a) Show that the length of the arc of parabola y? =16x measured from the vertex to an extremity of its latus rectum is 4[/2 +log (1 + /2)].

Q: 3. Find the right triangle of largest area inscribed under the parabola y = 4 – r² with its base…

A: Given: y=4-x2 Vertex of the parabola will be at 0,4 and the points where parabola intersect the…

Q: How high is the point P on parabolic arc tunnel of the span of 20ft and height of 16 feet ,at a…

A: Let x be the horizontal distance from the span and y be the height. Therefore top of height of arch…

Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: Find the arc length of the graph of the function over the indicated interval. y -m (anon).

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Q: Find the arc length of the graph of the given equation from A to y = 6x2/3 + 1 А(-1,7), В(—8,25) B.

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Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

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Q: Find the arc length of the graph of the function over the indicated interval.

A: Using the power rule we find the derivative of y

Q: Find the arclength of y = 4x°/2 on 2 < x < 4 %3D

A: Given :  y=4x32     on  2≤x≤4   To Find : Arc length of y=4x32

Q: Find the length of the arc of the given parabola: x²=4y from x=-2 to x=2

A: We know that the length of the arc of the parabola y=f(x) from x=a to x=b is given by L = ∫ab1+dydx2…

Q: Find the length of the graph of y = (1/2) cosh 2x from x = 0 to x = ln sqrt(5).

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Q: find the total length of the arc of the function 6xy = x^4 + 3, x=1 to 2.

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Q: Find the length L of the arc formed by y=e^4x/4,0≤x≤3

A: To find the length L of the arc formed by y=e^4x/4,0≤x≤3

Q: Find the arclength of y = 4x - 2 on 0 < x < 1

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Q: Find the arclength of y = 2x + 5 on 0 < x < 4

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Q: Can you please answer this question and show all of the steps

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Q: 1. Find the length of the arc of the cycloid: x = t - sint, y = 1 – cost , 0st<2n

A: given that x=t-sint, y=1-cost, 0≤t≤2π find the length of the arc of the cycloid we know that length…

Q: Find the arc length of the graph by partitioning the x-axis. y = x3/2 + 2, from x = 3 to x= 5

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Q: 2 Find the arc length for y = 3x3 on [1, 8]

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Q: Find the exact arc length of the curve. x6 + 8 y = from x = 1 to x = 3. 16x2 Give the exact answer…

A: To Determine: find the exact arc length of the curve  Given: we have a function y=x6+816x2…

Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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Q: The arc length of the portion of the curve y =ex with 3 <x<5 is

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Q: Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference…

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Q: Find the arc length of the graph by partitioning the x-axis. y=(1-x2/3)3/2 , from x= 1/64 to x=1

A: Given function is y = y= 1-x2/33/2 from x= 1/64 to x=1 The arc length of a curve on the interval [a,…

Q: Find the arclength of y = 2x/2 on 1 < x < 3

A:

Q: 1. The graph of y--k is shown in the xy-plane above, where & is a constant. If the arca of APOR is…

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Q: Will a truck that is 14 feet wide carrying a load that reaches 10 feet above the ground clear the…

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Q: 28. Show that the graphs of y = tan x and y = cot x have nohorizontal tangents.

A: A horizontal tangent line is a mathematical feature on a graph located where a functions' s…

Q: Show that the length of the perpendicular from the foot of the ordi- nate of any point on the…

A: We know the equation to the tangent at the point (x0, y0) is y-y0 = m(x-x0), where m is the slope.…

Q: A bridge is to be built in the shape of a semi-elliptical arch and is to have a span of 80 feet. The…

A: The standard form for the equation of an ellipse with enter (h, k), horizontal major axis of…

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

A:

Q: Find the arclength of y = 4x + 3 on 0 < x < 2

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Q: From the vertex (0, c) of the catenary y = c cosh(x/c) a line L is drawn perpendicular to the…

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Q: Find the arclength of y 2x +1 on 0 < x < 2

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Q: Will a truck that is 12 feet wide carrying a load that reaches 11 feet above the ground clear the…

A: Here we use the basic equation of the ellipse.

Q: Find the exact arclength of y = 2x3 for 0≤ x ≤ 2:

A:

Q: Will a truck that is 16 feet wide carrying a load that reaches 11 feet above the ground clear the…

A: Here we have to uae the concept of conic section.

Q: Find the arc length of the graph by partitioning the x-axis. y=1/3 (x2 +2)3/2 , from  x = 3 to x =…

A: Given: The function y=13x2+232  fromx=3 to x=4

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Find the arc length from x=0 to x=100 of the catenary: 150cosh(x/150)

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Q: Find the value of a such that the arc length of the catenary y = cosh x for −a ≤ x ≤ a equals 10.

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Q: Find the arc length of the graph by partitioning the x-axis. y= x3/6+1/2x , from x = 1 to x = 9

A: Find the arc length of the graph by partitioning the x axis. yx=x36+12x for all x∈1,9.

Q: Find the arclength of the e given by ƒ(æ) = 1 + 6x³/2 for 0 < x < 1. curv

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Q: Find the length of the arc of the parabola y sq = x from  ( 0, 0 )  to ( 1,1)

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Q: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

Q: Use the formula for arc length to show that the length of a graph over [1, 4] cannot be less than 3.

A: Let a function be: Now for any given function y=f(x), arc length is given as:

Q: ne area of the sector MAG in terms of T and appro ximated to the nearest

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Q: Find the length of the arc of the parabola y sq = x cu .  from  ( 0, 0 )  to ( 1,1)

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Q: 1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

A: Given data  y=3x+2 Interval ÷ 0≤x≤3 Formula for arc length is given by  L=∫ab1+dydx2dx

Q: A storage room in a bakeshop has its roof inclined and meets the level floor 8 meters from the door…

A: Given: DX=8 m……1DT=3DX……2   Also, Width of tray=1 mHeight of tray=2 m……3   To find: Distance between…

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.