Sketch the plane curve represented by the given parametric equations Then use interval notation to give the relation's domain and range

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

A: Take different values of t from the given interval and then plot the corresponding points and…

Q: Describe the graph of the relation determined by   Indicate the direction in which the curve is…

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Q: 4. y = x2--Inx x = 1 ve x = e

A: Topic- application of derivatives to find angle between curves

Q: 3. Find a rectangular equation to represent the plane curve. x = 3 tant, y = 2 sect for tin (-7-7)

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Q: x(t) = (t +3)² − 4; y(t) = (t + 3) traces an ellipse. a parabola. O a circle. O a line. O a…

A: According to bartleby guidelines we supposed to do the first three sub parts of multiple sub parts…

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: (x = t³ + 7 y = t5 – 3t d²y calculate for a function given parametrically dx?

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Q: Give the coordinates of X-intercept for the line Y = 2(x – 1) + 7.

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Q: Find the midpoint of points A(-8,2)and B(-5,-5) graphically.

A: Explanation: Plot the points A and B on the graph. Then draw a horizontal line from A and Vertical…

Q: The elevation of a valley above sea level (in feet) is modeled by the function f(x, y) =…

A: Given,  The elevation of a valley above sea level (in feet ) is modeled by the function,…

Q: Find parametric equations for the line of slope 2 that passes through the point 13, 52 .

A: Equation of line in the parametric form form when it is passes through point x1,y1 and slope 'r' is…

Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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Q: the graph with one of the contour diagrams (I)-(III). Give explanations for your answers. You may…

A: Given is

Q: -2 8 and y = 4 Find the distance between x = - 8 The distance between x and y is (Type an exact…

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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.