An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)

Q: The owner of a hamburger stand finds that she can sell an average of 200 hamburgers per day if she…

A: Suppose, y is the number of hamburgers she sells and x is a price of a hamburger. And, for the…

Q: cruising altitude of 40,000 ft, a certain airplane travels 549 mph Write a function representing…

A: Given query is to find the function for the distance after x hours.

Q: Is the function even, odd, or neither?

A: From the graph of the given function, it is observed that the graph is symmetric about origin. Or it…

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=27x3            ⋯⋯1 In order to find the slope of the given…

Q: If possible, evaluate the function at the given value of the variable. f(x) = V5x-2 x=2

A: We need to evaluate the given function at x=2

Q: Determine whether the function is one-to-one.(a) y = 4x2 + 3(b) y = 2x + 3 - 5

A: Our Aim is to determine whether the function given below is one-to-one or not?(a)…

Q: Write the height h of the rectangle as a function of x.

A: In two-dimension cartesian-coordinate system, the value of a function at a point represented by the…

Q: A cell phone plan charges $49.95 per month plus $14.02 in taxes, plus $0.40 per minute for calls…

A:

Q: is the function even, odd, or neither?

A:

Q: suppose that the selling price P of an item to the quantity x is given by  P=-1/4x +50.   0<or= x…

A: To express the revenue R as a function of x.

Q: Determine whether the function is one-to-one y=9x

A: we can check it by two methods, mathematicall and graphically. Definition:                       If…

Q: Given the revenue function for emergency kits, R(x)= x(30,000 – 75x) that the company can make by…

A: The given revenue function is: R(x)=x(30000-75x)        =-75x2+30000x To maximize the revenue, let…

Q: The perimeter of a rectangle is 422 inches. If the rectangle is x inches long, find a function for…

A: Let us assume a rectangle with length x inches and breadth y inches.

Q: Determine whether the following linear functions are increasing, decreasing, or constant. f(x) = 5x…

A:

Q: Determine whether y is a function of x…

A: The given function is  y2 = x2 − 1

Q: Determine the points in which the function shifts from increasing to decreasing and vice- versa.…

A:

Q: Graph the function f(x)=3+4x. Then find the value of f(x) when x: :- 10 0. -8 -10 -5 -3 -2 2. fx)=…

A: Please refer the attached image for complete solution.

Q: A motel owner observes that when a room is priced at $90 per day, all 50 rooms of the motel are…

A: topic - equations

Q: Is the function g(x) = x2 one-to-one?

A: Take x=2. g(2)=22=4. Take x=-2. g(-2)=(-2)2=4

Q: Is the function odd, even, or neither

A:

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

A: An equilateral triangle is a triangle in which all the sides are equal. Perimeter of a triangle is…

Q: Determine whether the function is even, odd, or neither. f (x) = x5

A: We know that, A function f(x) is said to be an even function of x if f(-x) = f(x), for all x. A…

Q: The manager of a furniture factory finds that it costs $2600 to manufacture 70 chairs in one day and…

A:

Q: A function is modeled by the equation f(x)=2x+5f(x)=2x+5.

A:

Q: Express the gross salary G of Jackie, who earns $15 per hour, as a function of the number of hours…

A: topic - functions

Q: A shipping crate has a square base with sides of length x feet, and it is half as tall as it is…

A: Square base, with sides of length x feet, and it is half as tall as its wide.

Q: Write the most specific name of the function f(x) = ax + b.

A: A linear function has a standard form ax+b, where a, b are real numbers. The equation on the graph…

Q: The monthly profit, in dollars, of a company that sells a t-shirts is given by the function P(x) = 1…

A: The given question as belonging to the calculus in which application of derivative so we have to…

Q: Determine whether the function is increasing, decreasing, or neither: f (x) = 3−x

A: Consider a function fx A function is said to be an increasing function if f'(x)>0 & a…

Q: Find the value of f(14) from the function.

A:

Q: Show whether the function y=x² is considered as even or odd function

A:

Q: The number of visitors v(t) of a certain park is calculated as a function of the temperature t, in…

A:

Q: What is the ordered pair of the following function? a.  y = -1/2x + 1

A: To find  the ordered pair of the following function.  a.  y = -1/2x + 1     We put the value of "x"…

Q: . For an equation that represents y as a function of x, the set of all values taken on by the…

A: Consider the equation y=fx. Here, the equation y=fx represents y as a function of x. In the above…

Q: Write a function that reflects f（x）= 2x^3 + 1 across the x-axis and shifts it 3 units down.

A:

Q: If (4,y) is an ordered pair of the function,then y =

A: We have to find y, if If (4, y) is an ordered pair of the function.

Q: A cargo service charges a flat fee of $5 plus $1.50 for each pound or fraction of a pound. Graph…

A: A cargo service charges a flat fee of $5 plus $1.50 for each pound or fraction of a pound. Now the…

Q: For a long-distance phone call, the phone company charges $⁢0.70 for the first 8 minutes or less,…

A: The company charges a constant charge for phone calls if we are using phone calls for first 8…

Q: A taxi company charges $5.00 for the first quarter mile and $0.60 for each additional quarter mile.…

A: To find the linear function F for the total fare , if x is the number of miles  So, we can say ,…

Q: y = x2

A:

Q: 1 3 5 f(x)

A:

Q: A page that is x inches wide and y inches high contains 30 square inches of print. The top and…

A: Lets make a diagram using the given information

Q: Use the graph of f(x)=√x to write an equation for the function represented by each graph (a) 2 X 2 4…

A:

Q: the height of a ball Doreen tossed into the air can be modeled by the function h(x) =…

A:

Q: Use the graph of f(x) = x3 to write an equation for the function represented by 1 3 (a) g(x) = %3D y

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x ^ 2 - 9…

A: Given function fx=x2-9 The given point is (0,-1) ,To find the closest point on the graph First…

Q: Determine whether the function is one-to-one. h(x) = x3 + 8

A: Recall that a function will have an inverse if and only if it is one-to-one on its domain. Here…

Q: Get the coordinates and the graph of the piecewise function. f(x) = 2x + 1, if x ≥ 2 f(x) = x - 1,…

A:

Q: Decide whether the function is one-to-one. y= 2(x+ 3) -5

A:

Q: Is the function h(x)=-|x-4| +3 a one -one function?

A: This is an absolute value function , so for two values of x we will find same value of y.

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.