Skip to main content
Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBriggs 3rd EditionCh. 1 - FunctionsProblema 65c
Capitolo 1, Problema 65c

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


c. Find the inverse function that gives the time t at which the ball is at height h as the ball travels downward. Express your answer in the form t = ƒ⁻¹ (h)

Guida verificata passo dopo passo
1
The height function is given by \( h = f(t) = 64t - 16t^2 \).
To find the inverse, set \( h = 64t - 16t^2 \).
Rearrange the equation to solve for \( t \) in terms of \( h \). This involves solving the quadratic equation \( 16t^2 - 64t + h = 0 \).
Use the quadratic formula \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 16 \), \( b = -64 \), and \( c = h \).
Since we are interested in the time when the ball is traveling downward, choose the solution with the positive square root, which corresponds to the time after the ball reaches its peak.>

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Quadratic Functions

The height function h(t) = 64t - 16t² is a quadratic function, which is characterized by its parabolic shape. Quadratic functions can be expressed in the standard form ax² + bx + c, where a, b, and c are constants. Understanding the properties of quadratic functions, such as their vertex, axis of symmetry, and roots, is essential for analyzing their behavior, including finding inverse functions.
Video consigliato:
6:04
Introduction to Polynomial Functions

Inverse Functions

An inverse function essentially reverses the effect of the original function. For a function f(t), its inverse f⁻¹(h) allows us to find the input t for a given output h. To find the inverse of a function, one typically swaps the dependent and independent variables and solves for the new dependent variable. This concept is crucial for determining the time t at which the baseball reaches a specific height h.
Video consigliato:
4:49
Inverse Cosine

Solving Quadratic Equations

To find the inverse function in this context, one must solve the quadratic equation derived from the height function. This often involves rearranging the equation to isolate t, which may require using the quadratic formula, t = (-b ± √(b² - 4ac)) / 2a. Understanding how to manipulate and solve quadratic equations is vital for accurately determining the time at which the baseball reaches a given height as it travels downward.
Video consigliato:
5:02
Solving Logarithmic Equations
Pratica correlata
Domanda del libro di testo

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


e. At what time is the ball at a height of 10 ft on the way down? 

253
views
Domanda del libro di testo

Find a trigonometric function ff represented by the graph in the figure. <IMAGE>

288
views
Domanda del libro di testo

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


a. Is this function one-to-one on the interval 0 ≤ t ≤ 4?

319
views
Domanda del libro di testo

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


d. At what time is the ball at a height of 30 ft on the way up?

257
views
Domanda del libro di testo

{Use of Tech} Height and time The height in feet of a baseball hit straight up from the ground with an initial velocity of 64 ft/s is given by h= ƒ(t) = 64t - 16t²  where t is measured in seconds after the hit.


b. Find the inverse function that gives the time t at which the ball is at height h as the ball travels upward. Express your answer in the form t = ƒ⁻¹ (h)

243
views
Domanda del libro di testo

Simplify the difference quotient ƒ(x+h)-ƒ(x)/h

ƒ(x) = 4x-3

357
views