47412021 7. The water in a river moves south at 7 km/hr. A motorboat is traveling due east at a speed of 42 km/hr relative to the water, determine the speed of the boat relative to the shore. Let w represent the current; this means that |w| is the speed of the moving water and w points in the direction of the moving water. Assume that the vector vw gives the direction and speed of the boat relative the water, and the vector v, gives the direction and speed of the boat relative to the shore. Place the vectors in a coordinate system. Choose the correct diagram below. А. *B. С. D. N W E E W The speed of the boat relative to shore is approximately (1). (Round to the nearest tenth as needed.) (1) O km/hr. hr/km. km. hr. YOL ANSWERED: D.

Q: 27. Find a unit vector that is orthogonal to both i +j and i+ k.

A:

Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: Let v = (8, 15). a. Find a vector in the direction of v that is three times as long as v. b. Find a…

A: Given vector

Q: In Newton's theory of gravitation, the Earth's gravitational field is given by, -GM r3 where 7 = (x,…

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

Q: 140 N 14m 40N 240 N 3. Determine the resultant of the three forces acting on the pulley shown.

A:

Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: determine the unit vector from which f grows faster in P and determine a rate of change of f in P in…

A:

Q: ii) Find the dot product of the vector a in part (i) with the displacement vector AB such that…

A: Given that  Following vectors  To find the dot product

Q: The acceleration of an object after t seconds is given by the vector-valued function a(t) . | If…

A: to find the velocity equation, take integration  .............(1)

Q: Determine the flow of the vector field (image 1), through the surface S, outwards, with S being the…

A:

Q: Find the unit vector in the direction in which f (x,y) =x+ sin(x + 2 ·y) increases most rapidly at…

A: Given: The given function is fx,y=x+sin(x+2y) at P(0,0).

Q: 61-66 Find a unit vector in the direction in which f decreases most rapidly at P, and find the rate…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: a) An object is moving in space with an acceleration a(t) = -t i+3 j+ (t – 3) k. TM UTM UTM Find the…

A:

Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

A:

Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

A:

Q: 61-66 Find a unit vector in the direction in which f decreases most rapidly at P, and find the rate…

A:

Q: 18 as a linear combination of a and y Express the vector v y.

A:

Q: The path of a roller coaster is given by the vector function 7(t) = (x(t), y(t), z(t)). Which of the…

A: As we know that,  Whenever a body is in curvilinear motion with constant angular velocity, at any…

Q: Find the tangential and normal components of the acceleration vector  #39

A: Obtain v(t).

Q: Determine whether or not the vector functions are linearly dependent. 3-1 t+3 u- 1 -3+t -3 3 3 a) O…

A: The given vector functions are                               u=3-tt-3, v=t-13, w=t+3-3+t3 Then we…

Q: The position vector of a moving particle in space at time t is given by the vector function r (t) =…

A: position vector of particle in space r→(t)=12(5-t)2i→+(2t-1)j→+43(5-t)32k→

Q: Find the domain of the vector function r(t)= <e-t , (t-5)1/2 , (7-t)1/2.

A:

Q: ILS] Demonstrate how any vector x ER can be expressed as a linear combination of the following…

A: Please find the answer of the first question in next step

Q: (a) find the directional derivative of f at P in the direction from P to Q; (b) find a unit vector…

A: a) To find the direction vector PQ. PQ=0,-1,2-3,1,-4=-3,-2,6 That is the vector is -3i-2j+6k. The…

Q: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

Q: Vector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v =…

A: Initial point is P1=x1, y1 and terminal point is P2=x2, y2.

Q: (p957, #33) Suppose that over a certain region of space the electrical potential V is given by: V(x,…

A: Given electric potential is Vx,y,z=5x2-3xy+xyz. Therefore gradient of electric potential is…

Q: Vector Calculus For scalar functions u and v, show that B = (Vu) × (Vv) is solenoidal and that A = -…

A:

Q: In Exercises 15-18, find a unit vector in the direction in which f increases most rapidly at P, and…

A: Given function is  f(x,y,z)=x3z2+y3z+z-1point P(1,1,-1)

Q: Use the model for projectile motion, assuming there is no air resistance. Find the vector-valued…

A:

Q: Convert the given IVP to a first order IVP with a vector-valued dependent variable. B. Solve the IVP…

A:

Q: Find the domain of the vector function r(t) = (sqrt(25-t^2),e^(-2t),ln(t+3)

A: Given:        r(t)=⟨25−t2,e−2t,ln(t+3)⟩

Q: A. Find the vector equation of a line tangent to r(t) = (t², t², t³) at t = 1. B. Determine whether…

A: A parametrization of the line through a point a and parallel to the vector v is l(t)=a+tv. Setting…

Q: Which of the following vectors are linearly independent? (2) (0) 21

A:

Q: The acceleration of a moving particle in space is given by the vector function a (t) = 3t2 i + 4t +…

A:

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: In Exercise (a) find the directional derivative of f at P in the direction from P to Q; (b) find a…

A: Given:  f(x,  y) = sin(2x-y); P(-π/3, π/6), Q(0, 0)

Q: The xyz-coordinates of Methanol are given in the table below: Tag Symbol X Y 1 0.136 -0.458 0.000…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The vector-function gives a particle velocity as function of time: T(t) =, and the particle position…

A:

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of a P = b 1- b

A: The vector of stable probabilities, also known as steady-state probabilities, is a vector that when…

Q: 2 If a and b are vector functions and T a second-order tensor function of position, show the…

A:

Q: (c) Suppose the position vector of a moving particle at time t is given by 7(t) = (tv2) î + (e*) j+…

A:

Q: perpendicalar 1) A vector to both ij+3k and 21 +j + K is

A: Vector obtained by cross product of two vector is perpendicular to both of them

Q: a) A three dimensional motion of an object is given by the vector function UTM r(t) = 4 cos t i+…

A:

Q: Suppose that in a certain region of space the electric potential V is given by V (x, y, z) = 8x ^…

A:

Q: If two objects travel through space along two different curves, it's often important to know whether…

A: To solve this we must figure out at what t's positions are equal for each vector component. so, set…

Q: Find a non-zero vector u perpendicular to the vector u =

A: If  A non zero vector is perpendicular to anather vector then their dot product is equal to zero.

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

A:

Q: Match the vector fields: ? curl(F)=0 ? curl(F)=2 ? curl(F)=0 1. div(F)=4, 2. div(F)=0, 3. div(F)=-1,…

A: Note: As company policy, we solve first sub-parts only. Please re-submit those parts which you'd…

Q: Find the tangential and normal components of the acceleration vector at the given point.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…