Use calculus to find the length of the line segmentr(t) = ⟨t, -8t, 4t⟩, for 0 ≤ t ≤ 2. Verify your answer without using calculus.

Q: Find the distance between the point (5, 1) and the line y = 3x + 1. O 3V10 O 7/10 O 9/10 O 5V10

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Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.y = 1/(x2 +…

A: A function is symmetric with respect to the y-axis if f(x)=f(-x). Such a function is also called an…

Q: Find the egmation for the Line" dhint passes through the point (,0) and parallel to the Line…

A: NOTE:Kindly repost the other question as a separate question.

Q: find the distance from the point to the line. (0, 0, 12); x = 4t, y = -2t, z = 2t

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Q: -) that passes through (-1,3) that is parallel to 2x – 5y = 1

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Q: O Evaluate )ds where c is the line segment from (-2,0) to 0,2).

A: We will parameterize C and solve.

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Find r so that the line through (2,6) and (-4,r) a).parallel to 2x-3y=4 b). Pendicular to x+2y=1

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Q: What is the length of the part of the curve y squared = (x-1) between the points (1,0) and (2,1)?

A: To find- Length of the part of the curve.

Q: 5. Construct a copy of the line segment below. U V

A: To construct a linesegment by copying using a compass

Q: Find the closure of a straight line in R x R_.

A: Given: Straight line in ℝ×ℝ. To find: Closure of straight line in ℝ×ℝ.

Q: the segment XY

A: What is the length of the segment XY

Q: Evaluate (x+y)ds where C is the straight-line segment x = 2t, y = (8 – 2t), z = 0 from (0,8 C…

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Q: Use the Midpoint Formula three times to find the three points that divide the line segment joining…

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Q: Find the distance from the point to the given line. (0, 1, 2); x= 2t, y = 5 – 3t, z = 2 + t %3D

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Q: Use the side-splitter theorem to solve for x in the triangle below.

A: Given,

Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: Evaluate 3 x2 - 2y ds where C is the line segment from (3,6)to(1,-1)is C Non of the above -58.240…

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Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: Find the distance from the point (1,1,5) to the line x=1+t, y= 3-t, z=2t O 2.236 O 0.36 O 36

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Q: A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

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Q: Determine if the following lines are parallel (never intersect), perpendicular (int intersecting…

A: Given: - The equation of the lines, y=-x+11,2y=-2x+22 To determine: - The given lines are parallel,…

Q: Use the algebraic tests to check for symmetry with respect to both axes and the origin.y = x/(x2 +…

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Q: find the distance from the point to the line. (2, 1, -1); x = 2t, y = 1 + 2t, z = 2t

A: We have to find distance from the point 2,1,-1 to the line x=2t, y=1+2t, z=2t

Q: A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

A: Let P be the shore point Let R be the resort Let S be the point where the pipe gets the water.

Q: Used to determine the distance between two points (*11) and (*, V2) d= V(*-*)2 +(2 -1)2 and (X2 d%3D…

A: Given that distance between points                                                 (x1, y1)  &…

Q: 51. Show that the shortest distance from the point (x1, yı) to the straight line Ax + By + C=0 is Ax…

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Q: Find x so that the distance between (-2, 3) and (x, 1) is Ï29.

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: The functionals with in the calculus of variations are of the form V[f(x)]=∫abF(x,y(x),y'(x))dx The…

Q: Use the Midpoint Formula repeatedly to find the three points that divide the line segment joining…

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Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: How do you compute |PQ| from the coordinates of the points P and Q?

A: Suppose the coordinates of P and Q  are given as, a,b and c,d. Then to compute PQ⇀,   PQ⇀=c-a2+d-b2…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.

Q: 3. Find the area of the quadrilateral enclosed by the lines x y = 0, 2x – 5y = –15 and 5x – 2y = 15.…

A: Let's find.

Q: Find the length of the curve. x = 4t, y = 2/3t 3/2, 0 ≤ t ≤ 9     a)61/3     b)242/3     c)61/2…

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Q: Find the distance between the point (-2, 4) and the point of origin. * O 4 O 2v5 O 5v2 O 5

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Q: 13. XPOQY and AOB are straight lines. PO =0Q and 21 = L2. Prove that ZA = ZB. B. A

A: That's easy. Have a great day!!!

Q: Determine the length of the curve y = x +x in the interval 1 <a <2. %3D 59 24 O 2.86 O 3.01 127 50

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Q: Show that f(-ydx + xdy) where C is the line segment joining (x, y) and (x₂, y2).

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Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: show.. that. the line in.which. and. .5Xm2y.Z==.0. jntersect..is

A: Equation of the plane: - In three-dimensional space, a plane surface is represented by an equation…

Q: Find the length of the curve. y= x? + from x = 1 to x = 5

A: Please refer the attached image for complete solution. THANK YOU.

Q: A small house was built on an island off a perfectly straight shoreline. The point B on the…

A: The given figure is: To find the formula for the cost of laying the pipe in terms of x.

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: Prove that the equation ax² + 2hxy+by² + 2gx+2 fy+c=0 wi h²2 = ab and bg2 = af?. Also find the…

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Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Q: What is y = _ + x3 1 curve x = 1 and x = 2 the length of the part 12 х between the abscissa points?

A: We find dy/dx using the power rule

Q: distance

A: