With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are arbitrary constants, So what is the value of k?

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A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

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Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

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A: Length of curve

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Q: Find the exact length of the curve.   y2 = 4(x + 4)3 , 0 ≤ x≤ 2 , y&gt; 0

A: Given: y2=4x+43,0≤x≤2,y&gt;0 To Find: Find the Exact length of the curve. Concept: Length of the…

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Q: For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2…

A: Solution is here

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

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Q: 3. Find the length of the curve r = e® for 0ses 2n.

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Q: (6) Find the points on the curve 5x2 + 6xy + 5y² = 9 which are nearest to and farthest from the…

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Q: 11. Find the length of the curve y = 2x3/2 x!/2 from x = 1 to x = 4. 2

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

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Q: 9. Find the length of the curve defined by r(t) = (t, -1sts1.

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Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

Q: 1. Find the length of the curve y = x2 from x 1 to x = 4.

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

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A: No. The line is not tangent to the curve at the point (3,5). The following picture shows the graph…

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Q: 9. Find the point on the curve y x² closest to the point (0, 1).

A: As per bartleby guidelines we only give first question answers.

Q: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

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Q: 2 Consider the two graphs y = 2x and x - xy + 2y = 28. The absolute value of the tangent of the…

A: Introduction :

Q: Find the length of the curve defined by Y=5x^3/2+9y from x=1 to x=8.

A: Given that

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Q: B. Find the slope of the curve at the point indicated. 1. y = at x = -1 4-x2 %3D 2x+3 2. y = xv1 +…

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Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

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A: We have to find  the equation of tangent in the form of y=mx+c.

Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

Q: Suppose that/ (3r-x²) dr=Ax'+Bx'+C, for constants A, B, C. What is the value of C if the curve =…

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.

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.