Find parametric equations for the curve with the given properties. The line with slope -2, passing through (-25, –15) (x(t), y(t)) =

Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t2, y = 9 + 4t3,…

A: Given curve :

Q: find parametric equations for the given curve. y = 9 − 4x

A: The given equation

Q: In the given equation as follows , sketch the curve represented by theparametric equations (indicate…

A: Given the parametric equations x = 1+1t, y = t -1 x = 1+1t ,      y +1 = t x = 1+1y+1xy+1 = y+2xy…

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: Solve for "t" in the given x(t) and put the value obtained in y(t) and then simply to get the…

Q: For the plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. x- 2…

A:

Q: In  the given question as follows , sketch the curve represented by theparametric equations…

A: Explanation: Given that: x=t+1y=t2 Concept used: 1.For rectangular equation rewrite the equation in…

Q: Consider the following. x = e', X = y = e-3t (a) Eliminate the parameter to find a Cartesian…

A:

Q: find parametric equations for the given curve. y = 8x2 − 3x

A: Given- y=8x2-3x To find- Parametric equations for the given above curve.

Q: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: Given : x(t) =  e4t, and y(t) = e7t Let x = e4t       e4t = x Taking both side log, log(e4t) =…

Q: In the given equation as follows , sketch the curve represented by theparametric equations (indicate…

A:

Q: - For what value(s) of t does the curve given by the parametric equations x= -² -1 and y=t* +2r² –…

A: As per our guidelines we are allowed to solve one question at a time . Kindly repost the rest…

Q: Find parametric equations for the trajectory of a particle that moves along the circumference:

A: Given the trajectory of a particle that moves along the circumference

Q: Eliminate the parameter to find a Cartesian equation of the curve: x = VE ,y = 1 – t and then sketch…

A: Given,x=t...............(1)andy=1-t...................(2)differentiating both the equation w.r.t.…

Q: 32. y=-4x+1 a. x=t b. . C. x =-4t /27

A:

Q: Find dy/dx and d2y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Differentiating with respect to t, we get Now slope at t = -2 is,

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

A: The given parametric equation is: x=3+t and y=t2-5t, 0≤t≤6 Find the value of t, where y=0:…

Q: find parametric equations for the given curve.  x 2 + y 2 = 49

A: Given: find parametric equations for the given curve.   x2 + y2 = 49=72The parametric equation for a…

Q: Find the slope of the parametric curve x = -6t²-1, y = 2t³, for -∞<t<∞, at the point corresponding…

A: We can find the slope at the indicated point in the following steps.

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

A:

Q: • Sketch the curve represented by the parametric equations (indicate the Orientation of the curve),…

A: Given,

Q: Given the parametric equations, x = t - 1 and y = -t, find the point on the graph at time, t = 4.…

A:

Q: Find the parametric equation for the curve 12x + 17y = 18. (Use symbolic notation and fractions…

A: Given curve  12x+17y2=18

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

A:

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 pair of parametric equations is given. = 4t2, y = 8t3

A:

Q: Find parametric equations for the curve with the given properties. The line with slope -4, passing…

A:

Q: The graph of the curve described by the parametric equations x = 4t −1, y = 3t + 2 is a straight…

A: For a line passing through the point (a,b) and parallel to the vector (c,d) its parametric equation…

Q: Fing a rectangular equation of the curve with parametric equations x = 2t and y = 1-t2.

A: The objective is to find the rectangular equation of the curve with parametric equations x = 2t and…

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

A:

Q: Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value Parametric…

A: We are solving the first three subparts and for the next subpart post the question again and also…

Q: Find the slope of the parametric curve x = - 5t +8, y = 3t°, for - co <t< o, at the point…

A:

Q: find parametric equations for the given curve. . (x + 9) 2 + (y − 4) 2 = 49

A: To find the parametric equation of the given curve (x+9)2+(y-4)2=49 Given equation is in the form of…

Q: x = et – 1, y = e2t a) Eliminate the parameter to find a Cartesian equation of the curve.

A:

Q: B) (10 M) Find the parametric equation of the line through the point p (-2, 0, 5)- and parallel to…

A: Let's find.

Q: Sketch the curve represented by the parametric equations x = 2t/2, y = t4+ 1 (indicate the…

A: Given parametric equation, x=2t2 and y=t4+1we have to write the corresponding rectangular equation…

Q: Eliminate the parameter in x = -t^2+9t and y = t-4 and then identify the parametric curve and sketch…

A:

Q: Sketch the curve represented by the parametric equations x = t3, y = t2/2 (indicate the orientation…

A: Given a parametric equation,   x=t3                ...(1)  y=t22              ...(2)

Q: 1. The path of a particle is described by the parametric equations: x = 3t? + 1, and y = 2t + 1, -2…

A:

Q: find the parametric equation for each of the following a.) for the line of slope 2 passing through…

A: a) Firstly, we will find the equation of line of slope 2 passing through the point (-2,4) by using…

Q: Eliminate the parameter in x = -t+9t and y = t-4 and then identify the parametric curve and sketch…

A: x=-t+9t, y=t-4To Find: Identify the parametric curve and sketch it's graph.

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: Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a…

A: In this question we have to find the y(x)

Q: Consider the parametric equations x(1) = 1 + 3r², y(1) = 4 + 2r°, 0sts1. a. What is the length of…

A: If the parametric equations of a curve are x(t) and y(t), then the length of the curve over the…

Q: the parametric equal a) Find the slope at t 2

A: a) To find the slope at t=2 b) To find the time t at the point (1,0) and find the equation of…

Q: Given the parametric equation: x=2sint-3, y=2cost+5, 0 less than or equal to t less than or equal to…

A: Given x=2sint-3, y=2cost+5   , 0≤t≤2π

Q: find parametric equations for the given curve. Line of slope 8 through (−4, 9)

A: Given slope and a point are: The standard equation of line having a slope, m and a point (x1,y1) is…

Q: Find parametric equations for the curve with the given properties. The line with slope -4, passing…

A:

Q: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

A: Sketch the curve represented by the parametric equations x = et , y = e3t + 1 (indicate the…

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.