Eliminate the parameter to find a Cartesian equation of the curve. Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter t increases.

Q: y (x+1)²

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Q: Identify and sketch the curve xy = 1.

A: xy=1. It is in the form of xy=c2. Therefore it is a rectangular hyperbola.

Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: Determine at sight the direction in which the curve opens. Locate the vertex, focus, and ends of the…

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Q: Find curve sketching for the following equation-

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Q: Sketch the given curves together in the appropriate coordinate plane and label each curve with its…

A: Sketch the given curves together in the appropriate coordinate plane and label each curve with its…

Q: Consider the following. x = et - 4, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A: To find The cartesian equation of the curve by eliminating the parameter

Q: the points where the curve meets the axes.

A: y= (x-2)(x+1)(x+2) When x=0, y=-4 When x=1, y=-6 When x=-1, y=0 When x=2, y=0 When x=-2, y=0 When…

Q: Find the linear speed of a point moving with uniform circular motion, if the point covers a distance…

A: Given that distance= s= 18 ft  and time = t = 3 min

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: Consider the curve y = 4x3. The sketch of the portion of this curve between x = - 1 and x = 8 is…

A: Solution..

Q: Identify the curve by finding a Cartesian equation for the curve, r = 4sec(theta)

A: Refer to the question we have to find the Cartesian equation for the curve r = 4sec(theta)

Q: Identify the curve by finding a Cartesian equation for the curve r = 4secθ

A: The given curve is,

Q: What is the y-intercept of y = cot x?

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Q: State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

A: a. According to question,Given equation,y = 1-x2 ,  z = -2

Q: Find a curve y = ae* to the data : bx

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Q: Find a Cartesian equation for the curve and identify it. r2 = 14

A: We have to find Cartesian equation

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

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Q: Trace the curve sinecos³e. r =

A: Consider the given equation. r=12sinθcos3θ Check the the symmetry of the curve. he curve is…

Q: pleae please type by computer Describe how reversing the orientation of a curve C affects the…

A: Describe how reversing the orientation of a curve C affects the implementation

Q: Find a Cartesian equation for the curve and identify it. 12 = 2

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Q: Find the exact length of the curve 36y? (x² – 4)³, 2 0.

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Q: Eliminate the parameter to find the Cartesian equation of the curve, then sketch the curve and…

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Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: Find the equation in terms of x by substituting x=t in the given expression   y=t2-1=x2-1   To use…

Q: y =(+ + +)* x = 4t + 1, 4

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Q: find a Cartesian equation of the curve

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Q: 1 F(t) -1<t<1

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Q: I Discuss the properties of the curve and sketch fully: a) y = x? e-x 1+2nx b) y = =

A: Get  the asymptote of equation in a: y=limx→∞x2e-x   =0 Thus, plot the graph:

Q: DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y x- 3x2 + 4x- 12 2. y =…

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Q: Use the guidelines of this section to sketch the curve.

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Q: y X -

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Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

Q: Find a Cartesian equation for the curve and identify it. r2 = 10

A: Given, We have a polar equation  r2 = 10

Q: Eliminate the parameter to find a Cartesian equation of the curve.

A: Given  x=sin(t)  y=csc(t) and 0&lt;t&lt;π/2 We need to find the Cartesian equation and graph

Q: Consider the following equations. x = sqrt(t) , y = 4 − t Eliminate the parameter to find a…

A: given equationx=ty=4-t

Q: (b) Show that the origin is a node, cusp or an isolated point on the curve y? = ax? + bx3 according…

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Q: The equation of the curve is given as y = 3x + 1

A: topic - slope of curve at a point

Q: Find an equation for the tangent to the curve at the given point. Then sketch the curve and the…

A: topic - equation of a tangent line

Q: Consider the equation abaixo a) Calculate y′. b) Find the two points where the curve below crosses…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: 4. Convert the equation r =8cos0– 2sin0 to Cartesian coordinates and fully describe the resulting…

A: see below the answer

Q: Sketch a graph of y? = x* – 12x , find the coordinates of the points on the graph of y? = x³ – 12x…

A: giveny2=x3-12xwhen tangent line is Horizontal ,then slope will be zero.differentiate the…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = x3 – 3x? + 4x – 12

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Discuss the properties of the curve and sketch fully: a) y = x2 e-x b) y = 1+lnx

A: To sketch the curve : a) y = x2e-xb) y = 1 + ln xx

Q: Discuss the properties of the curve (w/ solution) and sketch fully: y = x?e-*

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Q: x = Vi, y = 3t + 4;

A: Given: x=t, y=3t+4; t≥0 For finding an equation in x and y, we put value oft=y-43 from second…

Q: 16) Eliminate the parameter and write the resulting rectangular equation whose graph represents the…

A: The given parametric equation is x=1t and y=2t2

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.