The number of mosquitoes M(x), in millions, in a certain area depends on the june rainfall x, in inches: M(x)=15x - x2. What rainfall produces the maximum number of mosquitoes?

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: The amount of cloth used to make four curtains is given by the function A = -4x + 40x, where x is…

A: The function is A=-4x2+40x.   Differentiate the function with respect to x. dAdx=ddx-4x2+40x=-8x+40…

Q: Find the interval in which the function given by y = 4x3 - 6x2 -72x + 30 is decreasing.

A: Given: y=4x3-6x2-72x+30

Q: A bus can accommodate a maximum of 60 passengers. If X denotes the number of male passengers, what…

A: If there are maximum 60 passengers that can be accommodated in the bus, then the possibilities of…

Q: A rectangular garden of area 50 square feet is to be surrounded on three sides by a fence costing $2…

A: First lets define some variable, let x= length of fence Y = length of brick of other dimension Thus…

Q: The profit per acre from a grove of orange trees is given by x(110 - x) dollars, where x is the…

A:

Q: Find the number of units x that produces a maximum revenue R. R = 171x2 – 0.06x3 X = units

A:

Q: Solve using quotient rule:  f(x) = (x^2 + 4) (x^4 – 4x^2 + 16)

A: Given function: fx=x2+4x4-4x2+16 We know that, a3+b3=a+ba2-ab+b2.

Q: Find the slope of f(x)=3x−2 at (4,10).

A: The slope of straight line is constant for every value of x. We observe that the given 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: Given the function y = x2 + 10x + 21, what is the least possible value of y? %3D

A:

Q: Solve f(2) for f(x) = -4x + 3 %3D f(2) = [? ]

A: Put x= 2 in equation We get  - 4(2) + 3 -8 + 3 - 5

Q: A projectile is thrown upward so that it’s distance above the ground after t seconds is h =…

A: Consider the given Function, h=-11t2+484t to find the maximum height of the projectile differentiate…

Q: Solve for x x'(t)=x-t

A:

Q: A manufacturer designs and sells each of the radios it produces for 75 soles. If x daily radii, then…

A: Since, the amount of the total daily cost of production is given by:-C(x)=x2+25x+96  -(i)Price of…

Q: The profit per acre from a grove of orange trees is given by x(190 – x) dollars, where x is the…

A:

Q: Solve for the zeroes of f(x) = x* - 4x2 and sketch the graph %3D

A:

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

A:

Q: Use the vertex (2,8) and a point on the graph (0,4) to find the equation of the quadratic function…

A: Given: the  vertex is 2,8 and a point 0,4. To find : the equation of quadratic function fx.…

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: Solve f(-2) for f(x) = -5x-4 %3D f(-2) = [?]

A: Given f(x)=-5x-4 To find f(-2) Substitute -2 for x

Q: The average cost in dollars of producing x units of golf clubs is C(x) = x2- 18x + 140. Determine…

A: Average cost of golf clubs - C(x) = x2-18x+140Given that,C(x) should be below 75$Then,C(x) <…

Q: The profit (in dollars) from the sale of x infant car seats is given by P(x) = 45x -0.025x2 - 5000…

A: The profit function on sale of x infant car is P(x)=45x-0.025x2-5000.

Q: The profit per acre from a grove of orange trees is given by x(230 - x) dollars, where x is the…

A: Given profit function :

Q: how

A: The given function is a third degree polynomial.

Q: A building worth $825,000 is depreciated for tax purposes by its owner using the straight-line…

A:

Q: The profit per acre from a grove of orange trees is given by x(270 – x) dollars, where x is the…

A: Given, The profit per acre from a grove of orange trees is given by x(270-x) dollars, x is the…

Q: Solve for f(2) f(x)=-3x+3 f(2)=?

A:

Q: The area of a rectangle is represented by 12x - x² where x is a side of the rectangle. For what…

A:

Q: A 100 inch strip of sheet metal starting out 16 inches wide is to be made into a small open trough…

A: Given, A 100-inch strip of sheet metal starting out 16 inches wide is to be made into a small…

Q: Find the domain of f(x)=2x+10/3x+4 Enter the solution in interval notation.

A: Consider the function  f(x)=2x+103x+4

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

A: In year 2002 , exports will reach $8.5 billion.

Q: What is the equation of a quadratic function y = f(x) with two irrational zeros,-h and h where h is…

A: Given,         The equation of a quadratic function y=fx with two irrational zeros, -h          and…

Q: The graph of f(x) = 2x + 6x2 – 90x + 21 has two horizontal tangents. What is the negative value of x…

A: Given that the graph of f(x)=2x3+6x2-90x+21-(i) has two horizontaltangents.Our Aim is to tell the…

Q: The path a diver takes from the diving platform is modeled by the equation f (x) = –,x² + 3x + 12…

A: find the maximum height

Q: The profit P (in dollars) for a company that produces antivirus and system utilities software is…

A: Calculate the derivative for P i.e. P’(x).

Q: Solve using quotient rule:  f(x) = (3x^2 – x + 4) (2x^2 – 1)

A:

Q: use quadratic functions. Suppose that the cost function for a particular item is given by the…

A: We have to use quadratic functions. The cost function for a particular item is given by the…

Q: A company has identified that the revenue for a particular product is given by the equation R = -x3…

A: To find: The number of units need to be sold to obtain the maximum revenue. Given: The revenue is .…

Q: Solve f(-6) for f(x) = 3x+ 15 %3D f(-6) = [ ? ]

A: Given: f(x)=3x+15

Q: Find a quadratic function with the roots 1 and 3

A:

Q: Find the length x. X 2.

A:

Q: The profit per acre from a grove of orange trees is given by  x(150 − x) dollars,  where x is the…

A:

Q: ivp

A:

Q: The profit per acre from a grove of orange trees is given by  x(290 − x) dollars,  where x is the…

A:

Q: The total revenue​ (in hundreds of​ dollars) from the sale of x spas and y solar heaters is…

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: The average cost function for the weekly manufacture of retro portable CD players is given by C(x) =…

A:

Q: The height of a ball after being dropped from a point 64 feet above the ground is given by h=…

A: When the ball hits the ground, the height of the ball from the ground is zero. The solution of the…

Q: distance above the ground after t seconds is h=-12t^2+384t after how many sounds does it reach it’s…

A: