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Phil is standing x+5 feet from the base of a building. The height of the building is 6x−1 feet. Find the function that the straight-line distance from Phil's feet to the top of the building in terms of x. Enter the simplified function.

Respuesta :

calculista

Answer:

[tex]f(x)=\sqrt{37x^{2}-2x+26}[/tex]

Step-by-step explanation:

we know that

To compute the required distance, using properties of triangles

Applying the Pythagoras Theorem

see the attached figure to better understand the problem

[tex]PT^{2}=(6x-1)^{2}+(x+5)^{2}[/tex]

convert to expanded form

[tex]PT^{2}=36x^{2}-12x+1+x^{2}+10x+25[/tex]

[tex]PT^{2}=37x^{2}-2x+26[/tex]

square root both sides

[tex]PT=\sqrt{37x^{2}-2x+26}[/tex]

Convert to function notation

[tex]f(x)=\sqrt{37x^{2}-2x+26}[/tex]

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