If the normal at (ap², 2ap) on y² = 4ax makes 90° at the vertex, then

Q: Find the area of one loop of the rose defined by the equation r=cos2θ.

A: Given

Q: Find the arclength of y = 4x³/2 on 1 < x < 3

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Q: • How. Find the lengths for the following curver.. 1= r = 1 + cosa

A: Explanation of the answer is as follows

Q: Find the length of the curve r= cos'(8/3). OsesT/4

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Q: Draw the following curves by extracting their points and then identifying their symmetries Y= Sin ()…

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Q: Find the length of arc of the curve 9y^2=4x^3 from the origin to the point (3,2 squareroot of 3)

A: The arc length of a curve y=f(x) from x=a to x=b is defined by the integral L=∫ab1+dydx2dx.

Q: Find the area of the loop OF the given corve Curve

A: fx=x1-x2Compute the integral from a to b: ∫abftdtVisualize the area under the curve: fx&gt;0: 0,…

Q: For numbers 11-14 consider trapezoid LOAF. L E F

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Q: Find the length of arc AB in terms of x.

A: Arc length is given by s=r.θwhere r = radius of the circle and  θ = central angle in radian

Q: 3 Select the angles with a tangent ratio of 4 ZA ZE

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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: 2. Find points P and Q on the parabola y = 1 - x² so that the triangle ABC formed by the r-axis and…

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Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

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Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: The perimeter of a circumscribed polygon was used to find an approximation for pi by the ancient…

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Q: If h(z) = arcsin(2)(4z + 3), find h'(z) =

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Q: Find the area of the loop OF the given curve

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Q: Find the exact length af te of the curve, 2. x-

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Q: S If y = arcsin(e?z), dy dr w

A: Solution is here

Q: Graph the limaçon. Cardioids r = -1 + sin u

A: Given- r=-1+sinu To Draw- The graph of the above equation of the limaçon.

Q: Consider the unit circle x² + y² =1 and the point P(1,0). Find the average distance from P to a…

A: The  average distance betwwen point and circle is zero  it shows that the point lies on the circle…

Q: Three line segments AC, AB and BD shown in the figure have the lengths of 2, 3 and 5, respectively.…

A: Given: Three line segments AC, AB, and BD showed in the figure have the lengths of 2, 3, and 5,…

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 4…

A: Given that  The figure is

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

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Q: If a = 10 cm and b = 16 cm to the nearest millimeter, what should you expect the maximum percentage…

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Q: Find the length of the arc of the curve in the given range, x3 + 3' 4(x + 5) ' 1 y = 25x + 5x²+…

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Q: Given the OC + xY +2y2 3D6 curve Find the Coordinates of all other Poīnts on the Curve with slope…

A: x+xy+2y2=6 Slope of the curve is the derivative of the given curve at the given point. So…

Q: Which of the following is the cross-section of this solid?

A: Find the cross section area

Q: find the arclength of the path (P- 1.-2) for 0<t< 4

A:

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Find the normal of slope 2 to the ellipse x2+2y2=3.

A: Given query is to find the equation of the normal with the slope 2.

Q: Find the equation of the normal line to the parabola y = x + 3x – 2, that is also parallel to 7x…

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Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the distance between point T(1,5) and point V(3,1). Round to the nearest tenth if necessary.

A: Given : T1,5 and V3,1

Q: Find the length of the curve. Vzti + etj + e-tk, Osts 3

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Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: Where should the point P be chosen on line segment AB so as to maximize the angle 0? (Assume a = 3…

A: Given query is to find the position of P to maximize the angle theta.

Q: Calculate the length of the astroid of a + ys = 3.

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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: Find the arclength of y 4x3/2 on 1 < x < 2

A: Here in this question given that y=4x3/2 and find the arc length. Between x=1 to x=2.

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

A:

Q: Find the arclength of y 3x3/2 on 1 < x < 3

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Q: The given curve is rotated y = 3 - x2,

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Q: Consider the following diagram, a=1, b=9, c=15. Where should the point P be chosen on the line…

A: The diagram is shown below. Consider the triangle BPE, tan α=axtan α=1xα=tan-11x Consider the…

Q: write equation for the normal Iine an to the circle with cr=3) at (x=J5)

A: Let the equation of circle                                          x2+y2=r2…

Q: Find the normal form of the line 3x + 4y – 10 = 0 and its where distance from the origin.

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Q: Find the equation of the sphere if one of its diameters has endpoints (8, -2, 8) and (11, 4, 17)…

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