The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and its arc has length S = r0. Find r and 0 so that 0 < 0 < 2n, the sector has area 1 square unit, and the perimeter is a minimum.

Q: Given line YZ tangent to OJ at point Y and mzWYZ = 119, what is the measure of arc WXY %3D Y W X.

A: Measurement of arc is the angle subtended by arc at the center of circle.

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A: The area under the straight line of the circle can be obtain by the formula, A=∫02πkaθdθ

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Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: The height h and semi-vertical angle a of a cone are measured and from them A the total area of the…

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Q: Let f(x) = x³/2. Determine the length of the arc swept over x E la, b).

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Q: 1. Find the total length of the curve r = 4(1 - sin 0) from 0 = 90° to 8 = 270° and also the total…

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Q: Find the arc length of the following curve on the given interval. x=24t+8, y = 7t+3, 0≤t≤2 The…

A: Given equation of function is  x=24t+8,y=7t+3, 0≤t≤2 The arc length of the given function is…

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Q: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

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Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: Find the mass of a thin wire shaped in the form of a helix, r(t) = ( 3 cos t, 3 sin t, 4t) with 0 <…

A: The curve is given by  rt=⟨3cost,3sint,4t⟩ , 0≤t≤3π2                   (i) Then,…

Q: At points on a circle of radius a, line segments are drawn perpendicular to the plane of the circle,…

A: We have to find the area of the surface formed by the perpendiculars to the xy-plane of length ks…

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: Now, we can say that the work done in stretching the spring 15 in. = X ft beyond its natural length…

A: Convert the length 9 inch to feet. Then use the Hooke’s Law to calculate the value for k.

Q: A point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt…

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Q: Find the area of the sector of the disk of radius r = 13 and with arc length s = 15.

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Q: Given YZ tangent to OJ at point Y, and mzWYZ = 104°, what is mW XY ? W mWXY

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Q: 4. Use the arc length formula to show that the length of a linear function f(x) = mx +c on the…

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Q: In the isosceles triangle ABC, AB=AC=5 units and BC=6 units. Find the location of the point D on the…

A: In the given Isosceles triangle ABC, AB=AC=5 units and BC=6. Point D is on the altitude from A to…

Q: Consider the region 2 enclosed by the curves I', and I': given by: T: y=1 Ti y=(x- 1)²

A: Given curves are, Γ1:y=1Γ2:y=x-12 So, the required diagram of the given curves are,

Q: Given a level suface 3x?y2 + 4xy = 2 with y = y(x). Find ! dy at the point (3, 2). Give your answer…

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Q: 2. Determine the arc length of the given curves a) y =+ 1<y< 2 3

A: s=∫y1y2 1+x'2 dyy'=3y23-14y2y'=y2-14y2s=∫121+y2-14y22dys=∫121+y4+116y4-2×y×14y dys=∫12y4+116y4+12…

Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: Given YZ tangent to OJ at point Y, and mzWYX=104, what is mW XY? W

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Q: R

A: Volume =1/3 * pi * r^2 * h

Q: sphere will reach point B as it swings about 'O' (a) If OA is a rope vertical plane. Determine the…

A: Answer:

Q: What is the area of:  To the right of Z = 0.29 and to the left of Z = -1 Show the solution and…

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

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Q: ) Let C be the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of…

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Q: Given a level suface 4x2y2 + 3xy = 5 with y = y(x). Find at the point (2, 4). Give your answer…

A: Given surface is: 4x2y2+3xy=5

Q: Find the arc length of the curve y=x+7 on the interval [0,3] O153 O 90 O 45 O18

A: Given that y=x+7.

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 2.

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Q: Find the required x-value. For a x2-cu -curve with 27 degrees of freedom, find the X-value having…

A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: 9. Find the area of the surface generated when the given arc is revolved about the x-axis: 4x² +…

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Q: (b) Consider the cycloid C parametrized by x = t – sin t and y = 1 – cos t, for all real t. Find…

A: Solution x= t-sint, y =1-cost C(0) = (0,0) C(pi) = (pi-sin pi, 1-cos pi) = (pi, 2) C(2pi) = (2pi-0,…

Q: The shape of a hole pored by a drill is a cone surmounted by cylinder. If the cylinder be of height…

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Q: Find the value of a such that the arc length of the catenary y = cosh x for −a ≤ x ≤ a equals 10.

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Q: 8. At points on a circle of radius a, line segments are drawn perpendicu- lar to the plane of the…

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Q: Blid E8ne thất iš čut up into 2 section 4 and B, such that section A is a cone similar to the…

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Q: What does the arc length formula give for the lengthof the line r(t) = ⟨2t, t, -2t⟩, for 0 ≤ t ≤ 3?

A: Given:          r(t)=⟨2t,t,−2t⟩  for 0≤t≤3.

Q: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: The tangent line to the graph of y = ecos x is parallel to y = 0 at Select one: Oa. x = 1/2 O b. x =…

A: We are authorized to solve only 1 question, please repost remaining questions Tangent line

Q: 4 Determine the surface area of a funnel that is generated by revolving the graph of 1 y = f(x) =…

A: Given  y=fx=x3+112xand interval 1,2

Q: 2 2 If C is the part of the circle E) + ) = 1 in the first quadrant, find the following line…

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Q: By revolving the semicircle x = r cos t, y = r sin t. (0 ≤ t ≤ π) about the x-axis, show that the…

A: