li) y²= x3 2. between XEo nd x=7 49x between X=0 nd X=1 (a) sketch the Curve (b) Lind its length.

Q: 2. Assume the lines that appear to be tangent are tangent. Find ZW. Y 12 X 20 ZW =

A: Theorem  The tangent at any point of a circle is perpendicular to the radius through the point of…

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) 25 O a. y = 7x 4 13 25 O…

A:

Q: Consider the curve z = 1 – 3t, y =t-3t. If tangent at point (1- 3t, t- 3t) inclined at an angle 0 to…

A: Consider the curve x=1-3t2,y=t-3t2If the tangent at point (1-3t2,t-3t2) inclined at an angle θto the…

Q: Find the exact length of the curve. y = 5 + + cosh(6x), 0 < x < 8 6 31

A: We have to find exact length

Q: Find the length of the curve 36y2 = (x — 4)3 , 2 ≤ y ≤ 3, y ≥ 0.

A:

Q: Find the exact length of the curve. x- 2, y =? - 2, Osts9

A:

Q: Determine the length of the tangent to the circle x2 + y2 − 4x − 5 = 0 from (8, −2)

A:

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: Find the exact length of the curve.   36y2 = (x2 − 4)3,    5 ≤ x ≤ 6,    y ≥ 0

A: NOTE: Refresh your page if you can't see any equations. . but here

Q: Find the exact length of the curve. 36y2 = (x2 – 4)³, 4 < x < 9, y 2 0

A: Given:

Q: 2.) What is line QP called? * U R. V S T Secant Tangent O Slicer Chord

A: In circle, all the point are at the same distance from the center.

Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

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

A:

Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

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

A:

Q: Find the length of the curve. 2,3/2,0 st s9 x= 4t, y 3 61 242 2 3 O 2. seçenek 4. seçenek 122 61 3 3…

A: We can find the arc length as below

Q: Find the exact length of the curve. 1 1<x<2 y = 8. 4.x *

A: solution.

Q: What is the area of the largest triangle in the first quadrant with two sides on the axes and the…

A:

Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

A:

Q: Find the exact length of the curve.42. x = et − t, y = 4et/2 , 0 ≤ t ≤ 2

A: Given eqn : x=et-t,  y=4et/2 ,  0≤t≤2 So, we use dxdt=et-1,  dydt=2et2   Length of the curve =…

Q: 1. Find the length of the curve 4Y, 1<Y<2 8

A:

Q: Q1/ Find the equation of the circle tangent at least to three lines (y = 1, y 5, x 2 and x = 7). %3D

A: We have considered the first 3 lines as the line of the tangents For more see below

Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: Find the distance from the origin to the point (x, y).

A: Distance between Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) %3D 25 ix + O b. y = 7 O…

A:

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Find the length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

A:

Q: 36y2 = (x2 − 4)3,    2 ≤ x ≤ 6,    y ≥ 0

A:

Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

A:

Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

A:

Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: Find the curve length 1 +2)?,0< y < 4 %3D 3

A: Given that, the function is x=13y2+232 and the interval is 0,4. Note that, the arc length of the…

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: What is the length of the curve I=1+32, y = 4+2t, (0 <t<1) ?

A:

Q: Examine the triangle. Y If XY = 7 km and XZ = 11 km, determine YZ. Correctly estimate the length of…

A:

Q: The siope of a line tangere to the curve y=fx)at(3 4) 0f iz cists) equais

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 4?

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: Determine the length of the latus rectum of the curve y² = 8x

A:

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

A:

Q: In the diagram below, XY is tangent to OCat point P. What is m2CPX? Explain.

A:

Q: Find the angle of intersection between the curves y = x- +1 and y = x+x-

A: y = x2 + 1,y = x+ x-1Points of Intersection;x2 + 1 = x+1xx(x2+1) =(x2+1)x = 1y = 2point of…

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

A:

Q: For what values of aa and bb is the line −4x+y=b-4x+y=b tangent to the curve y=ax2y=ax2 when…

A:

Q: Find the length of the curve. 33) y-승. from x = 1 to x= 5 2x

A:

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: Identify the length of the curve 1X = ²+2y — In(y + 1), for 0 ≤ y ≤ 2. - 8

A:

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.