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(a) Sketch the curve by using the parametric equations to plot points. Indicat with an arrow the direction in which the curve is traced as $ t $ increases.(b) Eliminate the parameter to find a Cartesian equation of the curve.
$ x = \sqrt{t} $, $ \quad y = 1 - t $
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Calculus 2 / BC
Chapter 10
Parametric Equations and Polar Coordinates
Section 1
Curves Defined by Parametric Equations
Parametric Equations
Polar Coordinates
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Lectures
16:57
In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.
01:59
Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).
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(a) Sketch the curve by us…
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Sketching a Curve by Elimi…
hot, eh? Scapes occurred by use of the parametric equations to broad points indicated with their own direction your veg secure. If it's tress, that's he increases, eh? When he could fool negative for Oh, your first day. With that, he got zero x equal to Cyril. Why go to why he go to one axe is you want? Why his secret to Cyril, What is equal to two ax is equal to the square root of two. Why is the door to connected War? He is three actually is equal to three. Why is the connective too? But he got four X is equal to two. Why is the connective three then? Not sketch the curve? Just that zero one No. Zero one here. And why Cyril squired it of two negative One square root of three Negative two and two Conectiv three. That's a curve is like this. Had to be eliminate the permitted to find a cottage in equation out the crew from here with half x squared is equal to And then look into this equation we have Why is he going to one minus x squared? So here ax is greed. San Siro! This's a petition in question of the craft
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