A ball is thrown down from a balcony with a vertical velocity (in ft/s) given by V(t)= –32t – 10. Chose the inequality that represents the time for which the velocity of the ball will be between –90 and –58 ft/s

If the ball is thrown downward, it has a negative velocity due to the direction is traveling. By just looking at the magnitude of the velocity 90 is greater than 58, the negative sign only represents that it is moving downwards. So the correct answer is choice 2

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MrRoyal MrRoyal · Answer 2 · 2021-09-21T17:25:47+02:00

Inequalities are used to represent unequal expressions or numbers.

The inequality that represents the time for which the velocity of the ball will be between -90 and -58 ft/s is: [tex]-90 < -32t - 10< -58[/tex]

Given

[tex]V(t) = -32t - 10[/tex]

[tex]V_1 = -90[/tex]

[tex]V_1 = -58[/tex]

From the numbering system;

[tex]-90 < -58[/tex] -- i.e. -90 is less than -58.

This means that:

[tex]-90 < V(t) < -58[/tex]

Substitute [tex]V(t) = -32t - 10[/tex]

[tex]-90 < -32t - 10< -58[/tex]

Hence, the inequality that represents the scenario is:

[tex]-90 < -32t - 10< -58[/tex]