(i) On the same diagram, sketch the eurves y? =-* and y x (ii) Find the exact r-coordinate of the point of intersection of the two curves.

Q: Find an equation of the tangent to the circle x2+y2=36 at the point (5,3)

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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: What is the shortest distance from the curve x^2+xy+y^2=16 to the origin?

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Q: calculate the length of the curve y=2cosh (x/2) for 0 < x < 2

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Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Find the exact length of the curve.

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Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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

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Q: Explain the steps required to find the length of a curve x = between y = c and y = d. g(y)

A: Given the curve x=g(y). We need to explain the steps required to find the length of a curve between…

Q: The a coordinate of the point of intersection between the two curves y = ellz and y= 1 is x =

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Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

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Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: Find the exact length of the curve. 1 y = 4 -x² - In(x), 1< x < 8 2

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

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

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Q: Find the length of the curve x = - (5 + 4t), y= 1- t, z= - (4+ 2t), for 3 <t < 5. length = (Think of…

A: Find the length of the given curve.

Q: 3. For the curve y = 3xtnx at the point (1,1) find the following using exact numbers:

A: Given y=3xlnx at point 1,1

Q: Find the exact length of the curve. 36y2 = (x² – 4)³, 4 < x < 9,

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Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

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Q: Find the exact length of the curve.y = 9 + 1/7 cosh(7x),  0 ≤ x ≤ 6

A: Given that: To find: Exact length of the curve

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

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Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the exact length of the curve. y = 9 +  1 7  cosh(7x),  0 ≤ x ≤ 6

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Q: Find the length of the curve Y = 4x^3/2 from x = 1 to x =8

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Q: Find the length of the curve. y= (16-x2/3)3/2 from x=1 to x=64

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Q: Find the equivalent DE for the given family of curves 1. All circle center at the origin. 2. all…

A: Let's find.

Q: Find the length of the curve y=x^3/2 from (1,1) to (2,2squareroot2)

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Q: Find the exact length of the curve. 1 + X = 8 , 1< y< 2 4y2'

A: It is given that,       x=y48+14y2,   1≤y≥2we have to find the exact length of the curve.   So, we…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx %3D

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Q: Find the length of the curve y=7x-13 between y=-6 and y=15.

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Q: Try to find the slope of the tangent to the circle x²+y²=5. at the point (-2, 1) Show solution

A: tangent

Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

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Q: Find the exact length of the curve. 36y2 = (x² – 4)3, 2 < x < 9,

A: Given:  36y2 = (x2 - 4)3 , 2≤x≤9,y &gt;= 0

Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

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Q: Find the length of the curve Y = 4x^3/2 from x = 0 to x = 5/16

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Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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Q: Find the exact length of the curve. 36y² = (x²-4)³, 4≤x≤6, y 20

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

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Q: i) Find the exact length of the curve y=+15x52 4x3 1 ≤ x ≤ 2,

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: What is the longest distance from the curve x ^ 2 + xy + y ^ 2 = 16 to the origin?

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Q: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

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Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: The length of the curve 4/2 3 y = xi - 1,0 < x < 1 is .

A: Given,            The length of the curve y=423x32-1 , 0≤x≤1 is 136.To find : Check whether the…

Q: Find the exact length of the curve. 36y² = (x²-4)³, 5≤x≤9, y 20

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.