find the exact work required to pump the syrup out of the top of the tank.

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

A:

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

A:

Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

A:

Q: Find the length of the curve y x² Inx 8 at (2 <x< 4)? -

A:

Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

A:

Q: Find an equation of the tangent line to the hyperbola y=3/x at the point (3,1)

A:

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

A: Given curve is 9y2=4x3, and the point is 3,23.   The objective is to determine the length of arc of…

Q: The slope of the tangent line to the parabola y= 4x2 + 2x + 4 at the point (-1, 6) is : ?  the…

A: Consider the equation of the parabola, y=4x2+2x+4 The first derivative dydx of the curve at any…

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

A:

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: Find the length of the arc of the curve 4y2 = 9x3 from the origin to the point (2,3v2).

A:

Q: A particle is moving along a hyperbola  xy= 8. As itreaches the point (4, 2) , the y-coordinate is…

A:

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

A:

Q: Find an equation of the tangent line to the parabola y = x2at the point (2, 4).

A: To find the equation of the tangent line to the parabola y = x2at the point (2, 4). For the parabola…

Q: What point on the curve y = Vx is closest to the point (5, 0)?

A: Use distance formula between two point and then differentiate

Q: Y = ce" || if the angles of the intersection are 7 radians.

A:

Q: Find the arclength of the curve y = 3x² + 5 on [0,3].

A:

Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: Find point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find the exact length of the curve. 1 y = 1 + cosh(8x), 0 ≤ x ≤ 1 8

A:

Q: The slope of the tangent line to the parabola y 3x? + 6x + 2 at the point (- 2, 2) is: The equation…

A:

Q: Find an equation of the tangent line to the parabola y = x - 8x + 9 at the point (1, 2).

A:

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

A:

Q: 9) Find the slope of the tangent line to the hyperbola defined by the equation y2 - x2 = 7 at the…

A:

Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

A:

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: Find the length of the curve (Sketch and Solve) One branched of the curve 9y2=4x3 from x = 0 to…

A:

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

A:

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y,  (−9,81/2)

A:

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

A:

Q: The slope of the tangent line to the parabola y 4x? + 7x + 3 at the point (0, 3) is: The equation of…

A:

Q: Find a cubic function  y = ax3 + bx2 + cx + d  whose graph has horizontal tangents at the points…

A:

Q: Find a point on the curve y = x2 that is closest to the point (18; 0)

A:

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

A:

Q: Find the length of the curve for 12x = 4y³ + 3y-¹ where 1 ≤ y ≤ 3 Enter your answer in exact form.…

A:

Q: Find the arclength of y = 4x2 - 4 where x is greater than or equal to 0 and less than or equal to 4

A: Concept Used: The arc length of the function is the length of the curve y=fx on the interval a,b is…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

A: NOTE: Refresh your page if you can't see any equations. . The diameter of the dish is 18 feet and…

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

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 water tank has the shape obtained by revolving the curve y = x^4/3 around the y-axis. What is the…

A:

Q: Find a cubic function y = ax3 + bx2 + Cx + d whose graph has horizontal tangents at the points (-2,…

A:

Q: The slope of the tangent line to the parabola y=2x^2+2x+7 at the point where x=4 is: slope =…

A: The equation of the parabola is y=2x2+2x+7

Q: Find the exact length of the curve. y = 9 + ¹ cosh (8x), 0≤x≤7

A: The curve y=9+18cosh8x, 0≤x≤7

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

A:

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.