21. A college professor recorded the speed with which students ran out the door after class after taking the final exam (using a

Answer:

-29.61m/s

Step-by-step explanation:

To find the average speed of the pencil after dropping it for 2.8 seconds, we start with the fall distance equation for the student, s(t) = −16t² + 8√t. First, we differentiate this function since velocity is the rate of change of distance with respect to time, expressed as

V = d(s(t))/dt

s(t) = −16t² + 8t^1/2

V = -32t + 1/2(8)t^(1/2 - 1)

V = -32t + 4t^-1/2

To find the average speed, we substitute t = 2.8 into the derived equation since the pencil reaches the ground precisely after 2.8 seconds.

V = -32t + 4(2.8)^-1/2

V = -32 + 4/√2.8

V = -32 + 4/1.6733

V = -32 + 2.391

v = -29.61m/s

Thus, the average speed at which it fell is -29.61m/s

Answer:

X ball bearings can be produced in 1 hour and 20 minutes

Step-by-step explanation:

Proportions

Proportions serve as an essential method for solving various common challenges. We understand that:

Company ABC manufactures X ball bearings in 3 hours.

Company DEF produces X ball bearings in 4 hours.

Company GHI generates X ball bearings in 6 hours.

In a single hour, each company is capable of producing:

ABC: X/3 ball bearings

DEF: X/4 ball bearings

GHI: X/6 ball bearings

By collaborating, they can produce

ball bearings. Operating together

If their output is 3/4 of a ball bearing in one hour, then it will take

hours to create one complete ball bearing. This translates to 1 hour and 20 minutes.

X ball bearings can be produced in 1 hour and 20 minutes

The value of x equals 60 degrees.

This is because alternate interior angles are equal by definition :)

Can I get the brainliest award please?

Answer:

The graph for the prepaid plan will exhibit a steeper slope and a lower y-intercept.

I trust this information is correct.

Step-by-step explanation:

prepaid plan: y =.20x

contracted plan: y =.02x + 50