Find the length of the line given by r(t) = (7t,10t) for a sts b. The length of the line is

Q: (d). Consider the line y = ax , where a is a positive constant. What is the shortest distance…

A:

Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Z is the midpoint of VY and X is the midpoint of WY. If VW = s + 47 and XZ = s, what is the value of…

A: Given,          Z is the midpoint of VY¯ and X is the midpoint of WY¯ .           VW=s+47 and XZ=x…

Q: b. Enclosed by the curves y² = 4x + 4 and the line y = 4x – 16.

A:

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 length of the curve y = x2, 0 ≤ x≤√3/2.

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

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Q: Find the lengthof the curve 」 9メ d S16 3_ %3D

A: Given curve is By fundamental theorem of calculus,

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 distance between the skew lines defined by L1: ri(t) = L2:r5 (s) =

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: Find the length of the curve x = 1+ 312, y = 4 + 213, 0 <t < 1. Length =

A: Given,

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

A:

Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

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.

A:

Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

A:

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: Find the length of the curve. 5 17) y = 3x3/2 from x = 0 to x =- 335 335 B) 162 335 A) 243 D) 1 3

A:

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: Find the length of the curve. y= (16-x2/3)3/2 from x=1 to x=64

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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: Find the exact length of the curve. y = 5 + 2x³/2, 0≤x≤ 1 2.268 X

A:

Q: Find the length of the curve: - for 1< y<3. 3 4y 4. x=

A: As we know that the length of a curve x=f(y) is given by:- L=∫ab(f'(y))2+1dy

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

A:

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

A: First differentiate wrt y

Q: Find the the point on the line l: +t 0 | closest to the point P(3, 2, –2). ||

A: The given line is                             l: xyz=101+t00-1 and a point         P(3,2,-2)

Q: Find a point on the line y = 2x 3 that is 5 units from the x axis. %3D

A: The given equation is, y=2x-3

Q: . Find the length of the curve C : r(t) = (4t, t2 – In(t²)), 1<t< 4.

A: Explained below

Q: Find the length of the curve x = 3t2 + 10, y=2t3+ 11, O<t<1.

A: Given,         The length of the curve x=3t2+10 , y=2t3+11 , 0≤t≤1We know that,         The length…

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

A: To find the length of the given curve

Q: Find the length of the curve 6t, t2, 13 0 st s1 r(t)

A: Given:

Q: Q2) find the distance between two lines L1: x= 1 +4t, y=5 - 4t, z=-1+5t L2: x=2 + 8t, y=4 - 3t, z-5…

A: Method 1:

Q: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: Find the length of the curve. r (t) = 9ti + 12tj+9t°k,0 < t< 3

A: Given r(t)=9t i +12t^3/2 j+9t^2 k Length of the curve =intergration|r'(t)|dt

Q: Find the missing coordinate of P given that PR is perpendicular to MN, which has a 4 and R(2,-9). 3…

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Q: Find the length of the indicated portion of the trajectory. r(t) = (1+2t)i + (1+8t)j + (4 – 4t)k, –…

A:

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Find the value of x that makes m parallel to n when m./4 = 5x – 17 and m26= 4x + 3

A: Here, angles 4 and 6 are alternate interior angles and if alternate interior angles are equal then…

Q: For the line given by, y = x +4, find the slope of a line that is: %3D a) Parallel to the given…

A: We have to find slope

Q: The length of the curve z=z(t)=5e", Ostsa is а) 12л b) л c) 157 d) 2

A: Sol :-                Are length in (a,b) if functions are                               x(t) , and…

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

A:

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

A: The solution for the above solution is as shown below.

Q: Find the distance between the parallel lines.

A: Here x1 = 1; x2 = 0; y1 = 0; y2 = 1; z1 = -1; z2 = 1

Q: Find the length of the curve. r(t) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

Q: For the following lines L1, L2, first verify the two lines are parallel, then find the distance…

A: Two lines are parallel if their direction ratios are proportional. Distance, d =nr1-r2n; where r1…

Q: For what values of aa and bb is the line −4x+y=b-4x+y=b tangent to the curve y=ax2y=ax2 when…

A:

Q: Consider the line y = ax , where a is a positive constant. What is the shortest distance between the…

A: Here we use the general formula for calculating the shortest distance between line and point.