if the point (a, b) is on the parabola y=6x^2-(5785/12) that is closest to the point (0,4) than a ?

Q: At what point of the parabola is the tangent line parallel to 7x+y-2=0? y=2x^2-3x+1

A:

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: Find the slope of the line through the point (12,15) that cuts off the least area from the first…

A: Given: (12,15)

Q: Is it possible to get a example which shows this applied to a model

A: To determine: An example which shows the application of Taylor series in a model.

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

A:

Q: Find the number x in the interval-;,1| so that the difference of the number from thrice'its cube is…

A: How to find point where the function f(x)  is minimum: find f'(x) and solve f'(x) = 0 for x. after…

Q: Use the Difference Quotient to evaluate the slope of the tangent line to the first parabola found in…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x X-axis…

A:

Q: Only part b, part a is solved but i was asked to upload b seperately

A: Given: Mean lifetime of technical part μ=2 Let X be the lifetime of technical parts X~Expλwhere,…

Q: Find the length of the arc of the curve 9y2 = 4x3 from the origin to the point (3,2v3).

A:

Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

A:

Q: <, y) = )-« lustrate with a sketch. y 4 3 3 2 2 2 1 -4 -3 -2 1 1 2 4 -4 -3 -2 4 -4 -3 -2 /1 -1 -2 -3…

A: Topic:- calculus

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - -2, and the line 4…

A:

Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

A:

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

A:

Q: Find the minimum distance from point (2, 5, -1) and plane 3x + 4y + z = 10.

A: Given query is to find the minimum distance.

Q: Find equations of both lines through the point (5, –6) that are tangent to the parabola y = x2 – 3x

A: topic - equation of tangent to curve

Q: Find the orthogonal trajectories of the family of parabolas with vertices at the origin and foci on…

A:

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

A:

Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: Find the root between (2,3) of x3+ - 2x - 5 = 0, by using regular falsi method correct to three…

A:

Q: Find the equations of the tangent line and normal line to the parabola y=2x2 at the point (2,8).

A: We find dy/dx at x=2 to find the slope of the tangent  Then we use the point-slope formula to find…

Q: There is a line through the origin that divides the region bounded by the parabola v X-axis into two…

A: Given- There is a line through the origin that divides the region bounded by the parabola y = 7x -…

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: Which hyperbolic functions are increasing on their domains?

A: First of all, consider all the six trigonometric hyperbolic functions and their domains.

Q: At whhat point on the parabola y = x - 3x-5 is the tangent line parallel to 3x-y 2

A: Given y=x2-3x-5 To find the tangent line parallel to 3x-y=2

Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

A:

Q: Find the slope of the tangent line to the parabola y = x2 at the point (2, 4) by analyzing the…

A: We have to find the slope of tangent line to the given parabola y=x2 at the point 2, 4 by analyzing…

Q: The slope of the tangent line to the parabola y = 3r2 + 6x + 2 at the point ( – 2, 2) is: The…

A:

Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: Find the orthogonal trajectories of the family of parabolas through origin and foci on axis.

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

A:

Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

A:

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

A:

Q: What is the equation of tangent to the parabola y^2 = 2x + 8 at (4,4) ?

A:

Q: What is the smallest possible area of the triangle that is cutoff by the first quadrant and whose…

A: Given that the triangle that is cut off by the first quadrant and whose hypotenuse is tangent tothe…

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x – 2x and…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 8x and…

A: There is a line through the origin that divides the region bounded by the parabola y=2x-8x2 and the…

Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

A:

Q: Find the image of the point (-2,4) under the compression with factor ½ in the y-direction. O (-1,2)…

A: The point is -2, 4To find the image of point under the compression with factor 12 in y-direction

Q: Find the slope of the line through the point (12,15) that cuts off the least area from the first…

A:

Q: Find equations of both tangent lines to the graph of the ellipse x2/4 + y2/9 = 1 that pass through…

A: We have given equation of curve x24+y29=1 and point 4,0 We will find slope of tangent at any point…

Q: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

A:

Q: Graph the given parabola by determining the vertices and using first derivative test y = 3x4- 8x +…

A: Given parabola:                              y=3x4-8x3+6x2            Let's find the y-intercept for…

Q: ) Find an equation of the tangent plane to the paraboloid defined by -- 4x² + 5y² at the point (,-2,…

A:

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

A:

Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.