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anonymous
 5 years ago
A paper drinking cup is being
designed in the shape shown in the accompanying figure.
The amount of paper needed to manufacture the cup is
determined by the surface area S of the cup, which is
given by s=πr√(r^(2))+h^(2)
where r is the radius and h is the height.
(b) Could the formula for S be simplified as follows?
πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)
anonymous
 5 years ago
A paper drinking cup is being designed in the shape shown in the accompanying figure. The amount of paper needed to manufacture the cup is determined by the surface area S of the cup, which is given by s=πr√(r^(2))+h^(2) where r is the radius and h is the height. (b) Could the formula for S be simplified as follows? πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nonono. In general \[\sqrt{a + b}\ \not= \sqrt{a} + \sqrt{b} \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Could you explain your answer to me Mr. Newton?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That simplification uses the assumption I listed above (splitting it up into two roots) The assumption is false.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It probably got confused with \[\sqrt{a\times b} = \sqrt{a} \times \sqrt{b} \] which is true.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So in the case of the paper, cup it false because it was split up into two roots?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes. In case you still don't believe me ¬_¬ try putting in some numbers for r and h. sqrt(5^2 + 6^2) = sqrt(61) =/= 5 + 6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0πr√(r^(2))+h^(2)=πr(√(r^(2))+√(h^(2)))=πr(r+h)
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