2r-1 The diagram shows part of the curve y = (2r+3)(x+1)²* Find the exact area of the shaded region, giving your answer in the form p+qlnr, where p and q are positive integers and r is a positive rational number.

Q: Two small arches have the shape of parabolas. The first is the graph of f(x) = 1 – x² for –1 < x < 1…

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Q: Find the length of the curve :   x=(y^3/2)/3-y^1/2 from y=1 to y=9

A: The given curve is: x=13y32-y12        from  y=1  to  y=9

Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Find the exact length of the curve. y =  3 +1/2 Cosh 2x,   0≤ x ≤ 1

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Q: Find the exact length of the curve. y = 7+ cosh (2x), 0 ≤ x ≤ 4 1 2

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Q: Y = (2x – 1)2 (x2 - 9) %3D

A: Given that, y=(2x-1)2(x2-9) The y is zero is, (2x-1)2(x2-9)=0(2x-1)2=0,…

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

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Q: For a y2-curve with 15 degrees of freedom, find the x2-value that has area 0.95 to its right. E…

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Q: Find the length of the curve. ¹) x = ¹ y 3/2 - y 1/2 from x = 1/2 from 4) 3 5) x x= 16 to x = 25 =…

A: If a function y=f(x) is defined on interval [a,b] the length of the curve is given as - Length (L)=…

Q: Bonus: 1. Find the area of the surface generated when the curve x2 - 12y + y2 = 0 is revolved about…

A: Given:          x2−12y+y2=0  is revolved about the y−axis for 2≤x≤10.

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: The nature of the multiple point at the origin for the curve z+3r+y'+3y²+2r?y² = 0 is O Node O Cusp…

A: For the solution follow the next steps.

Q: of the region described. atween the line y=x and the curve y= 2x/64 -x in the first quadrant a of…

A: Please refer to the image below

Q: 3. Curve A given by x(t) = 4cos(t) and y = 4sin(t), Curve B given by x(t) = 4cos(2t) and y = For…

A: Use trigonometric identities

Q: 4. Find the exact length of the curve. 36y2=(x²-4)3,2≤x≤3.y≥1

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Q: The temperature at point (x.y) on a metal plate is T(x.y) = 324x - 324xy + 81y. An ant on the plate…

A: Given that Tx,y=324x2-324xy+81y2 ∇T=648x-324yi+-324x+162yj and equation of the circle of radius 5…

Q: Find the exact length of the curve. 1 y = 3+ cosh 2x, 0<1<1 2

A: we need to evaluate the Length of curve where  0 ≤ x ≤ 1

Q: 2. Find the point on the curve y = VI thats is closest to the point (3,0)

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Q: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: Find the exact length of the curve. y = 5 + cosh (2x), 0≤x≤ 7

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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: The above diagram showš the curve y = (1 – x)(x– 4) and the straight line y =4-x that intersect у at…

A: Point of intersect → (k , 2)x = Ky = 2putting in equation of line :2 = 4 - kk = 2

Q: The region in the first quadrant bounded above by the line y = 6, below by the curve y = √6x, and on…

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Q: Calculate the length of the curve defined by Vy(y-3)on the interval 1 < y < 9. x =-

A: Solution: Consider the given curve: x = 13yy-3 on the interval 1≤y≤9 Since we know that the arc…

Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: + 2 Find the length of the curve y = from the point where a = 1 to the point where x = 2.

A: The length s of a curve with the function y=f(x) for the interval of x from a to b is given by the…

Q: Find the slope of the curve x^3=(y-x^2)^2 at (1,2). If q-p=Inq+Inp, find dq/dp.

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Q: Question 7 Determine the x - coordinate of the local ma Or - 18 O r = 16 O = 1.0 None of the choices…

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Q: The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of…

A: Given, surface, z = xy2Differentiating the z with respect to x assuming y as constant,∂z∂x = y2×1 =…

Q: To design the interior surface of a huge stainless-steel tank, you revolve the curve y = x3, 0 ≤ x ≤…

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Q: 5. Find the length of the curve y = 2(2+ x)², 1<x<8 %3D

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Q: Find the length of the curve x = (y − 5)3/2 from y = 5 to y = 6.

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Q: SOLVE STEP BY STEP Evaluate the length of the curve x = 5 - Vy+1 , 0<ys 3

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Q: Q1 Find extrema point of the Surface 2-ペ-S-12x+3}+2

A: Consider the given function  z=x3-y3-12x+3y+12 Find partial derivatives of the function with respect…

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

Q: 5. Find the length of the curve x = +22 from y =0 to y=3.

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Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

A: The plyboard has dimensions 3×5 ft2 So, the area of the board is 15 ft2 The area of the shape needed…

Q: Find the length of the curve y = (x/2)2/3 from x = 0 to x = 2.

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Q: The length of the curve defined by x =÷(y² + 2)E, y E [0,3] %3D

A: Arc length=∫ab1+dxdy2dy

Q: 3. Sketch the curve f(x) = x² +1

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Q: Question 14 Find the area bounded by the curve y = - -x 16 A 10 square units B) 4 square units C 8…

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Q: Consider the the curve y =(6x + 5)V6x + 5 from x =5 to x 11 a) Find the initial and terminal points:…

A: Consider the curve y=6x+56x+5 from x=5 to x=11.a To find the initial and terminal points.b To find…

Q: The curve y = V4-x², -1<x<1, is an arc of the circle x2 + y² = 4. Find the area of the surface…

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Q: Find the length of the curve y= (x+2)3/2 for a in the range 0 <I< 2. %3D

A: find the length of the curve y=x+232 for x in the range 0≤x≤2 solution length of the curve is…

Q: A garden lot is bounded by the curves y = x and y = 9. If its area is in square meters and it will…

A: We will find the area and cost.

Q: A wire has the shape of the curve y = 3x"2. Find the length of the wire between x = 0 and x = 1. %3D…

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