For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function. 26. (h, k) = (2,0), (x, y) = (4, 4)

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: f(x) = −x2 + 6x − 12 y-intercept(x, y)=

A:

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A:

Q: Determine two positive numbers e and f whose product is 27 and for which the value of 4f +3e is a…

A: Product is 27 and 4f+3e is a minimum.

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle ² +y² = 13.

A: We use formula of Lagrange's multiple Del(f(x)) = lamda * del(g(x))

Q: nissile is propelled from the origin of a coordinate system with the x units

A:

Q: Find the maximum value of ƒ(x, y) = 6xye^(-(2x+3y) )in the closed first quadrant (includes the…

A: Given and

Q: A manufacturer of wool roving has determined that the highest price per unit that can be charged to…

A: Here, D(q)=50-0.25qC(q)=100+5q2

Q: For the following exercises, consider the construction of a pen to enclose an area. 7 You have 800…

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: t's assume that the annual profit focus of the company for skiing is given as follows. P (x, y) =…

A: In the given question we have to find the maximum profit of the company where the profit focus of…

Q: Q1 Find thr relative maximum and minimum of: fx, y) = x² + y² + z?given that 9x? + 4 y² + 2z? = 36…

A: Consider the provided question,  minimize and maximize, fx,y,z=x2+y2+z2                        ....1…

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given R(x) = 10x  and C(x) = 2x + x2

Q: solve for the point on the graph y=√3x+ 2 that is closest to (3,0). What is the minimal distance…

A:

Q: What is the maximum value of the function f(x, y) = 4 – x² – 2y? subject to the constraint 2 + y? =…

A:

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: For the following exercise, use the vertex (h, k) and a point on the graph (x, y) to find the…

A:

Q: Find the relative maxima or minima. Maximum of ƒ(x, y) = 12xy - x2 - 3y2, subject to x + y = 16

A: f(x,y)=12xy-x2-3y2 , subject to x+y=16

Q: Find the maximum profit and the number of units that must be produced and sold in order to achieve…

A: Given: Revenue, Rx=52x-0.5x2 Cost, Cx=22x-1 Objective of the question is to find the maximum profit…

Q: Solve y′ = t − 5ty using both separable and linear methods, and verify that your answers are the…

A: Given data:   The given differential equation is: y’=t-5ty.     The given differential equation can…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Every second counts You must get from a point P on the straightshore of a lake to a stranded swimmer…

A: Since you have posted multiple questions. We will solve first two questions for you. If you want any…

Q: The area, in square units, bounded by the curves y = x² + 4 and y = 3x +4 is Your answer

A: Consider the given curves. y=x2+4 and y=3x+4 Put the both curve equal to find the limit.…

Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: The quadratic function y = ax2 + bx +c pass through (2, 1) and tangent to the line y = 2x + 4 at (1,…

A:

Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Assume the total revenue from the sale of x items is given by R(x) = 35 In (4x + 1), while the total…

A: Profit function, P(x)=R(x)-C(x)

Q: Suppose that f(æ, y) = e-2x² – 3y² + y Then the maximum is

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: For the following exercises, use the vertex (h, k) and a point on the graph (x, y) to find the…

A: 46. h,k=-2,-1, x,y=-4,348. h,k=2,3, x,y=5,12

Q: Find the best quadratic approximation, Q(r, y) of V9 – 6x – 4y for (r, y) (0,0). near

A:

Q: When a bus pass from Albuquerque to Los Alamos is priced at p dollars, a bus company takes in a…

A: (a)

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: This question can be solved using the concept of maxima and minima.

Q: The financial analysis department of a software design company determined that the cost of producing…

A: Given: C(x)=5000+3x p=23-x500 R(x)=px=23x-x2500

Q: ball is thrown vertically into the air has its height above ground given by  y(t)=112t−16t2 , where…

A:

Q: Ketura sells backpack danglies to tourists for $15 each, so her weekly revenue is R(x) = 15x. The…

A: weekly revenue function R(x)=15xThe cost function C(x)=15+8x+0.05x2

Q: A manufacturer determines that the profit P (in dollars) obtained by producing and selling x units…

A: Given:            Profit model:                              P(x,…

Q: Suppose a manufacturer of washing machines found that when the unit price is $x, the revenue R (in…

A:

Q: A manufacturer of lighting fixtures has daily production costs of  C = 800 − 30x + 0.75x2, where C…

A: Given Data The cost of daily production is C=800-30x+0.75x2.   Differentiate the cost of the daily…

Q: An electronics manufacturer determines that the profit P(in dollars) obtained  by producing and…

A: Consider the given function, Px,y=8x+10y-11000x2+xy+y2-10,000 Noe find the critical points by…

Q: The population density of a city is given by P(x,y) = - 20x - 20y + 560x + 440y + 200, where x and y…

A:

Q: In a concert hall, the ceiling can be described by the plane x + y + z = 30. An audio engineer is…

A: Lagrange multiplier method: If f(x, y, z) is a function such that g(x, y, z)=0 then optimal values…

Q: Given revenue and cost functions R(q)=80q−0.2q2 and C(q)=13q+500​, find the maximum profit that…

A: Profit is given by P(q) = R(q)-C(q)Given R(q) = 80q-0.2q2C(q) = 13q+500P(q) = 80q-0.2q2-13q-500P(q)…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…

Q: For the cost function C(x) = 8950 + 790x + 0.5x2 and the demand function p(x) = 2370, find the…

A:

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given is a revenue function as Rx=7x and the cost as Cx=160-2x+x2, where x denotes the number of…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.