Fuel Consumption: The gas tank of a certain car contains 16 gal when the driver of the car begins a trip. For each mile driven by the driver, the amount of gas in the tank decreases by 0.032 gal. a Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven. b What is the domain for the linear function in part (a)? The domain is the maximum amount miles that can be driven before the tank is empty. c.Use your function to find the number of gallons in the tank after driving 150 miles?

Q: Newborn blue whales have a length of about 24 feet and weight 3 tons. These young whales are…

A: Part (a):New born whale, at t = 0, length of whale, L = 24 feet and weight of whale, W = 3…

Q: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per…

A: Let fixed amount per surgery = $y and an amount per minute for use. = $x One patient was charged…

Q: (a). A survey shows that there is a linear function between population of a country and time. In the…

A: The linear relationship between x and y is defined by the equation, y=ax+b . Here, x is the…

Q: You bought a collectible Spock Pez dispenser for $9 in 2009. In 2021, it is now worth $15. (a) If…

A: A collectible Spock Pez dispenser cost $9 in 2009. In 2021, it is now worth $15 i.e. in 12 years the…

Q: A baseball team plays in a stadium that holds 56000 spectators. With the ticket price at $9 the…

A: In this problem in order to determine the maximize revenue by using given data. To find maximize…

Q: On a Celsius thermometer, water freezes at 0° and boils at 100°. On a Fahrenheit scale, water…

A: Given on celcius , water freezes at 0° and boils at 100° and on Fahrenheit water freezes at 32 and…

Q: A company has been hired to clear a quantity of contaminated soil from a site. The table shows the…

A: Introduction: Consider that x is the independent variable and y is the dependent variable. The…

Q: Tuition Costs In 1990, the cost of tuition at a large Midwestern university was $97 per credit hour.…

A: The linear cost function comprises a constant and variable.

Q: The manager of a furniture factory finds that it costs $2200 to produce 100 chairs in one day and…

A:

Q: ) A baseball team plays in a stadium that holds 55,000 spectators. With a ticket price at $10, the…

A:

Q: The resale value of a sports car declines as the number of miles driven increases. Data from a…

A: This question is based on formation of straight line equation.

Q: Retirement For Pennsylvania state employees forwhom the average of the three best yearly salaries…

A: Annual pension P is 2.5% of 75,000 which is multiplied by the number of years of service.  Let the…

Q: Chelsea and her friends are driving across the US from New York to Los Angeles at a constant speed…

A: Given when Chelsea and her friends have driven for 15 hours, they are 1800 miles away from Los…

Q: 9. Starbucks noticed that when they charged $2.50 for a cup of coffee, they sold 230,000 Ibs of…

A: Given                  C(x) = Coffee (in pounds ) sold.                       x = price per cup And…

Q: The chart to the right shows a​ country's annual egg production. Model the data in the chart with a…

A: Given that  The chart to the right shows a​ country's annual egg production. Model the data in the…

Q: A band will be paid a flat fee for playing a concert. Additionally, the band will receive a fixed…

A: Given that,  Let Number of tickets sold = x Amount of band will be paid = y For 30 tickets:…

Q: Example 1: Jennifer rents a bicycle for her hiking trip. The rental shop charges her an initial fee…

A: topic - linear function

Q: Shen is driving to Las Vegas. Suppose that the distance to his destination (in miles) is a linear…

A: Given query is to find the remaining distance when t = 69 min.

Q: 6. Felix is writing a novel. He already has 74 pages of the novel written, and he sets a goal to…

A:

Q: The table shows the distances, y, from a boat to a scuba diver beneath the surface of the ocean x…

A: Given query is to find the correct statement.

Q: 67. Diamonds The relation between the cost of a diamond and its weight is linear. In looking at two…

A: topic - linear equation in one variable

Q: A cellular phone company offers several different service options. One option, for people who plan…

A: Given Information :  A cellular phone company offers several different service options. One option,…

Q: 2004, in-state tuition at Purdue was $6,092. In 2013, in-state tuition was $9,992. If the cost of…

A:

Q: A salesperson is paid a base salary of $2000 a month plus a 4% commission on their sales of x…

A: A salesperson is paid a base salary of $2000 a month plus a 4% commission on their sales of x…

Q: ple represents a linear function. X. -2 -2 -1 1 0. 4 7 1. 2 10

A:

Q: Entomologists are biological scientists who study insects. Entomologists studying tree crickets have…

A: It is given that cricket do not chirp at all below 39 degree and at 59 degree they chirp about 90…

Q: The pilot of a Boeing 777 jet takes off from Boston's Logan Airport, which is at sea level, and…

A: Given query is to find the linear relationship and the height of the plane at x = 18.

Q: Sonny has entered a reading contest at the local library. After reading two books, he has read…

A:

Q: A bike rental company charges its customers p dollars per day to rent a bike, where 5≤p≤25. The…

A:

Q: Revenue The sum of the 2016 revenue and twicethe 2013 revenue for Mama Joan’s International,Inc., is…

A: Given: The sum of the 2016 revenue and twice the 2013 revenue is $2144.9 million. The difference…

Q: Ivan is driving to Philadelphia. Suppose that the distance to his destination (in miles) is a linear…

A: Here, remaining distance to its destination y, is a linear function of the total driving time t,…

Q: Brian is driving to Chicago. Suppose that the distance to his destination (in miles) is a linear…

A: It is clear from the question that the given scenario varies linearly. From the question, we need to…

Q: A car rental company charges its customers p dollars per day to rent a car, where 45≤p≤200. The…

A: Consider the given: The number of cars rented per day can be modeled by the linear…

Q: The monthly cost (in dollars) of water use is a linear function of the amount of water used (in…

A:

Q: The resale value of a sports car declines as the number of miles driven increases. Data from a…

A: answer is in next step

Q: Charlie is driving to San Francisco. Suppose that the distance to his destination (in miles) is a…

A: Given Charlie is driving to San Francisco. Suppose that the distance to his destination (in miles)…

Q: Ivan is driving to New York City. Suppose that the distance to his destination (in miles) is a…

A:

Q: Chelsea and her friends are driving across the US from New York to Los Angeles at a constant speed…

A:

Q: A baseball team plays in a stadium that holds 60000 spectators. With the ticket price at $9 the…

A: Given that a basketball team plays in a stadium that holds 60,000 spectators

Q: lice has a peach orchard. She knows from past experience that the number of kilograms of peaches…

A: To find the maximum possible total number of kilograms of peaches that can be produced.

Q: During school days, Yagami sells notebooks to college students. Last school year, he sold the…

A: To Determine:  a) Find the price-demand function , assuming that it is linear. What is the domain of…

Q: College Enrollment The total fall enrollment in 4-yearpublic institutions is given by y = 0.014x +…

A: Consider the given function as y=0.014x+2.290

Q: Fill in the Blanks Type your answers in all of the blanks and submit In 1997, the cost for a 30-sec…

A: We will find answers to all the parts as following.

Q: When a bill is not paid by the due date, a late fee is added each month until the bill is paid. The…

A:

Q: or each dollar a driver spends on gas, she can drive 1 mile. assume she bought her car with 20,000…

A: Let 'x' be the number of dollars she spends on gas.Let 'y' be the number of miles she drives.For…

Q: A book club has a membership fee of $25. Each book purchased costs $3. Find a rule for the linear…

A: Suppose x books are taken then find the linear function.

Q: The manager of a band gets paid $8000 a show, plus 5% commission on the ticket sales of x dollars.…

A: The manager of the band gets paid for a show = $8000 Commission on the ticket sales =  5% of x…

Q: (a) As dry air moves upward, it expands and cools. If the ground temperature is 20 Cand the…

A:

Q: The weight of a newborn is 7.25 pounds. The baby gains of a pound a month for its first year. a.…

A: Given the gain in weight per month is 38 pounds So, after t year, the gain weight is: 38t

Q: David is driving to Los Angeles. Suppose that the distance to his destination (in miles) is a linear…

A: let y be the distance from destination to David, and x be the driving time. Then, David has 59 miles…

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.