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

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

Q: y (x+1)²

A:

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

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

Q: Find the exact length of the curve. 0 < x < 6 %3D 3

A: Given:   To determine: Exact length  of the curve     Concept: Exact length of the curve y = f(x)…

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 properties of the curve ans sketch fully 6. Y^2 = (x^3)/(x^2 -4x +4)

A: Consider the given function. y2=x3x2-4x+4 There is y2 Therefore the value of y can be a positive or…

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: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Consider the curve y = 3x3, The sketch of the portion of this curve between x = - 1 and x = 8 is…

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Q: Determine the nature of the turning points for the curve y = x^5 − 5x^4 + 5x^3 − 1.

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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: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY   Y2 = x2+5x−4/x−5

A: Given,           y2=x2+5x-4x-5

Q: Consider the curve given by the equation 0 = y3 +xy +2ax + 1+x4  y'(0) = ?

A: Answer and explanation is given below

Q: sketch the curve  y=x/(x+1)²

A: Given equation is: y=xx+12 We have to find the graph of y. The set of x and y-values are given as…

Q: Find the exact length of the curve. y = 5 + 8x3/2, osxs1

A: Given: y=5+8x32,   0≤x≤1

Q: Q2- Sketch the curve: y = (x+1)

A: The function given to us is  y=x(x+1)2

Q: x3 Y2 = x2-4x+4

A: To determine the properties of curve, we will need to have function, its first order derivative and…

Q: Eliminate the parameter t and graph noting the direction of the curve. y а) 12 +1 X

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

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

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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 THE PROPERTIES OF THE CURVE AND SKETCH FULLY Y^2 =x^2+5x−4/x−5

A: We are given the curve: y2=x2+5x-4x-5 Sketching the curve , we have :

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

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Q: find a Cartesian equation of the curve

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Q: 6. Y = %3D x2-4x+4

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Q: (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.

A: Given equations in the parametric form as:x= cos2(t), ............................(1)y = sin2(t)…

Q: analyze and trace the given curve y = 2x3 + 3x2 - 12x + 7

A: Given:

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

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

Q: find a cartesian equation for the curve r2cos(2θ)=1

A: r2cos2θ=1

Q: 3x2 – 2y2 – 12x + 12y = 12

A: Given equation : 3x2-2y2-12x+12y=12

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

A: topic - slope of curve at a point

Q: Sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.

A: Arc Length formula in the interval [a,b] is given by, L=∫ab1+dydx2 dx This is applied only when dydx…

Q: Find the exact length of the curve. 1 y = + 10x37 6 1 ≤ x ≤ 3

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Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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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: Find the coordinates of the point/s on the curve y = 2x? which are closest to the point (9,0).

A: We have to find the closet point to the point    (9, 0)

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

A: see below the answer

Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

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Q: The curves x=y²and x = 2 y – y?

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: 4- Sketch the curve 9x + 16y = 144.

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: FIND THE PROPERTIES OF THE CURVE AND SKETCH FULLY 6. y2 = x²+5x-4 x-5

A: Given, the function y2=x2+5x-4x-5. We have to sketch the given curve. Also, find the properties.

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: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

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Q: Reflect the figure across the y-axis. Which is most likely the new figure?

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Q: Write the equation of a circle osculating with the curve f(x)=arctanx at the point x0=1.

A: Given: f(x)=arctanx x0=1.

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.