Clovis is standing at the edge of a cliff, which slopes 4 feet downward from him for every 1 horizontal foot. He launches a small model rocket from where he is standing. With the origin of the coordinate system located where he is standing, and the x-axis extending horizontally, the path of the rocket is described by the formula y = −2x2 + 80x. Give a function h = f(x) relating the height h of the rocket above the sloping ground to its x-co

Q: Find the point at which the line f(æ) = 5æ + 17 intersects the line g(x) 3x + 9

A: Given

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: Find the x-intercepts of the given function.  y = 3x2 + 10x + 3

A:

Q: The path of a diver is modeled by f(x)= -4/9x2 + 24/9x + 9 where f(x) is the height (in feet) and x…

A: Since, we have been given the path of driver by :-f(X)=Y=-49X2+249X +9 -(i)Our aim is to find the…

Q: Determine b and c for the quadratic function f(x) = −x2 + bx + c where the y-intercept is 2 and it…

A:

Q: 16) For the function: f(x) = 4x² +6x+1 A) Find the intercepts.

A:

Q: Find the x coordinate of the vertex: f (x) = x +5x+3

A:

Q: lovis is standing at the edge of a cliff, which slopes 4 feet downward from him for every 1…

A:

Q: Find the equation of the quadratic function f whose graph is shown below. (5, 4) s(x) = | 10 12 14…

A:

Q: The graph of f is perpendicular to the line whose equation is 3x−4y−12=0 and has the same​…

A:

Q: R = 840x + 207x² – x³ X = units

A:

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: Find the number of units x that produces a maximum revenue R in the given equation. R = 33x2/3 – 2x…

A: Given:- R = 33x(2/3) -2x To find:- Number of units x produces a maximum revenue R

Q: Find the x-intercepts of the given function.  y = 2x2 + 5x + 2

A:

Q: Find the point at which the line f(x)=5x+14 intersects the line g(x)=−2x (_,_)

A: Given that,  Line f(x) =5x+14 and line g(x) = -2x intersects. So, both the function gives the same…

Q: Find the equation of the quadratic function y = ax2 + bx + c whose graph is shown. Select three…

A: Consider the graph: The following coordinates on the graph are:3,0,4,1 and 5,0Point 3,0: a32+b3+c=0…

Q: Find the x-intercepts of the given function.  y = x2 - 3x + 1

A: The x intercept of a function or an equation is a point of the form x,0 . A coordinate point of a…

Q: A fast-food restaurant has a cost of production C(x)=11x+110 and a revenue function R(x)=6x. When…

A: I am going to calculate that when the company will start to run on profit just is when revenue…

Q: The pollution level in the center of a city at 4am is 22 parts per million and it grows in linear…

A: (A) The pollution level in the center of a city at 4am is 22 parts per million. It grows in linear…

Q: Find the x-intercepts of the given function.  y = 4x - 4x2 - 1

A: given the function: y=4x-4x2-1For finding the x- intercept , y=0

Q: Find the point at which the line ƒ(æ) = 2x intersects the line g(x) = 4x + 12

A:

Q: Find the x-intercepts of the given function.  y = 4 - 2x - x2

A: Our Aim is to find the x-intercept of the function given below:-y=4-2x-x2-(i)For x-intercept we will…

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A:

Q: At what point will f(x) = 2x+1 andf¯1 intersect each other?

A: Topic - functions and inverse function

Q: Find the slope of the curve y = 2x* + 3x³ + 2x2 – 1 at a point where it crosses the x-axis

A: y=2x4+3x3+2x2-1 A curve crosses the x-axis at a point where its y-coordinate is zero. Therefore…

Q: The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per…

A:

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

A:

Q: Is function  y=x2 a solution for equation of (1-x3)y'-2x+x2y+y2=0? If it is, find the solution.

A:

Q: Find the extreme of the values of the function  y = x2 - 2x + 1

A: Given:y=x2-2x+1

Q: Find the point on the line y = 2x + 1 that is closest to the point (2, 2).

A: Given: Given equation of the line is y=2x+1 We want to find the point on the line  y=2x+1 that is…

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: The net profit in dollars per day for a small business owner is given by the equation f (x) = -0.1x²…

A:

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: Find an equation for the collection of points for which the distance to (12, 0) is twice the…

A: Refer to the question we need to find an equation for the collection of points for which the…

Q: Find the point(s) of intersection. f(x) = 2x2 − 7x − 18 and g(x) = 3x + 10

A:

Q: For the function z = x3 - 2x2y2 - 2y2 Please solve Zx and Zy

A: To find: The value of zx and zy. Given: The function is z=x3-2x2y2-2y2. Formula used: Power rule of…

Q: Approximate the solution(s) to x3 = x2 - 5 using a graphing utility.

A: We have to approximate the solution(s) to x3=x2-5 using the graphing utility .

Q: Determine its vertex and axis of symmetry    f(x) = 3 (x +1)^2 - 6

A:

Q: The annual total revenue for Pilot V5 pens is given by R(x) = 1500x - 0.02x2 dollars, where x is the…

A: Given, R(x)=1500x-0.02x2

Q: For the quadratic function f (x) = −2(x+1)2 +2, find the vertex, x−intercepts (if possible),…

A:

Q: In the xy plane, the graph of the function f(x) = x2 + 5x + 4 has two x-intercepts. What is the…

A: x- intercepts are the points where the function touches the x-axis. So if the function touches the…

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

A:

Q: if you vertically stretch the quadratic parent function, F(x)=x2, by multiplying by 7, what is the…

A: Explanation of the solution is given below...

Q: The owner of a video store has determined that the profits P of the store are approximately modeled…

A: Profit function, P(x) = -x2 + 30x + 76

Q: The profit function for a company that produces shoes is given by y = - 2x ^ 2 + 12x +23, where "y"…

A:

Q: Find the point on the graph of the equation f (x) = x² – 8 that is closest to the point (0, -2)

A:

Q: A fast-food restaurant has a cost of production C(x)=11x+90 and a revenue function R(x)=6x. When…

A: Given:       Cx=11x+90       Rx=6x So, the profit function is:     Px=Rx-Cx

Q: Find the point at which the line f(x)=−5x−10 intersects the line g(x)=−4x−8.

A: We need to find a point of intersection of both the given lines.

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.