Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D

Q: Find the exact length of the curve. y = ln(Sec x),   0≤ x ≤ π/4

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Q: 2. dy sin x - y where f(n) = 0. %3D dx

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Q: Find the length of the curve using formula.  y= ln (cosx) bounded by 0 and pi/4

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x312 from (0, 0) to (4, 8)

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Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

Q: Find the arc length of y³ + y = x² + 6x on the interval [-5, –1].

A: Since the given graph is in implicit form (we can not find the explicit value of y in terms of…

Q: Find the arc length of y=((x^3)/6) + (1/(2x)) with the interval of [(1/2), 1].

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Q: Evaluate [12x. (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

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Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: Find the arc length of the graph of the function y=ln(cosx)y=ln(cosx) over the interval…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: Find equations for the tangent and normal to the cissoid of Diocles y2(2 - x) = x3 at (1, 1).

A: Find dy/dx using the given equation.

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: 1. Find the moment of inertia, with respect to the line x=1, of the area enclosed by the loop of the…

A: Given: Curve y2=x2(1-x)----(i)

Q: Зп 2. Find the exact length of curve y = ln (cosx), * < x < n. 4

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Q: Evaluate 112x C: arc on y = x5/2 from (0, 0) to (4, 32) (2x - y) dx + (x + 3y) dy.

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 8)

A: Here we have to evaluate        ∫c (2x-y)dx+(x+3y)dy

Q: 3. Find the area under one arch of the curve y = sin(2r).

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Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: A. Use Simpson's rule to evaluate -dx ,by taking n= 4. Inx B. Find the length of the curve y = x…

A: Answer

Q: Calculate the length of arc of y = 2x/² for 0≤x≤1

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Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

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Q: Find a curve through the origin in the xy- plane whose length is given by 1/2 L = [; (1+ *)"* dx 4

A: The arc length, L of a curve y=f(x) in the interval a,b is calculated using the formula below.…

Q: 4In(Arctan x) = 1-y

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Q: Find the arc length of the catenary y = cosh x between x = 0and x = ln 2.

A: Given y=cosh(x)

Q: Find the length of the curve y = ln (sec x), 0&lt;= x&lt;= pai/4

A: Given,

Q: Find the arc length of y³ + y = x² + 6x on the interval [-5,–1].

A: The arc length, L of a function, x=f(y) in the interval [a,b] is calculated using the formula below.…

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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Q: Find the length of the curve y = = cosh(x), 0 < x < 1. Arc length =

A: Arc length of a curve y=f(x) on [a,b] is given by, L=∫ab1+y'2dx ddxsinh(x)=cosh(x)…

Q: Find the arc length of the graph of y = √(16 − x2) over the interval [0, 4].

A: Given: y=16-x2 interval [0, 4]

Q: Find the arc length of the curve y = log(1/cosx) from x = (/4) tox= (/3)

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Q: 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

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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: Let y = sin(4z). If Az = 0.1 at æ = 0, use linear approximation to estimate Ay Ay x = Preview Find…

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Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: What is the arc length of the curve of x5 y = + 10 1 6x3 from x=2 to x = 5?

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Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

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Q: Determine the length of the arc x=ln y−(y^2)/8 for 1≤y≤2.

A: The solution are next step

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Which one is the arc-length of the curve y =2/7x + 11, x E [7, 11]? 147x+280 dx 7x+ 11 14x2 +…

A: The curve y=27x+11 , x∈7,11

Q: Given: y = arctan sinh find y' at x = 2 cosh 1 1+sinh 1 cosh 1 %3D 3(1+sinh 1) cosh 1 1+sinh 1 cosh…

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Q: Find the exact length of the curve x3 y = 6. 1 <x < 1. 2x Arc length

A: we have to find the arc length of the given curve

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

Q: Find the length of the curve y= ln sec x, Oln OIn 2+y3 V3 OIn 2+/3 OIn V3 2-V3

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.