# Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over the edge, where it hits the top of a 12 foot high boulder. The quadratic equation that models the path of the pebble is given below. How long did it take for the pebble to hit the top of the boulder? p(t)=-16t^2+12t+52

2 answers

###### Question:

Selena is standing on a rock cliff that is 52 feet high. She tosses a pebble upward over the edge, where it hits the top of a 12 foot high boulder. The quadratic equation that models the path of the pebble is given below. How long did it take for the pebble to hit the top of the boulder? p(t)=-16t^2+12t+52

## Answers

Answer: At [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.Step-by-step explanation:Since we have given that Distance at which Selena is standing on a rock cliff = 52 feetHeight of boulder above a rock cliff = 12 footSo, the given quadratic equation would be [tex]p(t)=-16t^2+12t+52[/tex]First we derivative it w.r.t t,[tex]p'(t)=-32t+12[/tex]Now, we will find the critical value,[tex]-32t+12=0\\\\-32t=-12\\\\t=\dfrac{12}{32}=\dfrac{6}{16}=\dfrac{3}{8}[/tex]Now, we will check whether it is maximum or not.[tex]p''(t)=-32<0[/tex]So, we get that it is maximum.Hence, at [tex]t=\dfrac{3}{8}[/tex], the pebble hit the top of the boulder.

Answer:The answer is t=3/8

#### Similar Solved Questions

1 answer

### A clothing truck is shaped like a rectangular prism. The volume of the truck 15 ft cubed. The area of the base of the container is 6 ft squared. What is the height of the clothing truck in feet?

A clothing truck is shaped like a rectangular prism. The volume of the truck 15 ft cubed. The area of the base of the container is 6 ft squared. What is the height of the clothing truck in feet?...

2 answers

### Will mark as Brainliest. Which statement correctly explains how magnesium and chlorine combine to form magnesium chloride? A) A Cl atom donates two electrons to a Mg atom B) An Mg atom donates two electrons to a Cl atom. C) A Cl atom donates one electron to each of the two Mg atoms. D) An Mg atom donates one electron to each of the two Cl atoms.

Will mark as Brainliest.
Which statement correctly explains how magnesium and chlorine combine to form magnesium chloride?
A) A Cl atom donates two electrons to a Mg atom
B) An Mg atom donates two electrons to a Cl atom.
C) A Cl atom donates one electron to each of the two Mg atoms.
D) An Mg atom...

1 answer

### A click beetle abruptly releases elastic energy stored in its body to launch itself into the air. the function h(t)=-16t^2+12t represents the height h (in feet) of the click beetle t seconds after launching. the height of a second click beetle t seconds after launching is shown in the graph. which click beetle went higher?

a click beetle abruptly releases elastic energy stored in its body to launch itself into the air. the function h(t)=-16t^2+12t represents the height h (in feet) of the click beetle t seconds after launching. the height of a second click beetle t seconds after launching is shown in the graph. which c...

1 answer

### 1. Ethanol is a biofuel made from what agricultural commodity? 2. What is the term used to describe the production of aquatic animals and plants under controlled conditions?

1. Ethanol is a biofuel made from what agricultural commodity?
2. What is the term used to describe the production of aquatic animals and plants under controlled conditions?...

2 answers

### Write 3 complete sentences in Spanish where you would need to use the “personal a”

Write 3 complete sentences in Spanish where you would need to use the “personal a”...

1 answer

### What are some of the benefits of reading to children? Include infancy through young school age children.

What are some of the benefits of reading to children? Include infancy through young school age children....

1 answer

### (Story is above) In the passage, Harry Potter and the Sorcerer’s Stone, humor is created by which of the following details? Select one: A.Mr. Dursley slipped on a banana peel. B.Mr. Dursley has no idea what the other man is talking about. C. The older man is wearing a violet cloak. D. The old man is happy that "You Know Who" is gone.

(Story is above) In the passage, Harry Potter and the Sorcerer’s Stone, humor is created by which of the following details?
Select one: A.Mr. Dursley slipped on a banana peel.
B.Mr. Dursley has no idea what the other man is talking about.
C. The older man is wearing a ...

1 answer

### An example of an algebraic expression is A. y = mx + b B. 3x + 4y – 7 C. 2x + 3y < 18 D. (x + y)(x - y) = 25

An example of an algebraic
expression is
A. y = mx + b
B. 3x + 4y – 7
C. 2x + 3y < 18
D. (x + y)(x - y) = 25...

1 answer

### The __________ is the set of guidelines issued by the Equal Employment Opportunity Commission (EEOC) and other agencies to identify how an organization should establish a recruitment process that is free and fair. Select one: a. Uniform Commercial Code b. Equal Opportunity Legislation and Policy c. Code of Federal Regulations d. Uniform Guidelines on Employee Selection Procedures e. Equal Employment Opportunity Commission's Employer Information Report

The __________ is the set of guidelines issued by the Equal Employment Opportunity Commission (EEOC) and other agencies to identify how an organization should establish a recruitment process that is free and fair. Select one: a. Uniform Commercial Code b. Equal Opportunity Legislation and Policy c. ...

2 answers

### Some tasks are ________. A lumpy B bitten C confusing

Some tasks are ________.
A lumpy
B bitten
C confusing...

1 answer

### Which of the following statements is incorrect about hexokinase? a. The reaction it catalyzes during glycolysis is reversible under intracellular conditions. b. It catalyzes the first step of the glycolytic pathway. c. It is a soluble, cytosolic protein. d. Humans have four different hexokinase enzymes, all of which catalyze the same reaction.

Which of the following statements is incorrect about hexokinase?
a. The reaction it catalyzes during glycolysis is reversible under intracellular conditions.
b. It catalyzes the first step of the glycolytic pathway.
c. It is a soluble, cytosolic protein.
d. Humans have four different hexokinase enzy...

1 answer

### If mZQOS = 49, mZPOR = 65, and mZPOQ = 28, what is mZROS? 0 mZROS = (Type an integer or a decimal. Do not include the degree symbol in your answer.)

If mZQOS = 49, mZPOR = 65, and mZPOQ = 28, what is mZROS?
0
mZROS =
(Type an integer or a decimal. Do not include the degree symbol in your answer.)...

1 answer

### (Help me with my Little sisters homework) What is the length of each line?

(Help me with my
Little sisters homework)
What is the length of each line?...

1 answer

### Which one of the following is not a major contributing factor to food-borne illnesses? time/temperature abuse the high cost of fresh produce poor personal hygiene cross-contamination

Which one of the following is not a major contributing factor to food-borne illnesses?
time/temperature abuse
the high cost of fresh produce
poor personal hygiene
cross-contamination...