The price of dance lessons depends upon the number of lessons that you select. If x is the number of lessons then 40x if0 8 lessons are increasing by 10% per lesson with a $5 processing fee for each student. What is the new function for the cost of lessons? 44x if0 8 35x + 5 if r> 8 44x+5 if0 8 35x if r> 8

Q: We have seen that temperature in Fahrenheit is a function of temperature in Celsius. Is it also true…

A: It is given that Farenheit is a function of temperature in Celcius.And the temperature in Celsius…

Q: Jason and Sheldon are neighbors who work for the same accounting firm. They leave the office at the…

A:

Q: A new television depreciates $140 per year, and it is worth $280 after four years. Find a function…

A: (1) Let y be the cost of the new television. Given that the television depreciates $140 per year. So…

Q: Personal Expenditures Personal consumption expenditures for durable goods in the United States,…

A: P(x) = 306.472x0.464, where x is the number of years after 1990. To rewrite this function with equal…

Q: Find x-intercept and y-intercept of the following given function. Also, draw the plot of the…

A: Fx=-x2+x+5 To find x-intercepts, put Fx=0, we get ⇒-x2+x+5=0⇒x2-x-5=0⇒x=--1±-12-41-521⇒x=1±212…

Q: Mike has created a function explaining the productivity of his company. He knows his employees…

A: GivenNumber of bicycle parts ready to be shipped=500Number of bicycle parts produced by the…

Q: STATE THE DOMAIN OF THE FUNCTION f(x), USING INTERUA NOTATION. if X <-4 flx%= (x+5)(x-6l if -4 x cs…

A: Given,            f(x) = 3 - x                    if x &lt; -4(x - 6) (x + 3)(x + 5)x -6       if -4…

Q: The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into…

A: We have to find the number of fish in the lake.

Q: f exactly 200 people sign up for a charter flight, Lesiure World Travel Agency charges $300 per…

A: Given that X denote the number of passenger above 200.   200 people sign up for a charter flight,…

Q: Tom wants to invest $500. He invests in a company that predicts his investment will double in value…

A: Initial investment is $500 and the money gets doubled in 3 years.

Q: A water line is to be laid from a well to an island 5 km cast of a straight north/south shore line…

A: Given: The figure of water line is  the horizontal distance between well and island is 5km and the…

Q: You plan to sell cupcakes to raise funds. A bakery charges you ₱15.00 for the first 100 cupcakes.…

A: Hint: Suppose the number of cup cakes is x. and f(x)= Charges It is given that charges per cup cakes…

Q: A store charges $15 per t-shirt for orders of 20 or fewer t-shirts, $ for orders of 35 or fewer but…

A: a.) Let x be the number of shirts. Consider the first condition. The store charges $15 per t-shirt…

Q: office depot sells TI-84 plus calculaters for $100 each. In a typical august (right before school…

A:

Q: If many people are going to hospitals to have their check-ups, there increase the demand. Due to…

A: Given: If Many people are going to hospitals, the demand for doctors increase, and as a result…

Q: A movie theater seats 700 people. For any particular show, the amount of money the theater makes is…

A:

Q: 14. A single pump is filling a storage container with water at a rate of 60 gallons per minute.…

A: Given data:   The volume of water in the container is V0=1,500 gallons The rate at which a single…

Q: A local garden store plans to build a large rectangular sign on the interior wall at one end of…

A:

Q: +3 if x 4

A: The graph of the function is show in step 2

Q: Write the domain of the following function using interval notation. 3x-5 f(x) 4-3x

A:

Q: Your cell phone plan costs P1000/month and gives you unlimited talk, and 500 text messages per…

A:

Q: A library has 50,000 books and is adding 500 books every year. Write a function f(x) for the number…

A: Initial books = 50000 Let x represents the number of years after initial year, x = 1 represents…

Q: The height of Danny's beanstalk decreases by 50% per day when he stops feeding it. Danny's beanstalk…

A: We are given: Decreasing rate of height of Danny's beanstalk is 50% per day.  Initial height of…

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.