57 Find the cartesian coordinate of the point P(r,0) = (2, ). Plot the graph

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: 8. Find the equation of the circle which is tangent to the y- axis, which passes through the point…

A: To find equation of Circle which is tangent to y axis, passes through point (-1,-1) and it's centre…

Q: A curve on the xy-plane passes through the point (0, a) for some number a, and has the property that…

A: This problem is based on a variable separable first order ordinary differential equation. We have to…

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

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

Q: i) Find the cartesian coordinate of the point P(r, 0) = (-3, ). Plot the graph

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Q: Determine whether the below statement is true or false. If the statement is false, make the…

A: The given statement is True . If a point is on y-axis then its x-coordinate must be zero .

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: Sketch a graph of I = t + 2t, y = t +2, t > –1 . %3D

A: Given equations are x=t2+2t,y=t+2,t≥-1. So list the values of t and obtain the coordinates in…

Q: Find the points of intersection of the curves. Then sketch their graphs on the same Cartesian plane.…

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Q: 2. Find the slope of parabola y = ²+3 at any point on the curve.

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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

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

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: Find the coordinates of the stationary points for the curve  y =-x3 -4x2 + 3x +18. Determine the…

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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: Consider the given equation as x=t3....(1) And y=t2....(2)

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

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Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

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

A: Parametrization is a way to change the parameters of a expression in such a way that domain of the…

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: Find the point on the curve g(I) z +5 that is closest to the point (-57, 5).

A: Q - Point on the curve g(x) = x2 + 5 that is closet to the point (-57, 5).f - If point on curve is…

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 2. y = (x2 – 3)2

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Q: Trace the curve r2 = 4cos etan2e. %3D

A: The given equation is r2=4cos4θtan2θ. Simplify r2=4cos4θtan2θ as follows:…

Q: The line y = ax + b is tangent to the graph of y = x3 at the point P = (-3, -27). Find a and b.

A: The line y = ax + b is tangent to the graph of y=x3 at the point P=-3,-27. we have to find the…

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

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Q: 3. Trace the curve y (x-1)(x+3)'

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the equation x2 + y2 + Dx + Ey + F = 0 of the circle that passes through the points. To verify…

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

A: r2cos2θ=1

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

A: y = x3 - 3x2 + 4x - 12y = x2(x -3) + 4(x - 3)y = (x2+4)(x - 3)   X-intercept: (3, 0)    [Real values…

Q: Find the x-and y-coordinates of the point E.

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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: 22=xy represents the origin. ) Prove that the equation with vertex at

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Q: 2.x? Sketch the curve y= x² - 1

A: y=2x2x2-1 y=2x2x-1x+1

Q: Sketch the graph of y = h(t), where h(t)=uπ(t)−u2π(t),t≥0.

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Q: Find the Cartesian equation of the image of the line y = 2 under the mapping z → z 2 Sketch the…

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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: The given parametric equation of curve is x=t3+1,    y=t3-1,     -2≤t≤2. This implies that, x=t3+1,…

Q: 2. Find the slope of the curve y = 3x +1 at the point (-0). Draw the graph of the curve.

A: GIVEN y2=3x+1 at(-1/3,0) we need to find the slope of the curve and graph the curve

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

A: The given parametric curve is, x=2ty=8t3-1≤t≤1 From the parameter of x, x=2tt=x2

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: Find the point on the curve y= v2a +5 which is closest to the point (6, 0). > Next Question.

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Q: Find the Cartesian equation of the image of the line x = 2 under the mapping z → e z.  Sketch the…

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Q: A bowl is in the shape of the graph of z = x2 + y2 from z = 0 to z = 10 in. You plan to calibrate…

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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: (2) find the (x,y) coordinates of all points of intersection ot the curves.

A: b.(2) Given the polar equation of two cardioids r=1+sinθ,r=1-cosθ. To find the points of…

Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: 11. Find the slopes of the curve y y?- r2 at the two points shown hcrc. 2 (V3 = y2 - x?

A: we have the curvey4=y2-x2

Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

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Q: Consider the graph of (x^2) - (y^2/10) - (z^2/10) =1 1.What does the cross-section in the -plane…

A: The given equation represents a hyperboloid of two sheets.

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…