State the formula for the distance d between (x1, y1) and (x2, y2).

Q: Find x so the distance between (x, 2) and (1, 5) is V13.

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Q: Find the length of the curve. x = 4, y = 3/2, 0 st 0st <9 242 61 2

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Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

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Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: (),-- dz For z = -5x* – 3y and a point PER², you have = -4. dz Determine the value of

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Q: If the length of the curve y = 3 x7 from the point (0, 0) to the point (xo, f(xo)) is L = 8 , then…

A: Length of curve

Q: use the disTance Formula to Find the distonce between (e)and(3,2)

A: We use the distance formula to answer the given question.

Q: Find the exact length of the curve. y - 4 + 2x 3/2, o sxS1 1.547

A: Note: We are authorized to answer one question at a time, since you have not mentioned which…

Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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Q: is parallel to D. he distance between L and D is v26.

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Q: Derive the distance formula between a point S and a plane through point P. |n· PS| d = |n|

A: We have to derive the distance formula between a point S and a plane through point P.

Q: Find the point (x, y) of x+14xy+ 49y = 100 that is closest to the origin and lies in the first…

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Q: dy Find for y = cot '(4 – 2²). dr

A: The given function is y=cot-14-x2. Take t=4-x2. Then, the function y=cot-14-x2 becomes y=cot-1t.…

Q: Find the length of the curve. y = 2 – 4x, 1<a< 3 O 54 3V17 O 17 O 2y17

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Q: Find the length of the spiral r= 402, 0ses 21.

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Q: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

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Q: Find the point (x, y) of x² + 14xy+49y = 100 that is closest to the origin and lies in the first…

A: we draw a shortest straight line from origin to line, which will we perpendicular then we will find…

Q: Find the distance between the lines: r = + t r; = + s

A: Given: r1→=1,1,0+t1,6,2 and r2→=1,5,-2+s2,15,6 where a1=1,1,0 , a2=1,5,-2,b1=1,6,2, and b2=2,15,6 To…

Q: f d(x, y) denotes the distance between two points

A: answer is in next step

Q: The distance d from P1 = (x1 , y1  ) to P2 = (x2 , y2 ) is d =__________

A: We fill the blank space as,

Q: x = t³, y = t²,0 <t < v3

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Q: The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2). Find th…

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Q: dy Given y= In(lnx³), Find dr

A: Here we use the formula:

Q: Find the length of the curve r = 02 from 0 = 0 to 0 = 14.

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Q: Find the length of the curve r= e2θ, 0≤θ≤2

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Q: Find the distance between the following two points: (0, -1) and (2, 0) O 2 O V5 O V13

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Q: use the distance Formula tO Find the distance between e) and(3,2)

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Q: Find the exact value of dyd.r.

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Q: (c) Repeat part (a) using midpoints. M3 = %D M6 =

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Q: The arclength of y 4x/2 for 2 < r < 4 is:

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Q: Find the length of the curve. 6t, , r(t) 0 <t< 1

A: Given:-r(t)=6t, t2, 19t3,         0≤t≤1since we have to find the length of curve.

Q: Find the length of the curve, L. y² = 4 (x + 5)* , 0 0

A: To find the length of the given curve

Q: I. Find I = ždz where C is the line segment from 3 +i to 3 - 2i.

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Q: Find the distance between the points (2, 1), (5, 3) using (a) the Distance Formula and (b)…

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Q: Find the value of x if H is the midpoint of GJ , GJ = 4x – 6, and GH = 27. 14. %3D

A: We have to calculate the value of x

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

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Q: Which of the following is NOT a formula for finding the distance between two points on the…

A: Topic = Coordinate geometry 1st option is correct answer.

Q: Find the point (x, y) of x² + 14xy+ 49y? = 100 that is closest to the origin and lies in the first…

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Q: Use one of the formulas in the equation A = f. x dy = £. -ydx = } Þc x dy – y dx to calculate the…

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Q: Find the length of the curve, L. y² = 64 (x + 1)° , 0 0 L =

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Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: Find the length of the curve. y 3x 3/2 from x = 0 to x = О 335 162 О 335 O 1 O335 243 559 3.

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Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

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Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

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Q: :Evaluate , V1 + x dx using Gauss-Quadrature formula (n=4).

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Q: For x=In /t y=2, find y" when

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Q: For y=In 2t, find the value of k so that ¿ky'=1 at x=e

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Q: A manufacturer of open steel boxes has to make a box with a square base and a capacity of 1 kl. The…

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Q: Find dy when r + y? = 5.

A: