Find the number of pounds of salt in the tank as a function of time.

Q: In economic theory, we let x represent the number of items (called demand) a supplier will produce…

A:

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given function is fx=x3

Q: On a certain route, an airline carries 9000 passengers per month, each paying $150. A market survey…

A: Given 9000 passengers per month @ $ 150 per monthEach $ 1 decrese in the ticket price , the…

Q: the number of bacteria in a culture was initially 8,000 and the number grew to 12,000 in 6 hours.…

A:

Q: The annual yield per orange tree is fairly constant at 270 pounds per tree when the number of trees…

A: Given: Annual yield per orange tree is 270 pounds per tree if the number of trees per acre is 30 or…

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

Q: A contractor is to build a warehouse whose rectangular floor will have an area of 4000 square feet.…

A:

Q: Two homes are located 6 miles apart, each 1 mile from a road that parallels the ocean, Sally can jog…

A: Solve the following

Q: The concentration of salt x in a homemade soap maker is given as a function of time by

A:

Q: The area of a rectangular garden is 125 square feet. The garden is to be enclosed on three sides by…

A:

Q: The education of women in Oman in the year 1999 was 31%. It was increased to 82%in the year 2015.…

A:

Q: The function f(x) = 5x2 describes the volume of a rectangular box, f(x), in cubic inches, whose…

A: Average rate of change is defined as change in quantity observed over a given interval of values.…

Q: A jogger ran 4 miles and then walked 2 miles. The average velocity running was 3 miles per hour…

A: Given  A jogger ran 4 miles and then walked 2 miles. Total time is T  The average velocity of…

Q: A 400-room hotel can rent every one of its rooms at $120 per room. For each $1 increase in rent, two…

A:

Q: The number of Instagram monthly active users (in millions) between 2013 and 2015 can be modeled…

A: The number of instagram monthly active users between 2013 and 2015 be the…

Q: On a particular lake, the difference between high and low tide is 6 hours. At low tide, 6 a.m., a…

A: Answer is in step 2.

Q: Given the function h(x) = x^2 + 10x * 21, determine the average rate of change of the function over…

A: Given function h(x)=x2+10x+21       , -10 <x<-3

Q: On a certain route, an airline carries 7000 passengers per month, each paying $150. A market survey…

A:

Q: A 1 lb sponge initially contains 5 lb of water. As it is lifted up from the ground, the sponge loses…

A: Answer is option d here decrement in water is linearly (as constant rate)

Q: The height of a ball that is launched from an initial height of 140 feet with an initial upward…

A:

Q: What is the constant function?

A:

Q: The second edition of a textbook was 799 pages long. By the time it got to the sixth edition the…

A: Suppose, L represents page length and n represents the edition number. The points are written as (n,…

Q: The equilateral trianhle is inscribed in a circle of radius 6r. Express the area A within the circle…

A:

Q: Express the area and perimeter of an equilateral triangle as a function of the triangle’s side…

A: Given Side’s length of equilateral triangle is x units.

Q: One company buys a new bulldozer for $126400. The company depreciates the bulldozer linearly over…

A:

Q: A pre-paid cell phone company charges $11.55 as a monthly access fee and $0.12 per minute of calling…

A:

Q: The rate at which photosynthesis takes place for a species of phytoplankton is modeled by the 841…

A:

Q: What does it mean for a function to be defined implicitly by an equation?

A: An implicitly defined function is a function that is presented as the solution of some equation or…

Q: A farmer wishes to fence the perimeter of a rectangular lot with an area of 1600 square feet. if the…

A:

Q: The function f(x) = πx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Given,  The area of the circle is described by the function  fx=πx2 in square inches. Where x is the…

Q: A rectangular piece of cardboard is 4 times as long as it is wide. shorter side is y inches and an…

A:

Q: A rancher wants to fence in an area of 1,500,000 square feet in a rectangular field and then divide…

A: Let the length of the rectangular field be y and the width be x. Assume the farmer divides the field…

Q: The annual yield per lemon tree is fairly constant at 320 pounds per tree when the number of trees…

A: Let x be the number of trees per acre. Then the decrease in number of lemons tree is original number…

Q: Express the perimeter P of a rectangle as a function of the width W if the length of the rectangle…

A: According to the given information:P is defined as the perimeter of the rectangleW be the width of…

Q: If an object moves along a line so that it is at y=f(x)=3x2−2x at time x​ (in seconds), find the…

A:

Q: The number of people afflicted with the common cold in the winter months dropped steadily by 25 each…

A: As ‘C’ denotes the number of people afflicted with common cold and let ‘t’ be the years after 2002…

Q: The function f(x) = ᴫx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Consider the function that describes the area of a circle  fx=πx2

Q: The rate of expenditures on public elementary and secondary schools, in billions of dollars per…

A: Given query is to find total expenditure.

Q: Life expectancy at age 65:  By using the Social Security Administration data for selected year from…

A: fx=0.077x+13.8

Q: My square orchid garden abuts my house so that the house itself forms the northern boundary. The…

A: The square orchid garden abuts the house so that the house itself forms the northern boundary. So,…

Q: The function f(x) = 4ᴫx2 describes the surface area, f(x), of a sphere of radius x inches. If the…

A: Given: The surface area of a sphere is, fx=4πx2 . Radius of the sphere is, x=6 inches. The…

Q: Find the slope of the graph of the function at the given point. f(x) = V1 - x3, (-2, 3) f'(-2) =

A:

Q: Express the area A of a rectangle as a function of the length x if the length of the rectangle is…

A: The area of the rectangle is given by the formula A=l×w where l is the length of the rectangle and w…

Q: A ball is thrown in the air from the top of a building. it’s height,and meters above ground,as a…

A:

Q: In 2000, the average weekly salary for workers in the United States was $567. This amount has…

A: In 2000, the average weekly salary for workers in the United States was $567. This amount has…

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

Q: The population of Boston, MA in 2019 was 692,600 people with an annual rate of increase 1.4%. In…

A: Given the function of population grows is P(x) = 692,600·1.014x where x is number of years. We have…

Q: A ball projected upwards with a velocity of 128 feet per minute from a Height of 5 feet above the…

A: Ball reach its maximum height at t = 4 minutes

Q: Two homes are located 6 miles apart, each 1 mile from a road that parallels the ocean, Sally can jog…

A: Here is the solution of the given problem.

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.