Question

The area of an equilateral triangle can be calculated as
A=(√3/4)(s^2) , where s is the length of one of the sides. Answer the following.
a) Find the differential dA.
b) If s is measured to be 15 centimeters with a maximum possible error in measurement of ±0.1 centimeters, use dA to estimate the propagated error in measuring the area.

Answer 1

\[A=\sqrt{\frac{3}{4}}s^2\]
To find dA we have to take this derivative:
\[\frac{dA}{ds}\]
Do you know how to get it?
Please tell me what do you get.

Answer 2

I honestly have no idea how to solve this question at all my teacher just piled me up to this and I'm only 14! He thinks I'm good in Math but I never really got the chance to study that much. I don't know how to get the the da over ds THANK YOU SO MUCH!!!!

Answer 3

Start with a sketch. OK

Answer 4

Draw an equilateral triangle, with an altitude vertically.

Answer 5

Okay

Answer 6

Since the big triangle is 60-60-60, and the altitude divides it in half, the small triangles are 30-60-90.

Answer 7

There is a theorem that for 30-60-90, the sides are 1, sqrt(3), 2, which you can check by Pythagoras thm.

Answer 8

OK with that?

Answer 9

Yes that's about it ?

Answer 10

More

Answer 11

If you look carefully at your sketch, you'll see that if the base of the big triangle is 2, then the area is s times sqt(3)/2

Answer 12

sorry sqrt(3) I rescaled the sides

Answer 13

Omg we are done right?

Answer 14

omg we are not done

Answer 15

lol sorry

Answer 16

Back up a minute. If you work through what we said, you will get the formula:
A=(√3/4)(s^2)
And as @rafabc02 said, to get
dA/ds we need to take the derivative of A with respect to s
any ideas on that

Answer 17

Yeah that's what we'd get. Yeah

Answer 18

So we have f(x) = A = ks^2
k = const
And the derivative is:

Answer 19

The power rule
d/dx (k x^n) = n k x^(n-1)
do you know that one?

Answer 20

I honestly don't know I was being put up a new level of Math when I don't even know Math that well. But I'll google it and see my chances with this rule. I'm really sorry for being a pest and I don't know how to really thank you for helping me out. I mean it, I appreciate it!

Answer 21

And I'm sorry I couldn't walk you through it.
Best.

Answer 22

It's alright thank you so much :) Have a great day!

Answer 23

I think that if you are 14 years old you have never heard about a derivative.
It's strange that you have this as a HW

Answer 24

Yes, I agree.

Answer 25

I know what derivative means but I was put up with this homework that seems really complicated i can do this derivative thing but when it's with numbers not things I don't understand.

Answer 26

I feel like I could have done it better. Don't be discouraged!

Answer 27

Thank you so much both of you seriously. I'll take notes of what you both did and try to find my way through it and see what I would be getting. Thank you so so much. I mean it.

Answer 28

message me if you want

Answer 29

Oh wow really? Awesome! I will I think I've been getting some kind of clues here and there thank you!

Answer 30

PD: You can say thanks with a "Best response" or a fan.
:D
We are here to help you!

Answer 31

I'll best responds both of you but I already Fanned you :D haha yeah I kind of go crazy with the thank you phrase I think you've noticed thanks again < and there we go lol.

Answer 32

What did you get?
\[\frac{dA}{ds}=?\]

Answer 33

Never mind got it , I think? Hahaha! I'm just going to recheck it with my sister maybe she'll lead me on but if she doesn't I'll definitely let you know thank you so so much!

Answer 34

I GOT IT!! I took 100% <3 Thank you guyssss! :D <3