4. Find the shortest distance between the lines x - 5 and 2 x - 2 y – 6 z - 5 y - 3 %3D z- 8 3 -2 -2 1 6.

Q: Find the length of the given curve. 4/3 3y2/3 X = -27 - 32

A: The arc length formula is L=∫ab1+f 'y2dy. Here, 3y43-3·y2332' =-1+64y2316y13. Thus, the length of…

Q: The equation showing a family of lines passing through the point (1, -1) is given by

A:

Q: 5- Find the Line that passes through the point (l,2) and througgh the point of inter Section of the…

A: In this question given that point (1,2). And two lines x +2y = 3 and 2x -3y = -1. And we find that…

Q: Find the exact length of the curve. y = 3 + 2x^(3/2), 0 less than x less than 1

A:

Q: Find the shortest distance from the point x = (-3, 0, -12)  to the line r = t(0, -2, -2).

A:

Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

A:

Q: x-2 y-3 z- 4 x+2_ y-2 z+ 4 and 3. a) Find the shortest distance between lines 4 3 5 4

A: We have given two lines;

Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the distance between the points (3,6) and the line x - 2y +3 =0.

A:

Q: 4. Sketch the graph of both lines on the coordinate plane. Use the graph to solve the systen S2x +…

A:

Q: 2) The line represented by the equation 4y = 3x + 7 is transformed by a dilation centered at the…

A:

Q: Find the shortest distance between the point A (3, 10) and the line y = x + 1.

A: Our Aim is to find the shortest distance between the point A(3,10) and the line y=12x+1 -(i)

Q: Find the intersection point of the line l.x=-1. y = - 3 + t z = 4 + 2t with xx - 1 .

A: In xz plane value of y = 0.

Q: the following curves. 33. y= 2.x+ 3x² + 1 34. y = x -x - 6x 35. y= x³ - 3x? + 3x – 2 36. y = 100 +…

A:

Q: nded by the curve y2=4x and the lines x = 1 and x = 4.

A:

Q: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

Q: - For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3-y = 1?

A:

Q: 1. Find the equation of the line passing through the point perpendicular to the line 5x + 3y = 5. 3…

A: Given equation of the line5x+3y=53y=-5x+5y=-53x+53 which is theform of y=mx+b whereslope of the line…

Q: 2. Find the line L passes through the point (-2,2) and perpendicular to the line L: 2x+y= 4.

A:

Q: 1. Find the length of the curve: y = x/2 , x = 0 to x = 4

A:

Q: 16) Identify the hortizontal line. A) y=x C) y=-5 E) x= 4 B) x -y 1 D) x+y 0

A: Line Parallel to x axis

Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: - For what value of k will the line kr + 5y = 2k be perpendicular to the line 2x - 3y = 1?

A:

Q: 2.1 côncept Q 018: List the given lines in order of their slopes from smallest slope to largest…

A: The graph of the lines are as shown below :

Q: Find the distance between the point (−3, 1) and the line 4x + 3y + 4 = 0.

A: Given standard equation of line 4x+3y+4=0 and a point (-3,1)

Q: A. Find the shortest distance between the point A (3, 10) and the line y=x+1.

A:

Q: Find the shortest distance between the point Q(2, 0, 0) and the line segment joining the points…

A: Formula used: Distance between the point and a line is, D=PQ×uu Where u=P2-P1

Q: Consider the following two lines: { -3s l1:= +t and l2 : 4+ 2s (a) Find the ( shortest) distance…

A: Introduction: The formula of the shortest distance between two lines l1: a1+n1t and l2: a2+n2t is…

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: 1. Find the point on the line y = x nearest to the point (4, 1).

A: Since, we have been asked to solve part(i) which aims to findthe point on the line y=x nearest to…

Q: Find the exact length of the curve y=x^4/4+1/(8x^2 ) , 1≤x≤2.

A: Given: The expression to calculate the length of a curve 'y=f(x)' is over the interval [a,b] is,…

Q: A. Find the shortest distance between the point A (3, 10) and the line y = x +1.

A:

Q: 1. Fit a (a) straight line (b) parabola to the given data points: X 1 3 4 6 7 8. y 1 1.5 2 3 4 5 8.…

A: (a) straight line

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

A:

Q: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

A: Find the shortest distance between the point Q (2, 0, 0) and the line determined by the points P1(0,…

Q: 4 - Which of the following is the shortest distance from the point (5, 0) to the curve y = V2x ? 7…

A:

Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

A:

Q: the

A: We will find the point.

Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

A:

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

A:

Q: 8. Find a line uniquely parallel to the line 3x-4y+12=0.

A:

Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: (1) ( ) Find the shortest distance between two lines given x +2 -8 y = and y 2

A:

Q: Find the shortest distance from the given point to the line whose equation is given.

A: 6. The shortest distance from the point (0, 10) to the line y=13x is:…

Q: 4) Find the point in which the line through the origin perpendicular to the plan 2x - y -z = 4 meets…

A:

Q: 9) Find the point on the line y = 3x - 4 that is closest to (2, 1).

A:

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

A:

Q: 2. Find the shortest distance from the point (2,0) to the curve: (a) y = 3x – 1 (b) y = x^2 (c) x^2…

A:

Q: 14. Find the equation for the line that passes through the point (4, 1) and is perpendicular to the…

A: As we know that the equation of the line slope intercept form is: y=mx+c Where 'm' is the slope and…

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.