What is the depth of the notch in a block of metal resting on a cylinder?

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The discussion revolves around calculating the depth of a 90-degree notch in a block of metal resting on a circular cylinder with a diameter of 2.0 cm. The lower surface of the block is positioned 1.3 cm above the base plane. Participants suggest using trigonometric principles by drawing triangles based on the geometry of the notch and its contact points with the cylinder. Clarification is sought regarding the reference point D in the geometric setup. The conversation emphasizes the need for a structured approach to solve the problem without providing a final answer.
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ok as when I list all of my problems I just need ideas of where to start and go towards no the final answer though. The problem states:

A block of metal has a 90 degree notch cut from its lower surface. The notched part rests on a circular cylinder of diamter 2.0 cm. If the lower surface of the part is 1.3 cm above the base plane, how deep is the notch?

I have attached a file that shows the diagram. Any help would be appreciated.
 

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ur5pointos2sl said:
A block of metal has a 90 degree notch cut from its lower surface. The notched part rests on a circular cylinder of diamter 2.0 cm. If the lower surface of the part is 1.3 cm above the base plane, how deep is the notch?

Hi ur5pointos2sl! :smile:

(I can't see the diagram yet, but …)

If the apex of the notch is A, and the notch touches the cylinder at T and U, the bottom of the notch (part of the lower surface) is B and C, and BC meets AO at D, and the centre of the cylinder is O, then draw the triangles AOT and ABD, and use trig. :smile:
 
tiny-tim said:
Hi ur5pointos2sl! :smile:

(I can't see the diagram yet, but …)

If the apex of the notch is A, and the notch touches the cylinder at T and U, the bottom of the notch (part of the lower surface) is B and C, and BC meets AO at D, and the centre of the cylinder is O, then draw the triangles AOT and ABD, and use trig. :smile:

What exactly would the D be referring to? The line from B to O?
 
erm …
tiny-tim said:
… the bottom of the notch (part of the lower surface) is B and C, and BC meets AO at D …
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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