Calculate a 3 ydz t 13x'y dy, Where Cis the oriented curve given in the figure . 3 Bydr+43xy dy =? X.

Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

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Q: Which choice is correct?

A: A tangent of a curve is defined to be the derivative of the function at that point and for a…

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

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Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

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Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

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

Q: The curvature of the curve 7(t)=<6t, 6t+1, sin2t) at t= 4 is

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Q: For the Parametric curve x = a(t – sint), y= a(1 – cost) where 'a' | | is a constant. Find dy at t =…

A: Given:x=at-sint ; y=a1-cost where a is constantWe need to find dydx at t=π2.

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: What is the unit tangent vector to the curve r(t)=⟨cost, sint, et⟩ at the point where t=0?

A: Given:          r(t)=cost,sint,et at t=0           r→(0)=cos(0),sin(0),e0          r→(0)=1,0,1…

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

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Q: Starting from the point (3, 1, –1), reparametrize the curve x(t) = (3 + t, 1 – 2t, –1 – 2t) in terms…

A: We need to reparametrize the given curve in terms of arclength. The solution is given below.

Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: Find the arc length of the curve x = t², y =t-, 0sts v2. 2.

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Q: Com pute I = (22132°y+ 4xy)4x+(x'+2x²-y²)dytzk + 4xyLdx + (x°t2x² -y?) dy+zdz along The curve C C4U…

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Q: The length of the curve defined parametrically by: x = e*cost, y = e'sint,0 <t <, s equal to: Select…

A: tea

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Find 4 and 4y axz dx y=te* dy- -(t-1)et y t is Fov which values the curve con cave upwavd. U BRANDS

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Q: da 2 dy 3. Use L = ) dt find the arc length of the curve dt dt e (sint + cost), y = e'(cost – sint),…

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Q: Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

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Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: dy Find at t = T/4 for the parametric 2 sin(t), y = 3 cos(2t). curve x = dx2

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Q: At which of the points below is the tangent plane to the surface - 2y² + z²+ yz = 2 vertical? Select…

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Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

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Q: Consider the curve y = zy+1. What is the value of- dz at (0, 1)? None of the given choices

A: The solution for the above question is as shown below.

Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: Find the length of parametrized curve given by x(t)=−6t^2−6t,y(t)=−4t^3−6t^2 where t goes from 0…

A: Given information:  The parametric equations are x(t)=−6t2−6t,y(t)=−4t3−6t2 over the interval .0≤t≤1…

Q: Determine the length of the parametric curve given by r = 2t3, y = 3t² where 0 <t<V8. %3D CS Scanned…

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Q: The curvature of the curve 7(t)=6t, 6t+1, sin2t) at t= is 4 18 1 8 0 1 1/2 2.

A: we have to find the curvature

Q: Consider the curve f(y) = sy + for 1 <y < 3. Find the arc length of the curve. 4y %3D

A: The length of the curve is given by                                                    L=∫abf'y2+1dy

Q: Find the arclength of the curve r(t)=⟨10(2)^(1/2)t,e10t,e−10t⟩, 0≤t≤1 I am stuck on the…

A: Solution

Q: The arc length of the curve x|+lyl 1 is Select one: ut of a. 4/2 uestion b. 2/2 с. 4 d. 2 e. V2

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Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find the tangential and normal components of acceleration at the time            t = π/2 for the…

A: Given: The plane curve is rt=etcosti+etsintj To determine: The tangential and normal components of…

Q: Compute 1 dz , ty z - where +y is the curve parametrized by z(t) = i+3 e3t, 0 < t < 67.

A: Just take a close look.

Q: find the Cerrvature of the Curve x:(0,1|R? defined by x(t)=14Cost, 1sint,o), where %3D is coostant 2

A: α(t)=(1rcost ,1rsint ,0)r is constantTo find the curvature of the given curve

Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

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Q: Consider the curve parametrized by x = t +1 and y = t6 + 4t. dy in terms of t. d.x a) Find Preview…

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

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Q: A curve is given by parametric equations x = t – 2 cost and y = t+2 sin t. dy and d?y in terms of t.…

A: The given parametric equations  x = t - 2cost ..... (1) y = t + 2sint......(2) To find  dydx,d2ydx2

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Find the arc length of the curve given by x=t^2,y=2t^2+1,1≤t≤3

A: Given,

Q: Parametrize the given curve. 4x + 6y2 = 3 c(t) =

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Q: The 35-kg boy is sliding down the smooth spiral slide such that his z coordinate decreases 2 m per…

A: Solution is in step 2

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.