find the distance from A(4, 6, -3) to the line x = 3t + 1, y = -t + 3, z = 6t

Q: 3. u=8, |v|=3 and the angle between them is 125°. Determine b) the angle that u-v makes with vector…

A:

Q: A value= B value= Horizontal shift:

A: Given,          f(x)=-4cos(x)+2

Q: d). Integrate f(x, y, z) = -√√x² + z² over the circle r(t) = (a cost)j + (asint)k, 0≤t≤2.…

A: Solution:-

Q: m above, prove that for every real number c>0, there is a 1/N < c.

A: In every real number c, there is integer N which is N &gt; c.

Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: A lady 1.65 meters tall walks towards a lamp post 2.65 meters high at a speed of 1.5 m/s. How fast…

A: Given: Height of lady=1.65 m Height of lamp post=2.65 m Speed of lady=1.5 m/s To find: Shadow of…

Q: Consider the initial value problem u" + p(t)u' + q(t)u = g(t), u(0) = uo, u'(0) = u Transform this…

A:

Q: Estimate how much the value of the function will change f(x,y,z)= ysinx + 2yz if the point P(x,y,z)…

A: If the input of a multivariable function changes its output also changes. The directional derivative…

Q: a. Find -R(t), . give the parametric equations of the tangent line to the graph of -R(t) at t=0: 1…

A: Given that R't=4e2t,11+t2,2cosht R0=1,−2,3 To find: R(t) Parametric equation of the tangent line…

Q: Find the area bounded by the curve y=- 16 A 10 square units B) 16 square units Ⓒ 8 square units (D)…

A:

Q: Quantitative Comparison g and h are consecutive multiples of 4. Quantity A: 5(g-h)² Quantity B: 80…

A:

Q: solve: [x X2 X3 Б 1 0 002-20 X1 0-1/2 0 140x₂ 0 00 01 0-1] LxS) ха 0 -12 + +2] 3et+ - 1/4 0 0 with…

A: As per the instruction, we will be answering the part (b). For (b), We are given the following…

Q: x² T +3y² = z + 3. Consider the surface T with equation 3 1. Find the equation for the trace of T on…

A: Solution

Q: 20102211 is in base 3 convert it in base 10

A:

Q: 0 -2-4 8 15 1. A = 1 4 1 6

A: We need to find the determinant of the given matrix using raw operations and cofactor method…

Q: Let f C D be a function, with C being the domain and D being the codomain. Show that for any C₁, C₂…

A: Solution: Let  x ∈ fc1∩c2⇒∃  y∈ c1∩c2such that fy=x⇒y∈ c1 and y∈ c2⇒fy ∈ fc1 and fy ∈ fc2⇒fy ∈ fc1∩…

Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

A:

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

A:

Q: I. Let C be the curve with parametric equations 3t-1² I= and yIn(t-1) for t€ (1.+00), t-1 and let P…

A: The parametric equations of the curve C is given as, x=3t-t2t-1 and y=lnt-1 for t∈1, ∞ The given…

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: We will use integral to find force on trough . 1st will find force on a horizontal slice of trough…

Q: 1. Find all solutions to the system of congruence. (Use CRT) x = 1 (mod 2) x = 2 (mod 3) x = 3 (mod…

A:

Q: describe xy - trace, xz - trace, yz - trace. draw each trace a) z^2 - 4x^2 = 9 - 4y^2 b) z^2 -…

A:

Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

A: Any vector parallel to the vector: a, b, c is ka, kb, kc, where k is a constant. If two vectors are…

Q: Q11) Determine if 8 (t) and 8' (t) even or odd by utilizing properties of Fourier transforms. What…

A: Solution : δ(t) and δ'(t) are real functions. Fourier Transform property : Fourier Transform of even…

Q: The volume of the solid generated by revolving the region bounded by x2-4y and y2-4x about y=4 is to…

A:

Q: Show that -ydx+xdy) = x₁y₂-₂₁ where C is the line segment joining (x,y) and (x₂,₂).

A: We have to prove ∫C-ydx+xdy=x1y2-x2y1 Where C is the line segment joining x1,y1 and x2,y2 Now…

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Option (A) is correct.

Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Using differential

Q: 3. Determine whether the sequence converges or diverges. If it converges, find the limit. an 21+3n =

A: Solution:an=21+3nnOn rewriting this equation, we get 21+3nn which turns into [21n(23)]Here 23=8 that…

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: Solution

Q: Which of the following can be solved by both trapezoidal rule and Simpson's 3/8 rule? How to solve…

A: Trapezoidal Rule: For applying this rule, the number of subintervals must be a multiple of 1.…

Q: ould you write it out on paper or write each step clearly

A:

Q: Toss a coin repeatedly, and let X, be the number of heads after n coin tosses, n ≥ 1. Suppose now…

A: Given: Xn|P=P∈Binn,p with P∈U0,1 To find: Distribution of Xn

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

A: Given curves are  x2+4y2-z=0    ......(1)2x-z=0              ......(2)

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A:

Q: Exercises To Solve [No.5] Lim 9-5 -4 S= a dx -x²-8x-15 of Los x Sinx+25inx+5 ka

A:

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: Evaluate [√x² + y² ds_ along the curve r(t)=(4cost)i+(4sint) j+3tk, −2π ≤t≤ 2a.

A: To find- Evaluate ∫Cx2 + y2 ds along the curve rt = 4costi + 4sintj + 3tk, -2π ≤ t ≤ 2π.

Q: Let S be the solid inside the sphere p = 6cos and below the cone Ø = π/4 Set-up the iterated triple…

A: We have to Set-up the iterated triple integral representing the volume S using Cartesian…

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The quadric equation given is as follows: 4x2-y-32+4z2=4 (a) Rearrange the above equation.…

Q: Suppose we want to choose 7 colors, without replacement, from 10 distinct colors. (a) If the order…

A:

Q: xxx (e)

A:

Q: 5. || x+y cosx 1+sin x

A: Solution

Q: Consider J x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 1/2…

A:

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

A:

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

A:

Q: 9) If f(z) = u - iv is analytic in the z-plane, then the C-R equations satisfied by it's real and L…

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

Q: IV. Consider the plane : +3y - 2z = 6 and the line with parametric equations l:x=4-3t, y=2+t, z = 2t…

A:

Q: Consider the linear system : -11 = = [] 83], -2 -3 6 y(0) = [9] 2 Solve this IVP and enter the…

A:

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…