A small antenna fell from the top of a communications tower that is 900 feet tall. The height in feet of the antenna above the ground at t seconds is given by h(t) = -16t2 + 900. How far above the ground is the antenna after it has been falling for 4 seconds? 4 Do not use commas or spaces in your answer. For example, if your answer is 254.67 feet then input only 254.67 Answer:
A small antenna fell from the top of a communications tower that is 900 feet tall. The height in feet of the antenna above the ground at t seconds is given by h(t) = -16t2 + 900. How far above the ground is the antenna after it has been falling for 4 seconds? 4 Do not use commas or spaces in your answer. For example, if your answer is 254.67 feet then input only 254.67 Answer:
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.4: Solving Quadratic Equations By Factoring
Problem 59HP
Related questions
Question
![### Example Question on Falling Objects
**Problem Description:**
A small antenna fell from the top of a communications tower that is 900 feet tall. The height in feet of the antenna above the ground at \( t \) seconds is given by the equation:
\[ h(t) = -16t^2 + 900 \]
**Question:**
How far above the ground is the antenna after it has been falling for 4 seconds?
**Instructions:**
Do not use commas or spaces in your answer. For example, if your answer is 254.67 feet, then input only `254.67`.
**Answer:**
\[ \_\_\_\_\_\_\_\_\_\_ \]
### Explanation:
1. To determine the height of the antenna after 4 seconds, substitute \( t = 4 \) into the equation \( h(t) = -16t^2 + 900 \).
2. Calculate \( h(4) \):
\[
h(4) = -16(4)^2 + 900
\]
3. First, calculate \( 4^2 \):
\[
4^2 = 16
\]
4. Multiply this by -16:
\[
-16 \times 16 = -256
\]
5. Add 900:
\[
-256 + 900 = 644
\]
Therefore, the antenna is 644 feet above the ground after falling for 4 seconds. Enter `644` in the answer box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbdbdb0e-ffa7-4a7f-a16d-cbd5f72e5119%2Fbefe43f7-2d57-4cb6-bcee-5145aa585b32%2F0fl8ygd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Question on Falling Objects
**Problem Description:**
A small antenna fell from the top of a communications tower that is 900 feet tall. The height in feet of the antenna above the ground at \( t \) seconds is given by the equation:
\[ h(t) = -16t^2 + 900 \]
**Question:**
How far above the ground is the antenna after it has been falling for 4 seconds?
**Instructions:**
Do not use commas or spaces in your answer. For example, if your answer is 254.67 feet, then input only `254.67`.
**Answer:**
\[ \_\_\_\_\_\_\_\_\_\_ \]
### Explanation:
1. To determine the height of the antenna after 4 seconds, substitute \( t = 4 \) into the equation \( h(t) = -16t^2 + 900 \).
2. Calculate \( h(4) \):
\[
h(4) = -16(4)^2 + 900
\]
3. First, calculate \( 4^2 \):
\[
4^2 = 16
\]
4. Multiply this by -16:
\[
-16 \times 16 = -256
\]
5. Add 900:
\[
-256 + 900 = 644
\]
Therefore, the antenna is 644 feet above the ground after falling for 4 seconds. Enter `644` in the answer box.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage