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Sagot :
That's possible when function tends to zero
[tex]\\ \rm\hookrightarrow 0.25x^2-x+9.5=0[/tex]
[tex]\\ \rm\hookrightarrow 1/4x^2-x+19/2=0[/tex]
[tex]\\ \rm\hookrightarrow x^2-x+38=0[/tex]
[tex]\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{1-152}}{2}[/tex]
[tex]\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{151}i}{2}[/tex]
Answer:
8.5 ft
Step-by-step explanation:
[tex]f(x) = 0.25x^2 - x + 9.5[/tex]
To find the minimum point of the function, differentiate:
[tex]f'(x) = 0.5x - 1[/tex]
set to zero and solve for x:
[tex]f'(x) =0\\ \implies0.5x - 1=0\\\implies x=2[/tex]
Substitute found value of x into function to find y (height):
[tex]f(2) = 0.25(2)^2 - 2 + 9.5=8.5[/tex]
Therefore, the lowest point on the bottom edge of the banner is 8.5 ft above the floor.
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