2. Find the angle of intersection between the following pairs of curve. Express your answers in degrees with 1 decimal. y = x3 + 3x + 2 and y= 2 - x

Q: 48. x = e' – t, y= 4e"², 0<t<2

A:

Q: Find the length of the curve. x = 4, y = 3/2, 0 st 0st <9 242 61 2

A:

Q: Q/ Find the angle between two curves: 3 y = ==- x? , y = x? 2

A: The angle between the two curve is                                         tan θ =m1-m21+m1m2…

Q: Find the lengths of the following curves: b. x = cost and y = t + sin t, 0<t<n

A: we have to find the length of the given curve

Q: Find the length of the arc of the curve in the given range, y3 1 x = 16y + 4y? ++ 0sys4 4(y + 4) '

A:

Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

A:

Q: = y}2 /3 – y!2, 9 < y< 81 %3D

A: By using length of the curve formula, we calculate the required length of the curve.

Q: Find the length of the following two-dimensional curve. 3/2 (2t + 1) 2 r(t) = for 0sts4 3

A:

Q: Find T,N and k for the curve:

A:

Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: Find the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

Q: 1 use the formula L= [, ct to find the length of the curve 1 X=-ť. y = 1 for 0St<1

A:

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: Find the exact length of the curve. x = 1 + 9t2, y = 8 + 6t, 0 sts 4

A: Answer is mentioned below

Q: Find the lengths of the following curves: a. x = 1-t and y= 2+3t, - 2/3 sts1 y =t + sin t, 0stsn y =…

A:

Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

A:

Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

A:

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: Which of the following curves pass through the point (1, 4)? c(t) = (t 2, 3 − t)

A: A point lies on a curve if it satisfies the equation of the curve. Substitution of the point into…

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: At what point do the curves r¡(t) = (t, 1 – t, 3 + t²) and r2(s) = (3 – s, s – 2, s²) intersect?…

A: Given Data: Curve 1: r1t=t, 1-t, 3+t2 Curve 2: r2s=3-s, s-2, s2   For the intersection point,…

Q: Find the lengths of the following curves. x? 2 а. у %3 + In x, 3sx<6 8 2 y - 8 In 8 y .3sys 18 b. x…

A:

Q: Y = x2 ex X- %3D

A: the given equation of the curve is: y=x2e-x we have to solve and sketch the given curve.

Q: Find the length of the following curve. 3 y = x* from x = 0 to x = 8

A: Given,            y=x32 from x=0 to x=8To find : The length of the curve.We know that,          The…

Q: Q3/ Find the angle between two curves: 3 x2 , y = x² y = 2

A: Please see the answer in step 2

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

A:

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

A:

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 exact length of the curve. x = et − t,    y = 4et/2,    0 ≤ t ≤ 5

A: We will use arc length formula to solve this questions

Q: Find the length of the arc of the curve in the given range, y3 3 4(y + 5) ' 1 x = 25y + 5y? + Osys3

A:

Q: Find the length of the following three-dimensional curve. r(t) = (2+5t,9-3t, -6+3t), for 1st≤4

A:

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: Find the lengths of the following curves: a. x = 1– t and y = 2 + 3t, - 2/3 <t<1

A: we have to find the length of the following curve

Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: For what values of a and b is the line-5x +y b tangent to the curve y = ax when x = 37 a = b D %3D…

A: Given: Equation of line is -5x+y=b. Equation of curve is y = ax3 .

Q: 3. Use the Secant method on the circle function (x + 1)²+(y – 2)²= 16 to %3D find the intersection…

A:

Q: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

A:

Q: Find the length of the arc of the curve in the given range, y3 +. 3 1 x = 16y + 4y² + 0 < y< 4…

A:

Q: Find the length of the curve. 2ti + etj + e k, 0<tS 4

A:

Q: 9t4 – 1dt, 1< x < 5 y = L = %3D

A:

Q: At what points do the curves y=x2 and y=√x intersect? Find the angles of intersection between the…

A:

Q: r(t) 12t i + 813/2 j + 3t² k, 0 < t<1

A: Here We have to find the length of the given curve.

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 5< xs 6,

A:

Q: Find the length of the given curve:  r(t) = (4t, 5sint, 5cost) where -4 ≤ t ≤ 2

A:

Q: Find the length of the curve r

A:

Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: 23/ Find the angle between two curves: 3 y = 2 - x² , y = x²

A: The angle between two curves is given by the formula tan θ=f2'x0-f1'x01+f1'x0f2'x0 Given,…

Q: At what point do the curves r;(t) = (t, 4 – t, 24 + t2) and r2(s) = (6 – s, s – 2, s2) intersect?…

A: The curves are r1(t)=t, 4-t, 24+t2 and r2(s)=6-s, s-2, s2

Q: Which of the following curves pass through the point (1, 4)? (a) c(t) = (t2, t + 3) (b) c(t) = (t2,…

A: