The monthly advertising revenue A and the monthly circulation x of a magazine are related approximately by the equation A=5x2-576 (the x2-576 is in a square root box)(the 5 is on the outside) for x≥24​, where A is given in thousands of dollars and x is measured in thousands of copies sold. At what rate is the advertising revenue changing if the current circulation is x=26 thousand copies and the circulation is growing at the rate of 1 thousand copies per month.​ (Hint: Use the chain​ rule: dA/dt=dA/dx dx/dt​) The advertising revenue if changing at a rate of_____________ thousand dollars per month

Q: If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: Answer

Q: How can you relate the following situations into quadratic functions? a. The number of kilograms of…

A:

Q: The revenue for a company producing friendship bracelets is given by f(x) = -15x - 30x + 200 %3D…

A:

Q: The profit function P(x), in dollars, for a product is given by the equation P(x) = - 0.4x +…

A: The profit function is given by Px=-0.4x3+56x2-760x-84000. a) The break even point is given as x=70.…

Q: The quadratic equation for the cost in dollars of producing automobile tires is given below where x…

A: Given:

Q: Find the x-intercepts (if any) for the graph of the quadratic function. 2) f(x) = x2 + 16x + 47 Give…

A: The X-intercept is a point where the y-coordinate is 0. You can find the x-intercept of a function…

Q: A new manufacturer of automobiles in Canada has determined that the quantity demanded of their brand…

A: Given p(x)=-x^2+6x+36    and interval 3<x<9

Q: A student estimated based on the video that the ball left my hand 1.58 meters off the ground, and…

A: vertex form  y = f(x-h) + k  vertex (h,k)

Q: The cost function for a certain company is  C = 40x + 500  and the revenue is given by  R = 100x −…

A:

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(z)…

A:

Q: Write the equation of a quadratic function with roots at 5 and 1, and a vertex at (3, -4). Write the…

A:

Q: Solve for x. Show your work. 4x + 5 = 23 4x - 5 = 8x +7- 6x 6. 5.

A:

Q: The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x…

A: Substitution method: - The substitution method could be a straightforward approach for solving…

Q: In a certain Region, about 7% of a city’s population moves to the surrounding suburbs each year, and…

A: We have to Set up a difference equation that describes this situation, where x0 is the initial…

Q: The profit function P(x), in dollars, for a product is given by the equation P(x) = - 0.2x + 66x -…

A: Here we solve a polynomial equation

Q: The revenue from the sale of a product is given by the function R= 289x-x², (a) Use factoring to…

A:

Q: Find the X and Y intercepts of  y= 1 - the square root of 1 -x2

A: Given,

Q: If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: A projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its height…

Q: (a) Write down the piecewise form for the function |2x – 3|. (b) Hence or otherwise find all…

A: we have to write the given function in piecewise

Q: Solve for the zeros of the quadratic function f(x) = 9x2 + 6x + 1. Write the answer as a fraction.…

A:

Q: The revenue for a company producing friendship bracelets is given by f(x) = -15x2 - 30x + 200 %3D…

A: Given:- Revenue function f(x) = -15x2-30x+200 Cost function y=5x-12 x is price in dollars for each…

Q: 1. Find the zeros of the following quadratic equation by factoring. f(x) = 9x2 ‒ 36x + 36 Then…

A: The given function is  f(x) = 9x^2 ‒ 36x + 36

Q: Solve the quadratic for x: f (x) = x² – 7x – 18

A: The formula to find the solutions of the quadratic equation helps to find the required solutions.…

Q: Form a quadratic function f(x) for which f(1)3D0, f(-1)= -4, and f(2)= 5. The equation is f(x) =-

A: Given : fx is a quadratic equation. f1 = 0f-1 = -4f2 = 5

Q: The profit (P) for a company is given by the equation P=-0.02x^2 + 1.40x + 1500, where x is the…

A: Consider the given profit function: P=-0.02x2+1.40x+1500 Where  x is the number of units sold Here,…

Q: of f (x) = 1³ + 2z² + 3x + 6?

A:

Q: The cost function for a certain company is  C = 70x + 200  and the revenue is given by  R = 100x −…

A:

Q: A fast-food restaurant has a cost of production C (x) = 12x + 95 and a revenue function R(x) = 7x.…

A: Given cost function is Cx=12x+95 and a revenue function is Rx=7x. The profit function is given by…

Q: If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet…

A:

Q: Does x =12 satsify the equation 16- 1/2x + 3/4x +1?

A: The given equation is 16 - 12x + 34x + 1.We need to check that x = 12 satisfies the…

Q: The given figure shows that when a football is kicked, the nearest defensive player is 6 feet from…

A: (Note: we are entitled to solve only one question at a time and upto 3 subparts only)  Given: The…

Q: A student estimated based on the video that the ball left my hand 1.56 meters off the ground, and…

A:

Q: uppose the equation y=−125x2+2x+4y=-125x2+2x+4 models the height of an arrow where xx is the…

A: Given,

Q: find the value of (a) if the equation: f(x)=x2 – 2ax+9 has one root: -

A: The given equation is fx=x2-2ax+9. It is given that the equation has only one root. It is known that…

Q: Find the smallest root of the equation f(x) = 2x – 6x + 11x – 7 = 0

A:

Q: A fast-food restaurant has a cost of production C(x) = 14x + 108 and a revenue function R(x) = 82.…

A:

Q: If a rock falls from a height of 100 meters on Earth, the height H (in meters) after t seconds is…

A: a)We know that most of the quadratic functions are not one-to-one .For example, f(x)=x2 is not a…

Q: 5. Algebraically find the x-intercepts of the quadratic function whose equation is y=x² – 4x – 6.…

A:

Q: The spread of oil leaking from a tanker is in the shape of a circle.  If the radius r (in feet) of…

A: Below is your solution

Q: How do you find the roots of the equation f(x)=e-x-(x+4)/5 without a graph?

A: Note that intersection of line and exponential curve is a single point which is root of those two.…

Q: Use the vertex  (h, k)  and a point on the graph  (x, y)  to find the general form of the equation…

A:

Q: The revenue for a certain product is given by the equation R(x)=100−400x+5−x, where x is the number…

A:

Q: Solve for x 7.9= 10e-x(x3+2x2-3x+1)

A: Consider the given equation:…

Q: A rectangular box for a new product is designed in such a way that the Three dimensions always have…

A: Given: A rectangular box for a new product is designed in such a way that the Three dimensions…

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(z)…

A:

Q: The height of a stone catapulted into the air is given by h(x)=−1/480x2+3x+2 where x is the…

A: Given:  The height of a stone catapulted into the air is given by h(x)=-1480x2+3x+2 where x is the…

Q: Does x =12 satisfy the equation 16 - 1/2x = 3/4x +1?

A: Given equation,  16-(1/2)x=(3/4)x+1 X=12 satisfy the above equation if L.H.S of above equation is…

Q: Suppose the cost, in dollars, for a company to produce x items is given by the formula  C(x) =…

A:

Q: The cost function for a certain company is  C = 60x + 300  and the revenue is given by  R = 100x −…

A:

Q: The height, in feet, of a ball thrown by a child is modeled by the quadratic equation f(r) = 1 a2 +…

A: I am attaching image so that you understand each and every step.

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.