Textbook Question
Simplify the algebraic expression. (1/5)(5x) + [(3y) + (- 3y)] - (-x)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 19
A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula h=4+60t-16t2 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball's height 2 seconds after it was kicked?
Verified step by step guidance1
Identify the given height formula for the ball: \(h = 4 + 60t - 16t^2\), where \(h\) is the height in feet and \(t\) is the time in seconds.
Substitute the given time \(t = 2\) seconds into the formula to find the height at that moment: \(h = 4 + 60(2) - 16(2)^2\).
Calculate the value of each term separately: multiply 60 by 2, and square 2 then multiply by 16.
Combine the results by adding and subtracting the terms according to the formula: start with 4, add the product of 60 and 2, then subtract the product of 16 and \$2^2$.
The final expression after substitution and simplification will give the height of the ball 2 seconds after it was kicked.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Functions
A quadratic function is a polynomial of degree two, often written as h(t) = at^2 + bt + c. In this problem, the height formula h = 4 + 60t - 16t^2 is quadratic, representing the ball's height over time with a parabolic trajectory due to gravity.
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Substitution in Functions
Substitution involves replacing the variable in a function with a specific value to find the output. Here, to find the height at 2 seconds, substitute t = 2 into the height formula and calculate h(2).
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Interpreting Physical Context in Algebra
Understanding how algebraic expressions model real-world situations is crucial. The terms in the height formula represent initial height, initial velocity, and acceleration due to gravity, helping interpret the ball's motion accurately.
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