For this question, you will upload the work and the answer. Make sure the parts are well labeled. a) Draw the graph of a = 2t3 + 1 y = 4t² for t e -1,2] (No more, no less.)

Q: a Show that y = mx + b intersects y = |x + 1| if m > 1 or m < -1. b Given that -1 < m < 1, find the…

A: Given,y = mx + cFor m &gt; 1Take  m = 2 &gt; 1,

Q: Find the abscissa on the curve x²=2y which is nearest to a point (4, 1). А. 0 С.2 В. 1 D. 3

A: Use the distance formula then minimise using derivative.

Q: Find the coordinates of the point(s) on the curve y = Va + 3 that are closest to the point (8, 0). O…

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Q: Find the exact length of the curve.

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Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

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Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

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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: The graph of x+y = 4 is an ordinary right cireular cylinder. Indicate axis of the eylinder lies…

A: The equation of right circular cylinder is given by  x2+y2=4

Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

Q: Find the minimum distance from the point (2, 4, 10) to the paraboloid given by the equation z = x +…

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Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: For what values of a and b is the line 2x + y = b tangent to the parabola y ax? when x = 2?

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Q: The gruph o i shown here Ideatify the graph of the inerve finction - (B,

A: The inverse of a one-to-one function f(x) is another function that reverse the function f(x). That…

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

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Q: +y²)dx + (x² – y²)dy where C is the triangle with vertices (0,0), (2,1) and (0,1).

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Q: Find the length of the curve x = - (5 + 4t), y= 1- t, z= - (4+ 2t), for 3 <t < 5. length = (Think of…

A: Find the length of the given curve.

Q: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: I have taken the integral of A, and I'm towards the end of finding B but I'm confused on how I use…

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Q: Find the indreated equations over beund od by the grephs of the graphs of Hhe Crea He given interval…

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

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Q: Find the exact length of the curve. x = e' +", Osys 4

A: Given function is  x = e^y +(1/4)e^-y

Q: Solve the given problem. Show that v = (x + 2y + 4z)i + (2x – 3y – z)j + (4x – y + 2z)k is…

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Graph z(t) = i + 2eit

A: We have to choose abscissa as t and ordinate as y.

Q: The length of the curve y = Ey3/2 between x = 0 and X 1 is %3D

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Q: 1 x = + 6 2y What is the length br of the portion of the graph of the between the points with y = 1,…

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Q: Match the solution curve with one of the appropriate DE (explain your reasoning) a) y" -3y' – 4y = 0…

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Q: Find the length of curve x = t², y = t³ from x = 0 to x = 5.

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Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

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Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: The equation for the line of best fit for some data comparing the height of a candle (H) with time…

A: Let the independent variable denoted as time (T) Let the dependent variable denoted as height of the…

Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: 4. Find the are length of the curve from y=1 to y-4

A: The given curve is x=18y4+14y-2 from y=1 to y=4

Q: A straight-line fit y3 = e12), could be obtained with:

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Q: Find the length of the curve y = a +; from a = 0 to x = 1. O None 5/2 O6/2 3 O4/2 3. 3

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Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: ind the exact length of the curve. X = 8 4y2' 1sys 2

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Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: in R°sketch the graph of the cylinder x = (y – 2)?

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Q: 5. What is the equation of the curve AB? X Depth B Specific Energy a) y + 2gy Q? у + Q b) у + 2gy Q?…

A: The curve AB represents  specific energy

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: 6. trapezoid DEFG with vertices D(0,-3), E(1, 3), F(3, 3), and G(4,-3) in the y-axis ty O X D' =_ E'…

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Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

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: Two different level curves of the graph of z = f(x, ygan intersect. O True False

A: The level curve of a function f of two variables are the curves with equations f(x ,y)= k, where k…

Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

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.