2 of 8 Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as - 2i + 5j. (b) Oppositely directed to 6i- 4j+ 4k. (c) Same direction as the vector from the point A(-2,0, 2) to the point B(2, 1, 1). W = 2

Q: Let r(t) = (2 cos²t, 2 sin²t, 2t), find the exact value of the curvature of r(t) at the point 31 π…

A: This question can be solved using the concept of radius of curvature.Radius of…

Q: 2. Water runs into a conical tank at the rate of 9ft³/min. The tank stands point down and has a…

A: Given query is to find the the rate of change of height of water.

Q: Find the volume of the solid obtained by rotating the region enclosed by about the line y = 0 using…

A:

Q: f(x, y) = 3y-6x+3 In(1-x)+1

A: we know Domain of lnX=(x;  x>0 )

Q: angles betwe J A 180°, given equati nd a. Sin (0) = 2/ r/m

A: Topic:- trigonometry

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: Find the parametric equation for the line where the planes 2x - 2y + 8z = 24 and 10x − 3y + 6z = 18…

A:

Q: (A) The integrating factor for (2y - xy²)dx - (3x+x²y)dy = 0 is 5 2xy 5xy

A: If a differential equation Mx, y dx + Nx, y dy = 0 has the form f1xy y dx + f2xy x dy = 0 and if…

Q: 3. A ball is thrown vertically downward from a height of 240 feet with a velocity of 32 ft/s. How…

A: The initial velocity of the ball in downward direction is u = 32 ft/s The height from where the ball…

Q: 3 tan ³x dx

A: Given:      ∫tan3x dx Rewrite:     =∫tan2xtanx dx    we know that         tan2x=sec2x-1…

Q: - Which of the following is the general solution of 2 - y secx = y³ tanx ? dx

A:

Q: Find the center of mass of the given system of point masses lying on the x-axis. = 6, m₂ = 3, m² = 6…

A: To find the Centre of mass.

Q: Find the average value and the value(s) of c guaranteed by the mear theorem for integrals if f(x) =…

A:

Q: 297. Consider point C(-3, 2, 4) and the plane of equation 2x + 4y - 3z = 8. Find the radius of the…

A: I am attaching image so that you understand each and every step.

Q: Evaluate [sin(5x) cos(4x)dx COS X 2 cos 9x 18 -+C (b)

A:

Q: dT Consider the differential equation x +T=e* with 7(0) = 1. What is the approximate value dx of…

A:

Q: ƒ(x) = = (x + 1)(x+2) x² - 3

A: As we know that; The Sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Product rule:…

Q: r'(t), r"(t), r'(t) r"(t), and r'(t) r(t) = 2t²i - 5tj + 5t³k X

A: Topic:- application of derivatives in vector algebra

Q: Let f(x) = - 4 cos x + 9 tan x f'(x) = ƒ' 7T =

A:

Q: (20 points) Suppose that an object moves along the y-axis so that its location is y = x² + 8x at…

A:

Q: (a) (c) Evaluate √√2 √√2 tan -1 X dx √2x VII) + C +C + √√₂x²2² +2 X √2x tan-¹√23² +2 -1 27127)+4 +C…

A:

Q: Find the positive t when the vector →r(t)=⟨9t,9t2,9t2−23⟩ is perpendicular to →r'(t).

A:

Q: (4) Find the area between y = 2 sin x, y sin 2x, x = 0, and x T. Sketch the region.

A:

Q: Find the total area between the x-axis and the curve f(x)= = x = 1 and x = 9. O a.) (10ln5-5ln9)…

A:

Q: sketch the region R of integration and In Exercises switch the order of integration. 48. 50. LS,…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the instantaneous rate of change of f(x) = 2x² - 8x + O 16 O -8 -16 O-14 8x+1 when x = -4.

A:

Q: d is partial derivative show that z = xe^y + ye^x is the solution to the partial differential…

A: Note: Since the student has made an typing error by writing d^3z/ox^3 in the first term of the…

Q: Using the position equation of a particle, s(t) following: a) The velocity equation: v(t) = = b) The…

A: Using the position equation of a particle, st=3t3-63t2+405t+20 and t≥0, to determine the following:…

Q: Find the slope of the tangent line to the graph of the function at the specified point: a) f(0) =…

A:

Q: A) 3.14 B) 3.19 C) 3.23 D π dT Consider the differential equation x dx of T (2) ? +T=e* with T(0) =…

A:

Q: Solve

A: Topic:- vector algebra

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. X = y = X…

A:

Q: Intervals on Which f is Increasing or Decreasing Consider the following. y = 3x³ + 33x² + 57x Find…

A: Concept: If a number causes the derivative of an expression to equal 0, it is critical. For a given…

Q: 2-4 - 10 i. What is the domain of g? b. Suppose g(z) ii. What is the range of g? Preview Preview no…

A:

Q: f(t) = { t + 1/₁ 0 <t <2 2 ≤ t ≤ 10

A:

Q: 1 -1 2 a-c c+1 ¹] | = -1 2 7 1 0 c-3 0 1 0 {][ a 0 0 2a -2b 1 1 0 1

A: To create a system of equations to solve the variables.

Q: A 3.14 B 3.19 D 3.23 π Consider the differential equation x + T = e* with T(0) = 1. What is the…

A: The given differential equation is; x dT/dx +T =ex, T(0)=1.

Q: 7. Use Simpson's rule to approximate the value of sin xdx. Use four 0 subintervals. Express your…

A: The given integral is sinx , limit from 0 to pi.

Q: = 2 2 x²-3

A:

Q: 1. Find the general solution to the DE ye 2x (4+e ²*) dy = 0 dx

A:

Q: First, convert the equation into polar coordinates then sketch a graph of the rectangular equation.…

A: Consider the given equation. x2+y2+x22=16x2+y2

Q: 7. Find the derivative for the function f(x) =(√√√x)" 8. Find for √3x² +1(3x² +1)³ dz for Y 3x3x 9.…

A: 7) f(x)= sqrt(x)x 8)y= sqrt(3x2+1) (3x4+1)3 9) y= 3x3x

Q: Find the parametric equations for the tangent line to the curve at the point (0, 2, 1). Use the…

A:

Q: 3. Find the general solution to the DE (x+m) dy =(nx - py) dx where m, n, and p are constants.…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: We need to find  out the volume of revolution for the given function on the interval given.

Q: 12. Suppose that lim g(h) = L. h-0 a) Explain why lim g(ah) = L for any constant a 0. h-0 b) If we…

A: Let's solve limit problem.

Q: Use the Binomial Theorem to expand the binomial (2x3 - 1)4 and express the result in simplified…

A:

Q: 2. Prove that the general solution to ndm + mdn + mn (3dn + dm) = 0 -37-m is Cmn = e

A: Solution

Q: large tank is filled to capacity with 300 gallons of pure water. Brine containing 4 pounds of salt…

A: we will  find the required.

Q: Find the transform of the given function by use of a table. f(t) = 3e-4t sin 5t A B C D E F (s) =…

A: