write the equationns of the curves enclosing a reigon such that when it is rotated aboutthe x-axis, the resulting solid is a cone with base radius r=3 and height h=7 n SUC

Q: Sketch the graphs of the following cylinders. Properly identify a cross-section on the appropriate…

A: Given: Let's consider the given equation and graph the following cylinders. y=2x-4

Q: Find the area of the surface generated by revolving the curve about each given anis. *- 7t. y= st,…

A: We have to find  the surface area generation by revolving the curve about x and y axis

Q: 3. Find the right triangle of largest area inscribed under the parabola y = 4 – r² with its base…

A: Given: y=4-x2 Vertex of the parabola will be at 0,4 and the points where parabola intersect the…

Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: In  the given equation as  follows , find the area of the surface generated by revolving the curve…

A: Given: x=t ; y=4-2t; 0≤t≤2To find the area of the surface generated by revolving the curve about…

Q: Let L be a tangent line to the hyperbola xy=4at x=7. Find the area of the triangle bounded by L and…

A: Given: L is a tangent line to the hyperbola xy=4 at x=7. To determine: The area of the triangle…

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

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Q: The centroid of the half-ellipse-shaped-cross-sectional area shown is given by: 4 Ye 9 - 25m9-y² dy

A: Given half ellipse shaped cross section is:…

Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s & t as two parameters radius = a and height…

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Which solid of revolution is produced by rotating the shape below 360° about the given axis?

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Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: Find a parametrization for the curve described below. the line segment with endpoints (1, – 4) and…

A: Given:   Endpoint : ( 1 , -4) and ( -2 , -7)

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

A: Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8)

Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

Q: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: Find the arclength of the curve x= 4cos(6t), y= 4sin(6t) with 0 less than or equal to t less than or…

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Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: he segment AB by a scale factor of using point C as a center of dilation. Cons figure on the…

A: Please refer to the image below

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: Find a parametrization for the curve described below. the line segment with endpoints (5 - 1) and…

A: Given point :( 5 , -1 ) (10 , -6 )

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

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Q: Find the anea of the vegion in quadrant Ps bou nodod ist 4 the conie the by the right by the line…

A: Given curves, y=ex+12,y=e-x+12,x=2 ln2 To find the area of region bounded by these curves.

Q: The arc length of the portion of the curve y =ex with 3 <x<5 is

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Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = &lt;t, t2&gt;That implies,

Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

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Q: Find the area and centroidal distances of the curve that lies between the equations y=4-x^2 and…

A: Consider the region bounded between the curves is as shown in the figure below: Here, the objective…

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

Q: The curve y V4 – x², – 1 < x < 1, is an arc of the circle x² + y? = 4Find the area of the = 1…

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Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating…

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Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

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Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: Find the area of the surface formed by rotating the curve with the equation x ^ (2) - (y ^ (2)) /…

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Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: Find the area of the surface generated when the given curve is revolved about the x-axis. y = /5x +…

A: To find the surface area generated when y=√(5x+3) is revolved around the x-axis on [0,5]

Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: 28, Find the equa tion of arcle with Centre c(2;3) and touches the x-axis.

A: By using equation of circle formula, we find the required equation of circle.

Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

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Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: If x = 8cos3theta and y = 8sin3theta, find the total length of the curve swept out by the point…

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Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Find the exact arc length of the curve y = 3x3/2 − 1 over the ineterval [0, 1]

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Q: find the volune of the selid generated by revolving regron bounded by the graphts of dhe ģiven…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Show that 8r units is the length, L, of one arch of the cycloid described parametrically by: x (0) =…

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Q: Y=Ğ jfor exS3; about The X-axi's

A: The formula for the surface area generated by rotating the curve  A=2π∫abf(x)a+(f'(x))2dxHere…