Find the length of the catenary y = a cosh² from x = 0 and x = %3D X1.

Q: Obtain the general solution por the di fferential equation %3D .(yd -x² )dy= 2xy dx %3D

A: Given; 1) y'=(x-y)/y. 2) (y2-x2)dy=2xydx.

Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: The figure shows the graphs of the functions y1= x, y2= 1/2 x3/2, y3 = 1/4 x2 , and y4 = 1/8 x5/2 on…

A: Given: y1=x1y2=12x32y3=14x2y4=18x52On the interval 0,4

Q: 3 dgee 2. Calculate the arc length of y, from to2. (Hint: Remember to be creative with 6 2x…

A: We are given equation of curve with bounds as

Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: Two masses hanging side by side from springs have positionss1 = 2 sin t and s2 = sin 2t,…

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Q: Given that Sinh Ys 2. fnd sech x, eanh y with draw atiangle

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Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

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Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

A: Explanation of the answer is as follows

Q: Which of the following gives the arc length of the parabola 2y = x² - 13xS1 Hint: Use Trigonometric…

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Q: Use the arc length formula 2 dx 2 L = dy dt dt dt to find the arc length of the curve. x = cos 12t,…

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Q: Find the arclength of y = 3r/2 on 1 < a < 3

A: As we know that the expression for the arclength is:   l=∫x1x21+dydx2dx...(1)   Given: y=3x32x→1 to…

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: b. -2åx + 3d, - åz 2. If E = -xả, + yåy V/m, find the work involved in moving a unit positive charge…

A: We can solve using given information and calculate the work done

Q: Find the arc length of the following line. y = 2x+ 3; [0,3] Which of the following is a simplified…

A: To find the arc length y=2x+3 [0,3]

Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

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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: 2 Use the arclength formula: L= S"1+ () dx to find the arclength of: x2 y = 1+ where 0 < x<1

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Q: 3. Given DC is a tangent to 04 at B. Solve for the radius (r). 40 32 A

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Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

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Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: 127x+1 M. K 63x+1 JMK what is the meAure Of Arc

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The given question is the application of integration and solved as shown in step2.

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: 10. Find mAD (11r – 3) B (8x + 15) A %3D Measure of Arc AD =

A: Given: ∠ABD=11x-3° and ∠ACD=8x+15° The objective is to find the measure of Arc AD

Q: (xy + 1)dx + x(x + 4y – 2)dy = 0 %3D

A: Given (xy+1)dx+x(x+4y-2)dy=0 Let the integrating factor be xαyβ Multiply both sides by xαyβ , we get…

Q: Find the length of one arch of the cycloid a = 9(t – sin(t)), y = 9(1 – cos(t)). %3D

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Q: Determine which formula we are using when we are trying to find the arc length: cx=b •y=d dy 2 dx dx…

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Q: Find the arclength of y 4x? + 4 on 0 < x < 2

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Q: y = x2 - 2x + 1, y = 1 about the line x = 3

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Q: Find the arclength of y = 2x? +1 on 0 < x < 4

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: a) Show that the length of the arc of parabola y? =16x measured from the vertex to an extremity of…

A: Given the parabola y2 = 16x.

Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: I keep getting different answers each time I attempt this question, so any help would be kindly…

A: We will find out the required volume.

Q: (2xy* + siny)dx + (4x?y³ + xcosy)dy = 0

A: The objective is to show that the  differential equation is exact and solve it.

Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: Solve the following DE 3 X dy %3D

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Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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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: W = C - sec?(3x) – V8 )dx. Evaluate W - 6х+9 *

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Q: Find the length of one arch of the cycloid x = 9(t – sin(t), y = 9(1 – cos(t)).

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Q: Find the arc length of the given curve on the specified interval. This problem may make use of the…

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Q: 2x? – 4 on Find the arclength of y 0 < x < 2 -

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Q: Which integral gives the arc length of the curve y = e2x on the interval 2 < x < 4? a)o (1+2e**)dx…

A: Given,  The curve  y = e2x on the interval 2≤x≤4  We have to find the integral which gives the arc…

Q: Find the arc length of the curve below on the given interval. y = In (x-√x² - 1), for 1 ≤x≤ √442…

A: Given y=lnx-x2-1, for 1≤x≤442   To Find: The arc length of the curve given on the given interval.

Q: x?dx – /16 – x²(3y+y²) sin 2y = 0 - %3D

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Q: Use the arc length formula 2 dy dt dx L = dt + dt to find the arc length of the curve. x = cos 61, y…

A: Arc length is the line integral of the curve along the given range. It is basically the length of…