AUTOMOBILES The engine torque y (in foot-pounds) of one model of car is given by y = º3.75x2 + 23.2x + 38.8 where x is the speed of the engine (in thousands of revolutions per minute). Find the engine speed that maximizes torque. What is the maximum torque?

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calculista calculista · Answer 1 · 2019-11-26T08:43:41+01:00

Answer:

Part 1) The engine speed that maximizes torque is [tex]3,093 rev/min[/tex]

Part 2)The maximum torque is [tex]74.683\ foot-pounds[/tex]

Step-by-step explanation:

The correct equation is

[tex]y=-3.75x^{2}+23.2x+38.8[/tex]

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the engine speed that maximizes torque

The y-coordinate of the vertex represent the maximum torque

Solve the quadratic equation by graphing

using a graphing tool

The vertex is the point (3.093,74.683)

see the attached figure

therefore

The engine speed that maximizes torque is

[tex]3.093(1,000)=3,093 rev/min[/tex] ---> because is in thousands of revolutions per minute

The maximum torque is

[tex]74.683\ foot-pounds[/tex]