Find the arc-length parameterization for r (t) = (t+ 3, 2t – 4, 2t) , t > 3 - and then use it to find the coordinates of the point on the curve at a distance of 1 from (6, 2, 6).

Q: etermine Z J f(x,y) ds with curve C is the curve of the circle x+y² =4 from (0, 0) to (- nd fly d

A: ∫c f(x,y) dsC ;  x2+y2=4   from   (0,0) to  (-3   , 1)and  f(x,y) =x(y+1)+y

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

A:

Q: curve ï = 3t — 5, y = 4t +6 with 5 ≤ t ≤ 6.

A:

Q: Find the arclength of the curve r(t) = (6/2t, e¤, e -ot), 0 < t<1

A: Given  curve   rt=62 t, e6t, e-6t  0≤t≤1To determine  the  arc  length  of the curve  rt    rt=xt…

Q: Find an equation, in slope-intercept form, of the line tangent to the curve with parametric…

A:

Q: Determine the arc lenght of the curve 9x2 = 4(y² – 1)³for 1 <y<2.

A: This question is related to calculus.

Q: For the following two parts, the curve C is the part of y = 4 - a² from (0, 4) to (2,0). (a)…

A:

Q: Find the arc length (s) of the curve r(t) = (-41³/2 +3, -4t³/2+2, -4t - 4) for 2 ≤ t ≤ 4 S =

A:

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

A:

Q: (- 4t + 3, t + 2, – 2t – 4) for -4 <t < - 1

A:

Q: Find the length of the arc of the curve-y = (x − 2) = from x = 0 to x = 6

A:

Q: Find the length of the curve. (2t + 1)3/2 2.y = Osts 16 x= 3

A:

Q: Find the arc length of the curve x = (10 – 2y)³/² ,-3 < x<

A:

Q: Starting from the point (3,−4,−2) reparametrize the curve r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k in terms…

A: Given r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k Let, x=(3+1t),        y=(−4−3t),         z=(−2−3t)

Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: The helix F(t) = 4cos(t)i + 2 sin(t)j + 5tk is shown below. By setting the last component to zero…

A: Given that,Equation of a helix isr→(t)=4cos(t)i^+2sin(t)j^+5tk^The projection of this curve into the…

Q: Find the arc length (s) of the curve 7 (t) = ( – 2t + 3, 4t%/2 + 2, – 4t/2 + 6) for 1 <t< 4 S =

A: Arc length is-  Integration with limits a to b [√(dx/dt)^2 +(dy/dt)^2 +(dz/dt)^2] dt

Q: Find the arc length of the graph of (v-1)³ = x² 1 <y<5.

A: Given that y−13=x2 and 1≤y≤5. We have to find the arc length of the graph of y−13=x2 and 1≤y≤5.…

Q: Find the arc length of y³+y=x²+6x on the interval [-5,-1].

A: Solution:   Given that,      y3+y=x2+6x,  interval -5, -1         Then, differentiating with…

Q: Find the arc length (s) of the curve 7(t) = ( - 2t + 2, – 2t3/2 + 1, – 4t3/2 4) for 0 <t < 3 - S =

A:

Q: For the curve x (t) = t², y (t) =t³ – 3t Given the curve crosses itself at (3, 0), a) Find the…

A:

Q: Find the arclength of the curve x = Y = 12/2² t² with 4 ≤ t ≤ 8.

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

Q: 11. In 1970 the Department of Natural Resources released 1000 splake (a crossbreed ofE fish) into a…

A: The Malthusian growth model is P(t) = P0ert, where P0 is the initial population.

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.