Answered

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A layer of water Δx m thick which lies x m above the bottom of the tank will be rectangular with length 8 m. Using similar triangles, we can see that it will have widt of_____m

Sagot :

Answer:

x

Explanation:

The question relates to the energy required to pump water out of the

spout at the top of the triangular prism tank.

The width of the layer of water Δx thick is x m.

Reasons:

The location of the layer Δx m thick = x meters above the bottom

The length of the triangular (cross-section) prism tank = 8 meters

The length of the layer Δx thick layer = 8 meters

From the attached drawing of the cross-section of the tank, we have;

The height of the triangular tank cross-section = 3 meters

The length of the base of the triangular cross-section = 3 meters

By similar triangles, we have;

[tex]\dfrac{Height \ of \ Tank}{Base \ length \ of \ tank}= \dfrac{Height \ of \ layer \ with \ thickness \ \Delta x }{Width \ of \ layer \ with \ thickness \ \Delta x}[/tex]

Which gives;

[tex]\dfrac{3}{3} =\dfrac{x}{Required \ width}[/tex]

[tex]\dfrac{3}{3} =1 = \dfrac{x}{Required \ width}[/tex]

Required width × 1 = x

The required width = x m

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