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Q: The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30…

A: The interval of the given graph is [0,30] Where a = 0 and b = 30 Here we have to use midpoint rule…

Q: If the first line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: If the first line has the form Ax + By + C = 0 the second line has the form Dx + Ey + F = 0 the…

Q: 2. Find the equations of tangents that can be drawn from the origin to the circle x² +y-2x+8y+2=0.

A: Given below the detailed solution

Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: 4. Sketch the curve of r2 = cos 20 and find the area that encloses it. Show your complete %3D…

A: Converting polar coordinates to rectangular coordinates  Put r=x2+y2,  θ=tan-1yx in r2=cos2θ…

Q: What is the most time-consuming part in using a graphing utility to graph a general second-degree…

A: To discuss about graphing utility.

Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

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Q: Analyze the graph of y = (arctan x)2.

A: Given- y=arctanx2 To Analyze- The above graph.

Q: Given a sine or cosine graph, the vertical translation is equal to the _________ of themaximum and…

A: Known facts: The average value of minimum and maximum of the sine or cosine graph is called vertical…

Q: Find all points on the graph of 3x2 + 4y² + 3xy = 24 where the tangent line is horizontal (Figure…

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Q: In the given question as follows,, verify that the two families of curves are orthogonal, where C…

A: Given :                      x2 + y2 = C2   ,   y = kx                     To show that they are…

Q: e for N = 6000 , n = 82 and c = 3 using about 10 points, and also provide your calculated values in…

A: N = 6000 , n = 82 and c = 3 po - sample probabilities po 0 0.01 0.02 0.03 0.04 0.05…

Q: 1- Find all of the points where the curve r = 2 cos (-) intersects the circle of 3, radius v2…

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Q: Let P(t) be the population of a bacteria culture after t days and suppose that P(t) has the line y =…

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Q: 2. Explore the asteroid given by the parameterization (CoS 7, Sin 7). Sketch its graph, determine…

A: Given :-  The asteroid given by the parameterization cos3 t , sin3 t . To Determine :-  Its graph ,…

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

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Q: 1. If f(x) = 3x2/3 - 10, find the arc length of the graph from the point A(8,2) to B(27,17).

A: Note:  We'll answer the first question. Since the exact one hasn't mentioned. Please re-submit the…

Q: have any horizontaltangents in the interval 0 … x … 2p? If so, where? If not, why not?Visualize your…

A: Consider the function, y=x-cotx…

Q: Find the length of the curve y = In(1-2) over the interval

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Q: Sketch the graph of the following between x = 4T and x = = 47. y = sin x 0.5+ -Зл -27 2л Зл 47 -0.5+

A: We have to sketch the graph

Q: Find the tangent line to the Witch of Agnesi (graphed here) at the point (2, 1). 8 y + 4 (2, 1) 1 2…

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Q: Find the length of the are of the e curve from point K(8,8) to M(!,5, -Y= -4

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Q: Solve for z. 4 12

A: Solve for x

Q: The tangent line to the graph of y = g(x) at the point (4, 2) passes through the point (1, 8). Find…

A: topic - slope of a tangent line

Q: At 6:00 am, ship A is 200 km west of port, heading east at 25 km/h. At the same time, ship B is…

A: Given:  At 6:00 am, ship A is 200 km west of Port, heading east at 25 km/hr.and at the same time,…

Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: 1. The graph of y--k is shown in the xy-plane above, where & is a constant. If the arca of APOR is…

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Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Use the guidelines of the section to make a complete graph of ƒ. ƒ(x) = sin x - x on [0, 2π]

A: Given function - f(x) = sinx-xIntervals = 0, 2πUsing value of π as 3.14 to draw the curve,let us…

Q: 28. Show that the graphs of y = tan x and y = cot x have nohorizontal tangents.

A: A horizontal tangent line is a mathematical feature on a graph located where a functions' s…

Q: Use simpsons rule  with n=4 to approximate the arclength of the graph y=x2+x+3 from A(-2,5) to…

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Q: Find the length of the arc of this curve and Sketch the curve y cu. = x sq.  from ( -1,1 ) and ( 8,4…

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Q: 7. Find the length of the curve y= x'+ I from x = 1 to x . 12x Give your answer as a simplified…

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Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

Q: 4) Determine the equation for the shortest arc that passes through the point (0, 0) and (1, 0) and…

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Q: Find the exact length of the curve over the given interval. 4 3/2 X= 3 1sys4

A: Given curve is x=43y32, 1≤y≤4

Q: 5.) Assume that the given graph gives the position function of a particle which is moving along a…

A: Consider the given graph showing the position function of a particle which is moving along a…

Q: Sketch the graph of the following between x = 4T and x = 4т. y = sin x 0.5 -Зл -2л 2л 47 -0.5-

A: y=sinx between x=-4π and x=4π

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a? + In(az + 1) at a =…

A: To find the slope of the tangent to the graph of the given equation

Q: An example of cissoid of Diocles is r = sin 0 tan 0 whose graph is below. Show this curve has the…

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Q: tior Use a graphing calculator to graph the curve over the given interval of t, and find a…

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Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.

Q: of the asclength /3 Curve Find the for 2 x 3.

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Q: Fined the arc leng th of the curve

A:

Q: Find the length of one complete graph of the hypocycloid given by r(t)= (cos't,sin't) for 0st<2n 3

A: One complete graph of hypocycloid looks as follows:   From rt=cos3t,sin3t, we have x=cos3t and…

Q: 3. If the graph of y=fcx) has a horizontal tangent at x=a, what is happening at this point ? I…

A: For a function ; a point is considered. A horizontal tangent exists at this point which means that…

Q: when i am asked to graph a tangent, cotangent, csc, sec. how do i label my x-axis? i am supposed to…

A: To plot the graphs mentioned above, The scale will have to be real numbers.  Plots of tan,…

Q: How can I get the result? Which is the result?

A: The function is given by,

Q: Find the arclength of the curve x = - with 3 ≤ t ≤ 4.

A: Given x=13t3, y=12t2 with 3≤t≤4. The objective is to find the arc length of the curve. Formula Used…

Q: The curve r= 1- sin( has a slope at 0 2n equal Select one: O1 and the graph is symmetric about…

A: