21. A constant force F = (3, v3) moves an object along a straight line from the point (0,1) to the point (V3, 4). Find the distance D. Find the work done. Find the cosine of the angle between the force F and the distance Ď. V3 21. W = 6v3 cos(0) 2 = -

Q: Jean throws a boomerang whose trajectory is given by the vector function: F(t) = +5 cos (t),20+5 sin…

A:

Q: Find the derivative, r'(t), of the vector function. r(t) = cos?(at) i + tebtj + s²(at)i sin?(ct) k…

A: Given that       r(t)=cos2(at)i + tebtj + sin2(ct)k

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places. Answer:

A:

Q: 3. Find the directional derivative Duf(x, y) if ƒ (x, y) = x³ – 3xy + 4y? and u is the unit vector…

A: First I have written the definition of directional derivative in the direction of given unit vector…

Q: Q3. For the motion vector r(t) = e cost i + e'sint j %3D find: (i) (ii) ат

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Q: Express the vectors in Exercises 9–12 in terms of their lengths and directions.

A: Q(9).  Given:  First find the length and then direction. Find magnitude. Find the direction of…

Q: | The equation 7(t) = (8t) i + (8t – 5t²) j + (7) k gives the position of a particle in space at…

A: Differentiate wrt t for velocity and again differentiate wrt t for acceleration

Q: f(x, у, 2) %3 ху+yz+zx What is the derivative of (a) 4 this function in the 44 (b) 7 direction of…

A:

Q: 1. Suppose that r(t) = (3 cos(3t) t,3 sin(3t), 5t). a. Determine the velocity, the acceleration and…

A: For velocity vector diffrenciate displacement vector. And for acceleration vector diffrenciate…

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A:

Q: 2. A BLOCK IS RESTING ON AN INCLINE OF SLOPE 4:3 AS SHOWN IN THE FIGURE BELOW. IT IS SUBJECTED TO A…

A:

Q: Find the unit tangent vector for the motion of r(t) = .

A:

Q: Q2: A boat is moved uniformly along a canal by two horses pulling with force P=890 N and Q=1068 N…

A: Equilibrium Law: Two forces can be in equilibrium only if they are equal in magnitude, opposite in…

Q: 5. An object moves along the curve r(t) (Vi, 1/Vi,) 1<ES 4, subject to the force F= In 2+ 11/3 (y,…

A: Explanation of the answer is as follows

Q: Q.9. Determine the magnitude of the resultant force F Fr+F2 and its direction, measured clockwise…

A: Opposite angles are equal.

Q: 2) Let two vector functions be defined by r₁(t) = (2t, t², t²) r₂(t) = (sint, sin(3t),5t) a. Find…

A: a. Consider the given vector functions, r1(t)=2t,t2,t4r2(t)=sint,sin3t,5t if two vector function…

Q: At the given find the moments when the two distance, vectors of velocity and acceleration are…

A: We have the distance vector is R→t=2i→ +5cost j→ +3sint k→ Now, the velocity vector is :…

Q: Find the work done by the force F = xyI+ (y– x)j over the straight line from 3) to (1,0). ..... The…

A: Given; F=xyi +(y-x)j.

Q: c) Given that the pressure of air at any point (X,y,z) is P(x, y, z) = e²" (x + 2²) – 4xz², At point…

A:

Q: Q3. For the motion vector r(t) = ti+ In (cos t) j, find (i) The velocity (ii) The speed at t=t (iii)…

A:

Q: Without finding T and N, write the acceleration of the motion a(t) to +P);+ (t- ) k the position…

A:

Q: Q.1 (20%) Find the resultant of two forces shown in Figure and its direction with X axis using Sine…

A:

Q: Transform pentagon BEARS according to (xy) → (x + 6, y+8). Write the coordinates for pentagon…

A: Given Data: Traformation: x, y→x+6, y+8   The given figure in the problem represents the pentagon…

Q: 'n 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: At first we have to find the parametric equation of the spirac staircase. Then we have to find its…

Q: A block of mass m1 = 3.24 kg on a frictionless plane inclined at angle 0 = 30.1° is connected by a…

A: We have to find a and T. The solution is following

Q: Utt = C°AU in IR3 Schve the equations welve %3D with initieh dotes U0)= ¢()ー 0 Ut(8っ0)= Y(R)=X

A: The partial differential equation given is as follows: utt=c2uxx The initial conditions given are as…

Q: nd torsion of the motion r(t) = . Leave your answer correct to two decimal places swer:

A: Solution is given below

Q: Q3. For the motion vector r(t) = ti+ In (cos t) j, find (i) The velocity (ii) The speed at t=T Write…

A: Given motion vector is, rt=t i^ +lncost j^ i To find velocity. vt=ddtrt=ddtt i^ +lncost j^=ddtt i^ +…

Q: ) find the resultant force, R. B) what additional force F is needed for the object to be in static…

A: According to the problem, we have

Q: y y = -2x + 8 y = x2 B 2 4

A:

Q: The path r(t)=(5 sin t) i+(5 cos t) j describes motion on the circle x^2+y^2=25. Find the​…

A: We have to find ​ particle's velocity and acceleration vectors at t=π/3 and π/6 . Given  r(t)=(5 sin…

Q: Ex.9 The work of the force F(x, y) = (x², xy²) along the boundary of the square [0, 1] x [0, 1]…

A: The given work force is Fx,y=x2,xy2 along the boundary of the square 0,1×0,1, counterclockwise…

Q: Uo (r² + a?) cos 0. u(r, 0) = ) Hence show that the velocity components of the flow are ди Ur = ax…

A:

Q: Use Newton's Second Law of Motion to find the force required so that a particle of mass 2 has…

A: Given: m=2r(t)=⟨t2,t4,sin(2t)⟩

Q: A. Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

A:

Q: 3. The given plate R is submerged vertically into a water with y = 4 as the water surface. Find the…

A: Given the plate R: y=1-x,y=0,y+2x=-2. Find the force due to liquid pressure on one side of R.

Q: 2. The block shown in Figure 2 is acted on by its weight W= 400 lb, a horizontal force F= 600 lb,…

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Q: / F - ds, where F 4 Evaluate and S , 0 < u < 3, 0 < v < T

A: Given that  F=(y,-x,z^4) r(u,v)=(ucosv,using,v) Find the integral

Q: he vector r(t) is the position vector of a particle at time t. Find the angle between the velocity…

A:

Q: A 0.75 kg toy cart is moving to the left (-z direction) with a speed of 1.0 m/s when it 2.…

A: Given query is to find the impulse delivered by the force and the effect of the impulse on the cart…

Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

A:

Q: The vector function r(t) = (1+2 cost) i+3j+(5 – 2 sin t) k | traces out a circle in 3-space as t…

A:

Q: 2) Let two vector functions be defined by r¡(t) = (2t,t²,t*) r2(t) = (sin t , sin(3t),5t) a. Find…

A:

Q: (2/3 equation r(t) = i+ (2t- 16t) j is the position of a particle in space at time t. Find the angle…

A: Velocity is the derivative of position vector and acceleration is the derivative of velocity vector…

Q: The equation r(t) = i+ 16t j is the position of a particle in space at time t. Find the angle…

A: r(t)=32t i+12t-16t2 jVelocity vector v(t) = drdt=32 i+12-32t j

Q: 3. For the motion vector r(t) = ti+ In (cos t) j, find (i) The velocity (ii) The speed at t=N Write…

A:

Q: r(t) is the position of a particle in space at time t.Find the angle between the velocity and…

A: To find the angle between the velocity and acceleration vectors at time t=0

Q: Without finding T and N, write the acceleration of the motion r(t)=(cost+t sint)i+(sint-tcost)j, in…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.