5. Find the center and radius of the circle whose equation is (z - 1)2 + y? = 4 %3D C(2, y) = (

Q: 1 find the length of the curve x = 7y* + y2, from y = 1 to 24 y = 2.

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Q: 3/2 Find the length of the curve. y = (x* +4)" OSxs2

A: see below the answer and calculation

Q: A circle is centered at (5, -4) and has radius 6. Write its equation in standard form. O A…

A: The standard form of equation of circle is given below: x-h2+y-k2=r2 where, h,k is the coordinates…

Q: tind the point on the curve y=Jx that is closest to the point (3,0).

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Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through point…

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Q: Find the center of the circle tangent to x^2 + y^2 + 2x - 6y + 5 = 0 at (1,2) passing through the…

A: First find the equation of the tangent. The point (1,2) is tangent to the given circle. The general…

Q: Given : The region is bounded by the curve y=4x-x^2, y=4 and the y-axis Problem : The intersection…

A: We have to determine the points of intersection of the given curves and find the value of a+b+c.

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Q: Problem 4: For what valnes of a and o s the line y=-2x+b tangent to the parabola y=Ox° whern X=2?

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Q: 1. Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A:

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: 16 6xy ds, where C is the right half of the circle x² + y² = 4. Evaluate the line integral

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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: Sketch the graph of the cylinder given by 4x2 + 9y2 = 36. show solution

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Q: dy Use the method of isoclines to draw several solution curves for the equation dr

A: First integrate the function using variable separation method and find y as function of x  Then draw…

Q: 26. A cross section of the parabolic mirror in a car headlight is modeled by y = 12x. Where should…

A: Given that a cross section of the parabolic mirror in a car headlight is modeled by y2=12x. Clearly,…

Q: Below is a plot of a cardioid, which consists of points satisfying x² + y² = (2x² + 2y² - x)² 0.6…

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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: If the infinite curve y = e-2x, x 2 0, is rotated about the x-axis, find the area of the resulting…

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Q: 7.) Find the shortest distance between (4,2) and the curve y? = 8x.

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Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: Please refer to the image below

Q: Find the equation of tangent to the circle x + y = 25 at the point (3, –4) %3D 25 ix + O b. y = 7 O…

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Q: stuck on the attached problem

A: Please refer to the white board. We have to find the volume shaded in the first diagram. This volume…

Q: Situation 7. Find the tangent to the parabola y? = 6x – 3 perpendicular to the line x + 3y = 7. 26.…

A: Given that parabola y2=6x-3 , tangent perpendicular to the line x+3y=7To find : equation of tangent…

Q: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

A: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

Q: Evaluate f. y3 dx - x3 dy where c is the circle x2 + y2 = 4

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Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

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Q: 3x + xy? 2y + x?y dy dx

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Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: Find the equations of the tangent and normal line 4x2 + y? + 8x + 2y = 20 at x = -3 %3D

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Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…

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Q: consider the circle X^2+y^2=25  1. find dy/dx 2. find the equation of the tangent line at the point…

A: Given an equation of circle

Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: (3²+ 3a)dA, where D is the region in the 3rd quadrant between the circles 2² + y² = 1 and x² + y² =…

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Q: in R°sketch the graph of the cylinder x = (y – 2)?

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Q: The equation of a circle in the zy-plane is 2 + 4x + y? – 10y = 20. If the line z= k intersects the…

A: Consider the equation of circle in xy-plane given by x2+4x+y2-10y=20 If the line x=k intersect the…

Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

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Q: 3. Find an equation of the circle with center at (5, –6) that is tangent to the y – axis in the form…

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Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

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Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &amp;…

Q: Calculate y in degrees. (Image 21] (2x - sy (3x - 25) (Sx+ 45)

A: (3x-25) +(5x+45) =180 8x + 20 =180  8x = 160  x = 20

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Q: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

A: