30. Find the shortest distance from the point P(0, 1, – 1) to the line (x, y, z) = (1, 1, 0) + t(1, –1, –2). (a) / 66 (b) V65 (c) (d) v62 (e) V61

Q: Given that f(x) = (x - 4) and g(x) = 2 - 3x, find (a) (f + g)(4)= (b) (f – 9)(4)= (c) (fg)(4)= (d)…

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Q: GIVEN: L: c(t) = (−1+ 2t, 2-t, 3+t) B = (0,1,2) FIND: The distance from B to the line, L. d(B, L).

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Q: Find y as a function of tif y(0) = 2, y'(0) = 3. y(t) = 0 16y" + 104y' + 169y = 0,

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Q: x(t) Find the point at which the line y(t) z(t) = = = 4 - 8t -4+ 5t intersects the yz plane. 6 + 2t

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Q: Find y as a function of x if y(0) = 10, y(0) = 10, y"(0) = 18. y" - 16y" +63y = 144e",

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Q: Find R(t) if R′(t)=⟨sint3,cost2⟩ and R(π)=⟨12,12⟩.

A: According to the given information it is required to find R(t).

Q: 2. Let l be the line x² + y² − 4x + 2y +1 = 0 and drop a perpendicular from O to Q E l. (a) Explain…

A: Step 1:Part (a): Finding the coordinates of (Q), where a perpendicular is dropped from the origin (…

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: Two sharpshooters will simultaneously shoot once at a target. Let Xi , i = 1, 2, be marksman i's…

A: Given that, the errors are modelled by X1~N(0,0.5),X2~N(0,1). To solve this problem z table values…

Q: Evaluate the value of I = f(e6 − 3x)dx + (6xeº + y)dy, r where I is the straight line from (0, 0) to…

A: On the curve Gamma , which is straight line from (0, 0) to (3,0) we have, y=0 and x  ranges from 0…

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Consider the function f(x, y) = x6-7xy and the path r(t) = (cost, sin t). What is the value of…

A:

Q: A circle of radius r centered at the point (0,r) in the plane will intersect the y-axis at the…

A: We have to draw the suitable diagram first.

Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located…

A: Let A=(-1,0), B=(2,0), C=(0,2). Now,∫path 1v.dr =∫path 12x2-y2+4dx+5y+3x-6dy…

Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

A: