3. Given that 7 sin(5t)â + cos(5t)ŷ represents the position of a particle at time t, find î. and comment on your answer. dr 4. Given a scalar function o = x?yz³, find (a) Vø. (b) |Vø| at the point (1, 0, 2).

Q: 1 5. y = %3D sin2 x

A: The given function is y=1sin2x. Obtain the derivative as follows.

Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

A:

Q: A particle in rectilinear motion has a velocity of v(t) time (s) when the particle is m from its…

A:

Q: Q. Suppose a vibrating string is governed by the equation f (x, t) = 2 cos(5t) sin x, where x is the…

A:

Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

A:

Q: T/2 T (² cos 2y + 3y° sin z) dz dy . Evaluate -1/2 Jo

A:

Q: A particle is moving with the given data. Find the position of the particle. v(t) = sin(t) – cos(t),…

A: Given that  v(t)=sin(t)-cos(t) and s(0)=3. We have to find s(t).

Q: laplace transporm to de y" ~ y' - 24 yo = 1 "D sin (3+) y' (o) = -1

A:

Q: A particle is moving back and forth on the x-axis. Its position at time t is s(t) = sin t + cos t.…

A: The position of the particle at time t is represented by the equation s(t)=sin t+cos t  ts(t)=sin…

Q: Which of the following is not linear? a. 3. 2x + Vy? – Vz3 = 4 (sin T1/2)x1 + 4x2 = cos245 b.…

A: Which of the following is not linear? a 2x+y2-z33=4b sinπ2x1+4x2=cos245c 12x-y+πz=4d…

Q: the order of the d.e. () + cos(x)y= x³ Select one: a. NOTA b. 3 С. 2 d. 0 e. 1 OO O C

A:

Q: then A(-2u - 20) = -2 ---B 5 and Au 3 Au = 2 4

A:

Q: Suppose z = f(x, y) = (x² + 2) sin(y) + xy². By setting one variable equal to a constant (either x =…

A: Given surface is,This equation represents a surface in three-dimensional space.To find the:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.