The length of the curve that results from the intersection of r = 1,0 <0 < T,0 < ¢ < 0.5n, with 0 = 60° is O a. 1.36 O b. 1.57 O c. 0.45 O d. 5.44 O e. 6.28

Q: find the length of the indicated portion of thecurve.r(t) = (et cos t)i + (et sin t)j + etk, -ln 4…

A: Given, r(t)=etcosti+etsintj+etk length L=∫-ln40r'(t)dt            .......(1) now derivate given…

Q: Which of the following curves are regular? Find a unit-speed reparameterisations of those that are…

A:

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Find the length of the curve: "(1) =/21i +e'j+e°k, 0 si sl

A:

Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: Find the moving trihedral of the curve 7(t) at the indicated value: 7(t) = cos? t î + sin? t ĵ + 1…

A:

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

A:

Q: Find the arc length of the curve below on the given interval. y= 2x3/2 on [0,9] Which of the…

A: To find the arc length of curve

Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

A:

Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: Find the length of the following curve at the given distance. Rie). cos'e ?a sin? t } Cos t i 2

A: Given curve is R→t=cos3ti^+sin3tj^ where 0≤t≤π2. We have to find the length of the given curve at…

Q: Find the length of arc of the curve y = In r from r = 3 to r= 9. 8

A:

Q: CT & DT are tangents of circle E = m/BMF = 70° A C B F LL H E # D M T Find m/DHC Find m/CTD

A: Since ABMF is a rhombusSo,…

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

A:

Q: PR is tangent to circle Q at R and PS Is tangent to circle Q at S.Find mZP.

A: Given: PR is tangent to Q at R and PS is tangent to Q at S ∠P =  x° ∠Q =  4x° ∠R =  90° ∠S =   90°

Q: Given the curve with parametric equation x= e* and y= In(2-r²) Find the equation of the normal to…

A:

Q: Find the length of the curve 7 (t) = (cos(3t), sin(3t), 2t) for – 8<t< 7 - Give your answer to two…

A:

Q: Find the length of the curve. r(t) (7t, 3 cos t, 3 sin t), -2 sts 2

A:

Q: given curve i's rotated adout OU

A:

Q: Find the length of the following two-dimensional curve. r(t): = (cos t, sin t) , for 0stsT The…

A: The formula for finding the length of the curve is explained in step 2 with a general observation…

Q: 9. Consider circle H below. a) If XH = 10 feet and XY = 100°, then determine the arc length of XY. Y…

A: Use the relation between arc length and central angle with radius.

Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

A:

Q: nd the points on the given curve where the t r = 1 + cos(0), 050 < 2n prizontal tangent r, 0) = %3D…

A: Given curve is  r=1+cosθwhere 0≤θ≤2π.

Q: Find the length of the curve. r(t) = , −4 ≤ t ≤ 4

A: The length of the curve is given by  r(t) = &lt;5t, 3 cos(t), 3 sin(t)&gt; r'(t) = &lt;5, -3…

Q: Find the arc length of the curve 3y = 4x between the points (3,4) and (9, 12). А. 8 В. 9 С. 10 D. 11

A: The solution is:

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

A:

Q: The arc length of the curve r(t) = (3t², 41² ) for 1<t<6 is (a) 175. (b) 100. (c) 10.

A: Given curve  r(t)=3t2, 4t2,      1≤t≤6

Q: ind the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π (b) r = 4 sin…

A:

Q: 2. In 00, AE is tangent to 00 at E, mZBCF = 112 and mBE:mDE = 3:7. Find: (а) тBЕ (b) тLA E A В (c)…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find a°y*dx where C is the arc of the curve x = = y? from (0,0) to (9,3)

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Q: Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -5 sts 5

A: To determine the length of the curve.

Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

A:

Q: 6. Trace the curve r? = 4cos*etan?e. %3D

A: The equation r2=4 cos4 θ tan2 θ can be resolved to get two equations:  r=±2 (cos2 θ)(tan θ)=±2(cos…

Q: Find the length of the curve. A) 18 3 sin(t)+3t, y 3 cos(t), 0 sts B) 6 %3D %3D C) 3T D) 12

A:

Q: q (s) = ( a (9) Show that q (s) = cos (ø (u)) du, sin (ø (u)) du So is a unit speed curve with k± dø…

A:

Q: Find the arc length of of the line segment c(t) = (3+ 4t, –1 – 5t) fromt = 0 to t = 10- O 410. O…

A:

Q: Find the length of the curve over the given interval: r=3acos(theta) Interval: [-pi/6,pi/6]

A:

Q: 1. Let the curve C be given E (a) Reparametrize the cur in the direction of inc (b) Give the…

A: Given that the curve C is rt→=32t2,t3. a)It is required to parameterize the curve with respect to…

Q: Find the length of the arc of the curve x = t, y= t° between the points for which t = 0 and t = 2.…

A:

Q: Find the length of the portion of the arc given by r(t) = (e 'cos t) i + (e 'sin t) j + 7e'k, -In 2…

A:

Q: Find the length of the following three-dimensional curve. r(t)= (sin t, cos t, 2t), for 0sts4

A:

Q: Find the arc length L of the graph of r(?). r(t) = f i+tj+Vor k, 2<156 L =

A: Pls follow step 2nd .

Q: Find the length of the following two-dimensional curve. r(t) = (5 cos t, 5 sin ), for 0sts

A: Recall: Length of the Parametric form :L=∫t=at=bx'(t)2+y'(t)2 dt

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

A:

Q: The arc length of the portion of the curve y=x? with 0<. O none s=7.7868 Os29.0734 sx10.1938

A: Given that: y=x3/2,    0≤x≤4

Q: For the diagram below with a bearing from 1 to 2 of N21°E and a bearing from 2 to 3 of S7*E,…

A: We are given a figure and some information about the angles. First of all, we draw a diagram…

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.