Find the exact value of the number a so that the length of the curve defined parametrically by

Q: 5. The curve C has parametric equations = (In t)? – Int, y = In t2 - t2, (1) Find the exact…

A:

Q: Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval…

A: To eliminate t and find cartesian equation.

Q: Write Parametric Equations to Represent a Curve for the given curve for the given definitio:

A: In question number 32, we are asked to form only parametric equations, that means equation of x and…

Q: 1. Consider the parametric curve given by x = e-t, y = 1 – e-2t. Eliminate the parameter, sketch the…

A: Sketch the graph of the given parametric curve and determine the limits on values of x and y.

Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: Find parametric equations for the lines with the given description.Perpendicular to the xy-plane,…

A: The line is perpendicular to the xy-plane and passes through the origin;

Q: The graph of the curve given by the parametric equations X=sint and y=cos2t IS à Select one: O ircle…

A:

Q: This is the problem  If a and b are fixed  numbers, find parametric equations for the curve that…

A: It is required to define the point P in a, b  and θ.

Q: Give parametric equations that describe a full circle of radius R, centered at the origin with…

A:

Q: 62 can be drawn with parametric equations. Assume the curve is traced clockwise as the parameter…

A: For ellipse equation  x^2/a^2 + y^2/b^2 = 1 It can be parameterized as <a cos(t) , b sin(t)>…

Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: To sketch the graph of the parameric curve ,first we find  x and y values corresponding to each t…

Q: (a) Find parametric equations for the tangent line to the curve -tcost, y-t, -tsint at the point…

A: We have to find parametric equations for given point-

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. If you…

A:

Q: (ii) Express the unit circle centred at position (1,2), using parametric, implicit and explicit…

A: Follow next step

Q: Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the…

A: Here, the given parametric equation is: x=1-t2, y=2t-t2, -1≤t≤2

Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

A:

Q: Obtain the parametric equations of: An epicycloid curve described by a point on the circumference of…

A:

Q: Sketch the surface represented by the parametric equations x = cos³ t and y=sin³ t with 0st≤n/2.…

A: Given: x=cos3t and, y=sin3t we have to find the surface area by rotating about x-axix. Suppose the…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A:

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

Q: t. A projectile is fired from a height of 8.2 feet with an initial velocity of 122 ft/sec at an…

A:

Q: Sketch the plane curve represented by the given parametric equations Then use interval notation to…

A: Given Plane Curve equation in parametric form is     x=3t,   y=t2+t+5  Now, Plane Curve equation in…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. If you…

A:

Q: ;Assume time t runs from zero to 27 and that the unit circle has been labled as a clock. Match each…

A: Consider the clock as the unit circle. Then the angle 0 corresponds to 3 o' clock, π2 corresponds to…

Q: The parametric equations for the graph are x =- V1-ť², y=arccost Determine the equation of the…

A: First, find the point at t=1. So substitute t=1 in x=1-t2 and y=arccos t to find the coordinates of…

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A:

Q: find parametric equations for the lines with the given description.  Passes through (1, −1, 0) and…

A:

Q: A parametric curve is given by C : [0, π/4] --> R2: Determine the length of the parametric curve

A: Consider the given functions. xt=e-2tsin2tyt=e-2tcos2t Now, find the derivative of x(t) and y(t)…

Q: The parametric equations: x = a cos 0,y = a sin 0;0 <e < 2n, define a curve called an asteroid

A:

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A:

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

A:

Q: iminate the parameter in x = -t +2t and y =t-4 and then identify the parametric sketch its image in…

A:

Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: Questlon a.- Fad the parametric form of the Curve x =a Cos (-)-Jy (zaryo Curve is a reqular Curve…

A: To find the parametric form of the curve,

Q: Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

A:

Q: Find the slope of the tangent line to the polar curve r = cos(e) at e =. Enter as an integer or…

A:

Q: (a) Determine the Cartesian equation for the parametric curve defined by x(t) = 5 sin t and y(t) =…

A: We have to find the equation of the curve ,tangent equation to the curve.   Note - As per our…

Q: If a and b are fixed numbers, find parametric equations for the curve that consists of all possible…

A: Any point on the Cartesian coordinate system is defined as x, y. Start from the origin, move m units…

Q: Sketch the curve by using parametric equations to plot points. Indicate with an arrow the direction…

A: Solution of above problem is as follow...

Q: Sketch the plane curve represented by the given parametric equation x = 2 sin t - 3, y = 2 sin t +…

A: To sketch a plane curve, first write the equation in terms of two variables. Now, substitute random…

Q: This is the problem    If a and b are fixed numbers, find parametric equations for the curve that…

A: Let the coordinate of point P is (x,y). In the triangle OCD, sinθ=CDOCsinθ=yby=bsinθ Similarly,…

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

A: cos2x+ sin2x=1

Q: A circle of radius 1 rolls around the outside of a circle of radius 2 without slipping. The curve…

A: Radius of fixed circle a=2 Radius of rolling circle b=1 ∠ICP=φ   aθ=AI=PI=Bϕ…

Q: Find parametric equations for the curve with the given properties. The line passing through (5, 7)…

A: To determine the parametric equation of the line.

Q: Suppose parametric equations for the line segment between (7,-3) and (8, 2) have the form: Т a + bt…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: The surfaces are provided as z=x2+y2, z=16-y. We need to determine the set of parametric equation…

Q: Consider the curve parametrized by: x = sin t, y = sin2t a. Eliminate the parameter b. Sketch the…

A: x = Sin t  ,  y= Sin2 t(a) Pw  sint = x          y  = x2

Q: 3) (i) Eliminate the parameter to find a Cartesian equation of the curve. (ii) Sketch the parametric…

A: Our objective is to eliminate the parameters to find the cartesian equation of the curve and sketch…

Q: The parametric equations: x =ac a cos³ 0,y = a sin 0;0 <0s 2n, define a curve called an asteroid

A: Please refer the attached image for complete solution. THANKYOU.

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.