Yeniselfongidn
Answered

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A rocket is launched into the air. The path of the rocket is modeled by the equation y = -10x + 160x + 10. What is the maximum height reached by the rocket, in feet?​

Sagot :

MrRoyalidn

Real life events can be modeled by a function.

The maximum height is 650 feet

The function is given as:

[tex]\mathbf{y = -10x^2 + 160x + 10}[/tex]

Differentiate the function

[tex]\mathbf{y' = -20x + 160}[/tex]

Set to 0

[tex]\mathbf{-20x + 160 =0}[/tex]

Collect like terms

[tex]\mathbf{20x = 160}[/tex]

Divide both sides by 20

[tex]\mathbf{x = 8}[/tex]

Substitute 8 for x in [tex]\mathbf{y = -10x^2 + 160x + 10}[/tex]

[tex]\mathbf{y = -10 \times 8^2 + 160 \times 8 + 10}[/tex]

[tex]\mathbf{y = 650}[/tex]

Hence, the maximum height is 650 feet

Read more about functions at:

https://brainly.com/question/21397197

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