For what values of k does the family of curves =² + (y – c)² = kc² have an envelope?

Q: 7x – 4xy = C

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Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

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Q: a bounded by the curve y = 3VI and the lines z = 6 and z= 8 above the z – azis is Võ+ 12v6 O 10

A: We have to choose the correct answer

Q: 7. Find the exact length of the curve: y = 1 + 6x³/², 0 < x < 1.

A: The length of the curve is calculated from the graph.

Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

A: Given that x23+y23=a23 To find the length of the curve:…

Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

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:

Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: 1. Find the length of the curve y = 3 xi - () x , from x = 1 to x = 4.

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Q: 8. Show that the one parameter family of curves y² = 4k(k + x) (k E R) are self orthog- onal.

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Q: 1 Find the exact length of the curve: r(t) = , 6.

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Q: 1. Consider the curve C given by y = 5 + 2x3/2, 0 < x <1. (a) Find the length of the curve C.

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Q: Find the exact length of the curve. x =Vy ( - 3), 1sys 25

A: given: x=13yy-3

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: / Fit a curve of the form y = ax + bx² to the data

A: Given,    x 1 2 3 4 5 y 1.8 5.1 8.9 14.1 19.8 To find             y=ax+bx2…

Q: by eliminating the arbitrary constants "A" and "B" from the family of curves Ae³x y = + Be-7x O None…

A:

Q: Find the exact length of the curve. y = In(1-x), 0sxs 8.

A: Given that: y=ln 1-x2, 0≤x≤18

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

A:

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

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: 2 =(x² - 1)³/²,1 ≤ x ≤ 3

A:

Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

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Q: What are the control points of the splines Bezier curve from the two equations given below: a(x) =…

A: Given, ax=1+5x2+2x3...1bx=1-x+x3...2 The control points are lie on both the curves. So, to get…

Q: 8) Wihat is the length of the pot Df the curve y2=(x-1)between the points (4,0) ond (2,4) ?

A: Let f(x) be a smooth function over the interval [a,b]. Then the arc length of the portion of the…

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

A:

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

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Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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

A:

Q: Find the length of the curve given by S(x) = (a -) defined on the interval (1, 2].

A: Consider the given curve:

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: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: Find the length of the curve y=z from z 0 to z=4.

A: The length of the curve is given by:

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

A:

Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 &amp; c2 are arbitrary constants. Let us…

Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

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Q: Find the length of the curve. y = (4 - x2/3) 3/2 from x = 1 to x = 8 O 9 O 12 O 18 O 6

A:

Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

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

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

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Q: Q1. Find the length of the of the curve y= from x = 0 to x = 3.

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Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: Find the orthogonal trajectories of the family of curves ey + 2x2 = k.

A: Given,  ey+2x2=k

Q: Find the paths orthogonal to the family of curves: cy ^ 2 = xe ^ x

A: Orthogonal path is a curve if it cuts every member of a given family of curves at right angles.

Q: find the under the curve y=7-t^2 and above the t-axis

A: