Parametrize the given curve. 4x + бу? - 3 c(t) %D

Q: A Curve a with aca) = (2,4,4), 2e2) = (0 ,2 54). %3D %3D Find Kea), B)

A: We will find out the required value for given curve.

Q: a Z(t):t+?ti (ists4 (-35t53) こ 6. 2E) = 5- 2it

A: Given: (a.) zt=t+3ti (1≤t≤4) (b.) zt=5-2it  -3≤t≤3   To describe: The trajectory of the given…

Q: Sketch the curve (2² + y*)³ = 4.x²y? 2.2

A: To sketch the graph of:(x2+y2)3=4x2y2

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: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

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Q: Find the length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

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Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: Find the length of the curve. The spiral r= 30 2,0ses

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Q: Find the exact length of the curve. y? = 64(x + 5)3, 0sxs1, y > 0

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

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

Q: Find the length of the curve x y? – 2y, 0< y < 2.

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Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

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Q: Find the exact length of the curve. x = e - 9t, y = = 12e2, 0 sts 4

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Q: 6. Find dyldx and d 2yldx 2. For which values of t is the curve concave upward? x = t 3 - 48t, y = t…

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Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: find the eauatjo aof the nor ma l to the curve 2. (x + 3)?y =3y-3x2

A: For any curve y=f(x), slope of tangents and normal at any point x1, y1 can be given by mT=dydx(x1,…

Q: Find the the given curve e length of -64e4€ 27 3. 3y 34 32

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Q: Зу — 4у 3D —х — 2 The curve above can be parameterized as which of the following pairs of equations?

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Q: The tip of the minute hand of a clock is 7.6 in. from the center of the clock. Find the linear…

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Q: Find the orthogonal trajectory of the curve a2 + 31 = c [a] A. 3z =c B. y = cr C. y = ca D. z - 3 =…

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Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

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Q: Find the orthogonal trajectory of the given family of curves: 1. e* + e¬y = C1

A: We will solve the problem

Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

Q: (a) Eliminate the parameter to find the Cartesian equation of the curve. (b) Sketch the curve and…

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Q: 9. The Pength of the Curve ņ = 206ti t2dintj ,0ts IT is :- (0)21 (6)47 (c) 87 (d) 1677

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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: Q5) Find the length of the curve: r = asin? ,0 0.

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Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Which of the followings can represent the curve y=x? Choose all that apply. O O O 3t, 9t2>

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Providing a proper explanation, trace the curves: (1) a?a = y°(2a - y), where a > 0,

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Q: The length of the curve defined by x =(v² + 2)E, y € [0,1]. Select one: none O 12

A: Arc length of the curve x=g(y), y∈[a, b] is, S=∫ab1+(g'(y))2 dy

Q: 2(m+1)x2 + 4mxy + (m+2)y2 + 2x - 2y = 0 Investigate which curve the equation shows according to the…

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Q: x = Vt, y = 4 - t (a) Sketch the curve by using the

A: (a) Put t=0. x=0=0y=4-t=4-0=4 So at t=0, the point on the graph is (0,4). Put t=4 x=4=2y=4-4=0 So at…

Q: Solve the problem. Find the length of the curve y = In(csc x), 7/4 T/2 VI E

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Q: FIND THE PROPERTIES OF THE CURVE (w/step-by-step solution) AND SKETCH FUL х2 — 4х — 12 y? - х2 — 2х…

A: The domain and range of any function can fully describe about the nature of any figure or curve. The…

Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

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

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Q: How far trom the y-axis is the center of the curve 2x? + 2y? + 10x - 6y - 55 = 0? O 2.50 O 2.75 O…

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

A: Solve for the equation

Q: The orthogonal trajectory of the 1-parameter family of curves, y = cr will be given by: r² + y? = c…

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Q: x = et – 3, y = e2t (a) Eliminate the parameter to find a Cartesian equation of the curve.

A: As per company guidelines, I'm restricted to answer your first question only. So if you want other…

Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: Write the equation of the cone with the top point (1,2,3) and t he rectification curve fx= cost,y=…

A: The generator line for a cone is the line that connects the vertex and the point on the…

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem