The distance s between the planes is given by the formula, s = Vx2 + v². Thus, s? = x² + y?. One plane is 90 miles away and moving towards the point of convergence at 450 miles per hour so x = 90 dx and dt The other plane is 120 miles away and moving towards the point of convergence at 600 miles per hour, so y = dy 120 and dt

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

A:

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 9t3 – 48t, then the…

A:

Q: Suppose that a particle moves along a straight line with a velocity v(t) = 4– 2t, where t is in the…

A:

Q: The position of a moving particle is given by s(t) = t2 – 7t + 4 on the interval 0 <t< 4, where 's'…

A:

Q: Given y = s, s = 20 – v? and v = -2t, dy determine at t = 1 dt A V3 в 2 с 1 D-1

A:

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

A:

Q: he position of a moving particle is given by s(t) = 3t2 – 18t on 3 <t< 6 here 's' is in meters and…

A: Instantaneous velocity = ds/dt

Q: The time of oscillation, 1, of a pen- dulum is given by t 27 1. wherel is the length %3D of the…

A: Write this equation in standard form then diffrenciate.

Q: The acceleration of a particle at time t is given by a(t) = 4e2t¸ If the initial velocity was 5, and…

A: We will use integration to first find the velocity and then integrate velocity function to find…

Q: Two particles have positions at a time t given by the equations x1=t3-t and x2=6t2-t3 find the…

A: If x(t) represents position at time t then velocity = v(t) = dx/dt and acceleration = a(t) = dv/dt =…

Q: Find dt(t=1.s=0) dz when z 2x3 + 15y, where x t? -s and y =t+ 2s? %3D Enter the answer in the space…

A:

Q: b) Use the velocity function v(t) = 2e" to compute the distance traveled by an object over the time…

A: The detailed solution is given below  Thank you

Q: Show that the displacement after time t for motion in a straight line with constant acceleration a,…

A: Given Data: The constant acceleration is: a The initial velocity is: v0 The initial displacement is:…

Q: Suppose the length of rod, L = 50 cm is immersed in steam until its temperature is throughout u, =…

A:

Q: The work done W,to stretch a spring from its natural length to an extension of b meters Is 6. given…

A:

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

A:

Q: The maximum acceleration attained on the interval 0 <t < 3 by the particle whose velocity is v(t) =…

A: Given Data: Interval: 0≤t≤3 Velocity: v(t)=t3-3t2+12t+4 The acceleration can be obtained by…

Q: The position of a moving particle is given by s(t) = t2 – 7t + 5 on the interval 0 <t< 5, %3D -…

A: First I have find the Instantaneous velocity and then Average velocity then making them equal and…

Q: A) The position of a particle P(x, y) at time t is given by: (2t + 3)7 y +t . Find the distance it…

A:

Q: The position of a moving particle is given by s = 3t3 + 9, then its acceleration at t = 7 is O 27 O…

A: We will solve the following using derivative.

Q: 10. The sides of the rectangle at right increase in such a way that the instant when x = 4 and y =…

A: We need to find the value of dxdt, given that dzdt=1,dxdt=3dydt,x=4,y=3

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: Using a suitable substitution, the integral T/4 9 (13+tan t)8 sec? t dt of

A: Given,          ∫0π4913+tant8sec2tdt

Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10…

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the…

Q: 2. A plane travels 560 km from Los Angeles to San Francisco in 1 hour (h). If the plane's velocity…

A:

Q: Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. y' =…

A: We have first order differential equation and to slove this use Runge kutta 4 order method. Given…

Q: A sailboat is running along a straight course with thewind providing a constant forward force of 50…

A: Given: A sailboat is running along a straight course with thewind providing a constant forward force…

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

A:

Q: The position of a moving particle is given by s(t) = t2 – 2t + 6 on the interval 0 <t < 6, - where…

A: We will solve the following.

Q: An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 + 0.25x²…

A:

Q: A particle is moving along a straight line so that v ft/sec is the velocity of the particle at t…

A: Given v=t+3t2+3t+2. The objective is to find the distance traveled by the particle from the time…

Q: Given a particle is moving in a curve r(t) = cos 7t i + sin 7t j + 6t k. Find the tangential…

A: Given a particle is moving in a curve rt=cos 7t i^+sin 7t j^+6t k^to find the tangential and normal…

Q: The position of a moving particle is given by s 3t +9, then its acceleration at t = 7 is %3D 27 63…

A:

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 16t3 – 12t, - then the…

A: We will find out the required value.

Q: Use the Linear Approximation off (x, y) = ex2+Y at (0, 0) to estimate f (0.01, -0.02). Compare with…

A: By the method of linear approximation, if we are given a differentiable function f in two variables,…

Q: An element is moving along a straight line so that v ft/sec is the velocity of the particle at t…

A:

Q: Given a particle is moving in a curve r(t) = cos  7t i + sin 7t j +  8t k. Find the tangential…

A: Given a particle is moving in a curve, r(t) = cos  7t i + sin 7t j +  8t k. To Find the tangential…

Q: given the differeutial equation dy=0 t. 2 ) Show that the difterentiul equetium is exact

A: Exact Differential Equation: Consider first-order ordinary differential equations written in…

Q: The volume of a right circular cone of radius a and height y is given by V = dy volume of the cone…

A: Explained below

Q: How to solve the ordinary differential equation using separation of variables?

A:

Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

Q: An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 +0.25x² where…

A: Note:- As per our guidelines, we can answer the first of this problem as all the methods are…

Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

A:

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 16t - 12t, then the…

A: The position of a body s(t)=16t3-12t

Q: The radius r and height h of a right circular cone are related to the cone’s volume V by the…

A: If r is the radius and h is the height of right circular cone, then find the following parts.a).…