A bug is located at the point (9,0) at time t=0 and crawls at the rate of 6 units/minute in the counterclockwise direction along the circle centered at the origin of radius 9. Find the coordinates (x,y) which give the location of the bug after 29 minutes. After how many minutes will the bug first return to the location (9,0)? Give the coordinates (x(t), y(t)) at an arbitrary time (t) is greater than or equal to 0.

Q: A curve passes through the point (2,0) has gradient dy at point (x, y) that satisfy the dx equation…

A:

Q: We are given the function f(x,y)=sin(3x+2πy)+exy-π, and points A(π, 1), B(π + 1, 0). Find the rate…

A: Given function is, fx,y=sin3x+2πy+exy-π. To find the rate of change of f at A(π,1) along the…

Q: The thickness of the shell is a = 0.2 centimeter. Use differentials to approximate the volume of the…

A:

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find the differential of the function w=x^5sin⁡(y^5z^4) dw=  dx+  dy+  dz

A: Differential of a function is simply the derivative of a function. Also, d(uv) = u.dv + du.v

Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: sec( c)+y dy e sec do

A: Given differential equation is homogeneous equation

Q: 2. Find the equation of the tangent plane and the normal line at the point (0 ,1 , 2) on the surface…

A:

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

A:

Q: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…

A: The distance of a point (x, y) and the origin can be calculated as follows.

Q: Given a particle is moving in a curve r(t) = cos  6t i + sin 6t j +  10t k. Find the tangential…

A: I have appended the formula used in the solution part

Q: Find the total differential dz ZzxeX+y

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

A:

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: The equation of the upper semicircle centered at the origin with radius R in parametric form is…

A:

Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…

A:

Q: The coordinates of a particle moving in the metric xy-plane are differentiable functions of time t…

A: According to the information given, particle is moving in xy-plane with the coordinates which are…

Q: Find ðw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s +t, y…

A: We will find out the required value.

Q: dy 2. sec²y secx dx ;y(0)=0

A: The given differential equation is dysec2y=dxsecx and y(0)=0

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Find the total differential. z = 2x6y9 dz

A:

Q: find the soution of' the differential eq. System X= 3X+44 9=X+3y %3D

A: Given differential equations are                                     dxdt=3x+4y,dydt=x+3y…

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: 1. xy + z2

A:

Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ---->1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: Find the equation of the two lines that are tangent to the curve x 2 + 4y 2 − 4x − 8y + 3 = 0 at…

A: Given

Q: Find the total differential. z = 6x1°y8 dz =

A:

Q: Use the Chain Rule to find dz/dt. z = x2 + y?, x = cost + sin t, y = cos t – sin t. -

A:

Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

A:

Q: A girl is sliding down a slide shaped like the curve y = 3e-*/3, Her y-coordinate is changing at the…

A:

Q: at is the maximum rate of change of f (x, y,z) at P?

A:

Q: Find the total differential. z = 10x6y7 dz =

A: Differentiation of xⁿ = nxn-1

Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

A:

Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: 2. Suppose that a particle is moving along the curve 4x2 + 16y? = 32. When it reaches the point (2,…

A:

Q: Show that a particle, located at the origin at t = 1 and moving along the x-axis with velocity v(t)…

A:

Q: Find the total differential. z = 6x *y5 iz

A:

Q: Q. Find the rate of change of z = In Vx² + y² at (3, 4, In 5), (a) In the direction of the positive…

A:

Q: A 15 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding…

A:

Q: Find the rate of change of volume at the t= 2 sec If ri=2t-1 hisim hi=3ť-t r2= 3t+1 h2=2m h2=4t-1…

A: