**Educational Text:**Suppose that the price $ p $, in dollars, and the number of sales, $ x $, of a certain item are related by the equation $ 4p + 5x + 2px = 80 $. If $ p $ and $ x $ are both functions of time, measured in days, you are tasked with finding the rate at which $ x $ is changing when $ x = 4 $, $ p = 5 $, and $\frac{dp}{dt} = 1.6$.The rate at which $ x $ is changing is:[Input Box] [Dropdown Menu]- day(s) per sale- sale(s) per day- sale(s)- day(s)(Round to the nearest hundredth as needed.)*Instructions for Input:*- Enter your calculated answer in the provided answer box and then click "Check Answer."- Note that the input must be rounded to the nearest hundredth.This is an example of a calculus problem involving related rates, where you are asked to find the rate of change of one variable given the rate of change of another.

Answered: Image /qna-images/answer/60eb9c80-8801-414a-8ed1-db7e94861779.jpg

EQuestion Help Suppose that the price p, in dollars, and the number of sales, x, of a certain item are related by 4p + 5x + 2px = 80. If p and x are both functions of time, measured in days. Find the rate at which x is changing when x=4, p= 5, and =1.6. dp dt The rate at which x is changing is (Round to the nearest hundredth as ne day(s) per sale. sale(s) per day. sale(s). day(s).

EQuestion Help Suppose that the price p, in dollars, and the number of sales, x, of a certain item are related by 4p + 5x + 2px = 80. If p and x are both functions of time, measured in days. Find the rate at which x is changing when x=4, p= 5, and =1.6. dp dt The rate at which x is changing is (Round to the nearest hundredth as ne day(s) per sale. sale(s) per day. sale(s). day(s).

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: A painting was purchased for $50 000.00. The value of the painting increases by 4% each year. A…

Q: Estimate the instantaneous rate of change of the function at x = -2. 2 (2, 0) -4 4 -2 -4 (-3, –5) a)…

A: Given:

Q: A person invested $530 in an account growing at a rate allowing the money to double every 8 years.…

A: Given problem is : A person invested $530 in an account growing at a rate allowing the money to…

Q: price increases by 9% due to inflation and is then reduced by 10% · a sale. Express the final price…

A: Given query is to find the final price in terms of p.

Q: The number of bacteria Pt in a certain population increases according to the following function,…

A: The function f(t) is a rule that associates or fixes a number to the particular t. When the value of…

Q: On TV crime shows, the time of death is often determined by taking the temperature of the liver.…

Q: If your answer to the previous question was linear, find and interpret the rate of change. If…

Q: An oil spill is being treated by microbes which eat the oil molecules such that the oil…

Q: In 2005 a record 51.5% of paper consumed in the US was recycled. The American Forest and Paper…

A: Given, In 2005 a record 51.5% of paper consumed in the US was recycled. The American Forest and…

Q: As a log falls in a waterfall, its velocity is given by v(t) = -32t - 18 in feet per second. The…

Q: Use combining functions and rates of change to solve:

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 1 A police car is at rest and is located 8. mile due west of a street intersection. Another car is…

A: Let the police car be A, it is at rest and located 18 mile due west of a street intersection,…

Q: the operating expesnes of amazon increased from 3.6 billion in 2008 to 16.3 billion in 2012. use the…

A: Given that The operating expenses of amazon increased from 3.6 billion in 2008 to 16.3 billion in…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

**Educational Text:**

Suppose that the price $ p $, in dollars, and the number of sales, $ x $, of a certain item are related by the equation $ 4p + 5x + 2px = 80 $. If $ p $ and $ x $ are both functions of time, measured in days, you are tasked with finding the rate at which $ x $ is changing when $ x = 4 $, $ p = 5 $, and $\frac{dp}{dt} = 1.6$.

The rate at which $ x $ is changing is:

[Input Box] [Dropdown Menu]

- day(s) per sale
- sale(s) per day
- sale(s)
- day(s)

(Round to the nearest hundredth as needed.)

*Instructions for Input:*
- Enter your calculated answer in the provided answer box and then click "Check Answer."
- Note that the input must be rounded to the nearest hundredth.

This is an example of a calculus problem involving related rates, where you are asked to find the rate of change of one variable given the rate of change of another.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Your starting salary is $40000 and it increased by $10675 over the next seven years. Let t be years and s your salary, and your salary is a linear function of time. Find a formula for your salary in time years.
The population of a Ukrainian village is currently 500. Based on the observed growth of the population in past years it is estimated that after 1 year the population will be 600. Similarly, it is estimated that after 2 and 3 years, the population of the village will be 720 and 864 respectively.Which function describes the relationship between year and the village population?
Give a real life example of where you might be interested in the rate of change of y relative to x. That is, replace “y” with a variable name, and “x” with a variable name (e.g., y = heart rate, x = running speed
The function A = Age -0.00693x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are placed in the vault, how much time will need to pass for only 115 pounds to remain? Round to nearest whole number. O A. 190 years O B. 360 years O C. 185 years O D. 180 years
Suppose that a student carrying a flu virus returns to campus and that four days later fifty students have been infected. Determine the number of infected students as a function time. Assume that the virus spreads at a rate that is proportional to both the number of students that have been infected and the number of students that have not been infected. Also assume that the campus population is 5000 students.
A population of amoebas in a petri dish will triple in size every hour. At the start of an experiment the population is 800. The function , where x is the number of hours, models the population growth. How many amoebas are in the petri dish after 9 hours?
デジタル形式で段階的に解決ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT A steel bar is taken out of a furnace at a temperature of 900 °C and allowed to quench in air for 60 minutes, reaching a temperature of 50 °C. If the environment is at 20 °C and the rate of change of the temperature of the bar with respect to time is proportional to the temperature difference between the bar and the environment, determine: a) the proportionality constant b) the time it takes for the steel bar to reach 35 °C