another word problem

[calculusclueless]

a window has a shape of a square surmoiunted by a semicircle. the base of the window is measured as having a width of 60 cm with a possible error in measurement of .1 cm. Use differentials to estimate the maximum error possible in computing the area of te window.

thank you so much!!!

 

[tkhunny]

Are we stuck in a semester exam? If you REALLY cannot do this one, you're toast.

Please demonstrate SOMETHING.

 

[calculusclueless]

A= ((pi)r^2/2)+60^2=5013.7166. i am having trouble estimating the margin of error.

and honestly criticizing me isn't the help i came here for.

 

[tkhunny]

"criticize" is very subjective. Don't spend another second thining you are being criticized. You DID show some work. That is great. It appears to me that you were "encouraged".

You used 'r' quite nicely in the semi-circle piece. Why did you switch to the exact measurement for the square piece?

\(\displaystyle Area(r) = \frac{1}{2}\cdot\pi r^{2} + (2r)^{2}\)

Can you create \(\displaystyle \frac{dArea}{dr}\)?

 

[calculusclueless]

(1/2)*2pir+ 4r?
but how does the derivative of the area formula help me find the margin of error in the area?

 

[tkhunny]

You must use the differential version, not the functional version.

\(\displaystyle \frac{dArea}{dr} = \pi\cdot r + 2(2r)\) -- Still functional.

\(\displaystyle dArea = [\pi\cdot r + 2(2r)]\cdot dr\) -- There's the differential version.

dr is related to the margin of error.

 

[mmm4444bot]

honestly criticizing me isn't the help i came here for

Huh?

Would you like us to provide dishonest constructive criticism, instead? :wink: