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Sagot :
Answer:
A) 9 seconds
B) lowest point is -81 ft, or 81 ft below the top of the bungee jump
C) 18 seconds
Step-by-step explanation:
A) To find the x-value of the turning point (minima/maxima) differentiate, then set to zero and solve for x:
[tex]\dfrac{dy}{dx}=2x-18\\\\\implies \dfrac{dy}{dx}=0\\\\\implies 2x-18=0\\\\\implies x=9[/tex]
Therefore, it took 9 seconds to reach the minimum height
B) lowest point is when x = 9:
⇒ y = (9)² -18(9) = -81
Therefore, lowest point is -81 ft, or 81 ft below the top of the bungee jump
C) find x when y = 0
⇒ x² - 18x = 0
⇒ x(x - 18) = 0
⇒ x = 0 and x - 18 = 0
⇒ x = 0 and x = 18
So he returned to the top of the bungee jump at 18 seconds
Answer:
A) 9 s
B) -81 feet
C) 18 feet
step by step explanation:
A)
[tex]\sf y = x^2 - 18x[/tex]
use the vertex formula: [tex]\sf \frac{-b}{2a}[/tex]
Here a = -18 and a = 1, these are coefficients from ax² + bx + x
solve:
[tex]\hookrightarrow \sf \frac{--18}{2(1)}[/tex]
[tex]\hookrightarrow \sf \frac{18}{2}[/tex]
[tex]\hookrightarrow \sf 9[/tex] s
It takes 9 s for Jason to reach his minimum height.
B)
if taken 9 s then put it in x and find the height reached
[tex]\sf \hookrightarrow \sf h(9) = 9^2 - 18(9)[/tex]
[tex]\sf \hookrightarrow h(9) = 81 - 162[/tex]
[tex]\hookrightarrow \sf h(9) = -81[/tex]
The lowest point is - 81 feet, as it says lowest.
C)
solve for when the height, y is 0
[tex]\hookrightarrow \sf 0 = x^2 -18x[/tex]
[tex]\hookrightarrow \sf 0 = x(x -18)[/tex]
[tex]\hookrightarrow \sf x = 0, \ x -18 = 0[/tex]
[tex]\hookrightarrow \sf x = 0, \ x = 18[/tex]
[tex]\hookrightarrow \sf\ x = 18[/tex]
Jason returned to the top of the bungee jump at 18 s.
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