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

Q: Evaluate the following line integral.

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Q: The distance from the point P(3, 1,0) and the line x = 3 – 6t y =1+ 3t z = 7t equals to Answer:

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Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: Find the max. and min. values of (x, y) = x² – xy + y on the quarter circle x² +y =1 where x.y20.

A: I use langrange multiplier method

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: c. The curve y= Inx, the lines x 4 and the x-axis.

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Q: 4. Find the distance between the two points S(-5,-2) and T(-3,4).

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Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

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Q: Which of the following coordinates exists on the line y = 3x+ 1? А. (2, 6) В. (-1, -2) С. (3,4) D.…

A: Solution is B) (-1,-2)

Q: Find the distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: Find the distance d between the point M(5, 2, 4) and the line x- 8 y -2 Z-2 %D -8 -9 7.

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Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A: Answer

Q: B. Find the distance between the point (1. 1.3) and the line =z-3) OMI NOTL

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Q: Find distance the poinl- the between Cziz16) f * +y=0, J - Z =1 the line

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Q: Find the distance between the lines: ri = +! r2 = + s

A: We have to find the distance between given 2 lines.

Q: Find the distance, to the nearest hundredth, between the given points. P1(−5, −3) and P2(4, −2)…

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Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: find the distance d between the points P1 and P2, P1 = (a, b); P2 = (0, 0)

A: we have to find the distance d between the points P1 and P2 where P1=a,b and P2=0,0

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: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: 3. The line L is parallel to the line x t, y 2t, z =3 and passing through the origin.

A:

Q: find the distance d between the points P1 and P2.

A: We know, By distance formula, distance d between two points (a,b) and (c,k) is given by:…

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

Q: Q6) Find the distance from the point S= (1, 2, 1) to the line x = 2 -t, y=-1 + 2t, and z= 2 + 2t.

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Q: Find the distance, to the nearest hundredth, between the given points. P1(−5, −3) and P2(4, −2)…

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Q: Identify the segment bisector of XY. 5x + 8 9x + 12 M XM 10 line n YM The length of XY is

A:

Q: find the distance d between the points P1 and P2, P1 = (a, a); P2 = (0, 0)

A: Since, we know that the distance between two points A and B havingcoordinates (x1,y1) and (x2,y2) is…

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the distance between the two given points. S (-1, 6) and T (-1, 14)

A: We know that distance between two point (x1,y1) and (x2,y2) is  (x2-x1)2+(y2-y1)2 Therefore distance…

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1&lt;…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: find the distance between two given points 3. E(7,5) F(-5,0)

A:

Q: Let P be a point not on the line L that passes through the points Q and R. The distance d from the…

A: We have to find the distance between the point P and the line L.

Q: H.w.. Find the distance from the point (2,12)andthe Line

A:

Q: Find the distance between the given point Q and the given line. Q(- 9, 1, 10); x= - 5+ 3t, y = 1-t,…

A: Given that, the point is Q-9,1,10 and x=-5+3t, y=1-t and z=7+4t. Obtain the value of rt=xi+yj+zk.…

Q: Find the distance between lines x + 3y = 5 and x + 3y = 25.

A: The distance between two parallel lines can be calculated using the formula,

Q: Find the distance from the point S(- 6,6,8) to the line x = 6t, y = 4t, and z = 4t. The distance is…

A: The given equation of line is: x=6t,  y=4t,  z=4t

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: H.W: Find the distance from the point S(0,0,12) to the line L: x = 4t , y =-21 , z= 21 : =

A: According to the problem, we have

Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Find the midpoint M of the line segment joining the points P = (-7,-6) and Q = (-1, 2). M = OD %3D

A: We have to find the mid point between the two given points  P(-7,-6) ,Q(-1,2) .

Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: Find the distance of the point (4, 2, −4) from the line r(t) = (−1+ 2t, 1+ 2t, 7 – 3t). Answer:

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…