 and 506,25
Sum of which equals 1806,25
that divided by 4 equals 451,5625
Square root of which equals 21.25 and you are done.
Has to be a Green Orangutan
Good problem! My solution was identical, so I wonder if there's a significantly different way to approach this.
Blue giraffes are about 21 cm at birth.
Pink Catfish
Estimated 21.23, this is why Id fail math another time around. "Eh close enough" is as accurate as Ive ever needed to be
One day I will figure out the puzzle solo 😔
green cat
Green Dog
I liked the deep RRR xD
deep hard R 💪
ARrrrrRrr😂 2:13
Able to do that by myself, feel like still worthy
I noticed something at American math. You guys subtract, divide and so forth on both sides of = with the same amount. e.g. 123=x+45. You do 123-45=x+45-45. I've been taught that you move the 45 to the other side, i.e. 123-45=x. Seems more complicated your way.
pink squirrel baybeeee
white mantis
And suddenly I'm reminded about how much I hated geometry, trigonometry, and algebra in highschool.
green giraffe
Cool, now find the arc
It's already given to be 90⁰
Black cat
FOR THOSE SAYING IS APPROXIMATELY 9CM+12CM, IMAGINE THE FIGURE OF THE PROBLEM NOT BEING AT SCALE, NOW U CAN'T CONCLUDE THAT BY JUST WATCHING.
I use these shape video's to help me draw in fusion 360. Thx
Green tiger
i really like geometry, i can't believe that people can't understand the simpler things like this!
orange cat? orange cat!
Gotta love problem solving.
Purple Maned Wolf
I woodwork often to solve this is if i need something thats fits i use 9+12 and trim onstie later. If i need something bigger just use 9+12+2 extra cm should do the job
i solved it in basically the same way, but i just used decimals instead of messing around with fractions.
That was pretty slick mate, I enjoyed that.
It was really easy, but glad to solve it
Thanks bro
Green turtle 🐢
Blue Koala
If you have no idea what I'm talking about, you're just streets behind.
I don’t know, cats, big cats, hard to narrow down. Tigers, leopards, lynx, it feels wrong to pit them against each other. Anything feline.
Hello, I am from China and am a middle school mathematics teacher. Can you tell me which software is used for the demonstration? I want to use it for my students，万分感谢
most likely powerpoint
For precision, if your start numbers just have 2 digits accuracy eyballed generous 21cm is the right answer!
This because you can't generate precision out of thin air. At least not in engineering lands.
Teal beaver.
Cool stuff, I always forget you can draw radii as much as you want 😓
Emerald Spider
Technically, once reached the last equation, it is mathematically incorrect to just take the square root.
r might be positive or negative the square root of the value on the left. You should say that, and then explain that geometry adds the disequation r greater or equal than 0.
Though, as an engineer, I'd say "slightly more than 21"
purple, alpaca
I not only like maths but also your vids
Blue penguin!
blue elephant
a 10th grade problem in which i made same mistake again lol
Why are Pirates called Pirates?
They just arrrr... 😇
"It's a little more than 21. Next..."
Purple Fox
Yes, needing two ways to verify x in simultaneous equations. I got there eventually, but it took me a while to figure out where to make the second equation.
Blue rhino!
purple panda
Purple panda heheh
This is the process which my teacher want me to do 😂
Orange Seagull
blue seal
How exciting
Amazing
Blue German shepherd
Angle below 10°? That's a margin of less then 2%, lets call it quits
Nice one again, keep up the good work
I love how you explain seemingly complex thing in a simple way. Nice video Andy!!