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Chapter 6: Problem 75

A painter drops a brush from a platform 75 feet high. The polynomial \(-16 t^{2}+75\) gives the height of the brush \(t\) seconds after it was dropped. Find the height after \(t=2\) seconds.

Short Answer

Expert verified
The height after 2 seconds is 11 feet.

Step by step solution

01

Identify the given polynomial

The polynomial given is \[-16t^{2}+75\]. This represents the height of the brush in feet, after it was dropped from a height of 75 feet.
02

Substitute the given value of t into the polynomial

The value of t given is 2 seconds. Substitute t=2 into the polynomial \[-16(2)^{2}+75\].
03

Calculate the square of t

Calculate \((2)^{2}\) which equals 4.
04

Multiply by the coefficient of t^2

Now multiply 4 by -16, \(-16 * 4 = -64\).
05

Add the constant term

Add 75 to -64, \(-64 + 75 = 11\).
06

Conclusion

The height of the brush after 2 seconds is 11 feet.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

quadratic equations
The polynomial a function can be categorized under quadratic equations because it involves a term with t raised to the second power, a=-16t^2. Quadratic equations frequently model scenarios like object motion under gravity in physics. The quadratic term usually indicates varying velocity - in the scenario at hand, showing how the brush's speed changes as it falls. Solving quadratic equations requires carrying out operations on given polynomials, as we substituted t=2 seconds to find the height of the object in this exercise.

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Most popular questions from this chapter

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