Concave mirror positioning help

AI Thread Summary
A concave shaving mirror with a radius of curvature of 40 cm produces an upright image that is 3.30 times larger than the actual face. The user initially calculated the distance from the mirror to the face as 26.1 cm but later corrected it to 13.94 cm. The equations used were the magnification formula and the mirror equation. The discussion highlights the importance of correctly applying these equations to solve for the distance. The final answer provided is 13.94 cm.
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Homework Statement


A concave shaving mirror has a radius of curvature of 40 cm. It is positioned so that the (upright) image of a man's face is 3.30 times the size of the face. How far is the mirror from the face?


Homework Equations


M = Si/S 1/S + 1/Si = 2/R


The Attempt at a Solution


I have 2 equations with 2 unknowns. I isolated Si in the first one and substituted this expression into equation 2 to find S. I get an answer of 26.1cm.

The computer keeps telling me I'm wrong though. Could someone check my math or tell me if my equation setup is correct?
 
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oops never mind i got it... 13.94cm
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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