6 A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the function below, where x is the time in seconds. Exactly how long is the cannonball in the air? Write the equation you will need to solve to answer this question. f(x) = (50- 16x)(x + 3) %3D

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Problem 6

A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the function below, where \( x \) is the time in seconds. Exactly how long is the cannonball in the air?

Write the equation you will need to solve to answer this question.

\[ f(x) = (50 - 16x)(x + 3) \]

**Enter your answer:**

---

### Problem 7

A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the function below, where \( x \) is the time in seconds. Exactly how long is the cannonball in the air? (No decimals)

Solve the equation you wrote in number 6. Show/explain how you solved it. You may upload a picture of your work at the end.

\[ f(x) = (50 - 16x)(x + 3) \]

**Enter your answer:**

---

### Explanation for Educators

In these problems, students are tasked with determining the time it takes for a cannonball, fired from a cliff, to return to ground level. Given the height function \( f(x) = (50 - 16x)(x + 3) \), students need to set this function equal to zero and solve for \( x \), representing time in seconds. This requires understanding and applying concepts of quadratic equations and factoring. The solution involves finding the roots of the polynomial equation representing the cannonball's height as a function of time.
Transcribed Image Text:### Problem 6 A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the function below, where \( x \) is the time in seconds. Exactly how long is the cannonball in the air? Write the equation you will need to solve to answer this question. \[ f(x) = (50 - 16x)(x + 3) \] **Enter your answer:** --- ### Problem 7 A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the function below, where \( x \) is the time in seconds. Exactly how long is the cannonball in the air? (No decimals) Solve the equation you wrote in number 6. Show/explain how you solved it. You may upload a picture of your work at the end. \[ f(x) = (50 - 16x)(x + 3) \] **Enter your answer:** --- ### Explanation for Educators In these problems, students are tasked with determining the time it takes for a cannonball, fired from a cliff, to return to ground level. Given the height function \( f(x) = (50 - 16x)(x + 3) \), students need to set this function equal to zero and solve for \( x \), representing time in seconds. This requires understanding and applying concepts of quadratic equations and factoring. The solution involves finding the roots of the polynomial equation representing the cannonball's height as a function of time.
**Activity 8**

The area of a triangular flag, \( y \), is given by the equation below, where \( x \) is the length of the base.

**Question:**
What is the length of the base if the area is 48 units squared?

**Instructions:**
Write the equation you will need to solve.

\[ y = 2x^2 + 10x \]

**Input Box for Answer:**
[Enter your answer]

---

**Activity 9**

The area of a triangular flag, \( y \), is given by the equation below, where \( x \) is the length of the base.

**Question:**
What is the length of the base if the area is 48 units squared?

**Instructions:**
Solve the equation you wrote in #8. Show/explain how you solved it. You may upload a picture of your work at the end.

\[ y = 2x^2 + 10x \]
Transcribed Image Text:**Activity 8** The area of a triangular flag, \( y \), is given by the equation below, where \( x \) is the length of the base. **Question:** What is the length of the base if the area is 48 units squared? **Instructions:** Write the equation you will need to solve. \[ y = 2x^2 + 10x \] **Input Box for Answer:** [Enter your answer] --- **Activity 9** The area of a triangular flag, \( y \), is given by the equation below, where \( x \) is the length of the base. **Question:** What is the length of the base if the area is 48 units squared? **Instructions:** Solve the equation you wrote in #8. Show/explain how you solved it. You may upload a picture of your work at the end. \[ y = 2x^2 + 10x \]
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