Evaluate dwat the given value of t: W=X+ÿ x-Cost + Sint y=cost-Sint

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: This is a problem of Differential Geometry.

Q: cot z 183. y = 1+cot r

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Q: Ca) Supposed that w= xy – x2 with x = e¯"s²t and y = r²s sin t. Find the value of when r = 0, s =…

A: Given:  w=x3y-x2     , x=e-rs2t      and y=r2s sintsubstituting x=e-rs2t      and y=r2s sint in…

Q: is poured into the tank a te of 2 liters/min. Let y(t ial model for (t) and gol

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Q: Find the denivatine.cf.tha follow.ing.vecter. Fumctanss. -j.t.In(l+3t)...k. a. e.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: a) Find the average velocity for the time peric when t = 2 and lasting (i) 0.5 seconds (ii) 0.1…

A: Since you have asked multiple part question, we will solve the first3 part of the question for you…

Q: Find T(t) and N(t) at the given point. X = = et cost, y = et sint, z=et; t = 0 T(0) = N(0) || =

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Q: Differentiate the following function. y= e x6 to d y' = %3D dx Teto %3D

A: Given : y = ex6

Q: Find the displacement of an object on the interval 1 ≤ t ≤ 6 if its velocity is shown. 8.5 O 10.5…

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Q: The temperature at a point on a. metal plate is given by Tlx,y)= x²+y? 2 a.) Find the directien ot…

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Q: Find x() given r(t) =(d'.d sint,e cost)

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Q: Use Euler's method to approximate the indicated function value to 3 decimal places, using h = 0.1.…

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Q: Find the value of dw/dt if w = x2+y2, x = 26 cost and y = 26 sint

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Q: Q5. A particle moves alonga straight line with displacement s(t), velocity v(t), and acceleration dv…

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Q: Q4) find at t= from the following functions, x= cost . y= 1+sint

A: Given that  x=cost  y=1+sint  To find the d^2y/dx^2 at t=π/2

Q: A pole of length L is carried horizontally around a corner where a 3-ft-wide hallway meets a…

A: Given: Pole of length (L): (x+(L-x))

Q: A particle's velocity is given in ft/sec by the equation v(t) = 6r² – 6t – 12 , find: a) the…

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Q: The r.m.s. value of f(t) = t² across [1,4] is %3D

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Q: sint Given that f(t) = Cost Express f(t) in terms of a

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Q: A car starts from rest at time t = 0 and accelerates at – 0.61 + 4 meters/sec? for 0 <t< 12. How…

A: Given: a = -0.6t+4 and velocity at t= 0 is 0 Since, dvdt=a, here v is the velocity and a is the…

Q: Låt f(r, y) = 1+ y? Given the absolute errors Ex in x and Ey in y, derive a formula for the absolute…

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Q: Convert the equation f(t) = 355(1.16) to the form f(t) = ae %3D a = k = Give values accurate to…

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Q: dz Given the function z = xy + y ln|xy|, find ду

A: In this question we have to find differentiation of the given function with respect to y. Formula…

Q: Assume that the average molecular velocity v of a gas in a particular container is given by v(T) =…

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Q: f'(rr), where f(t) = sint cost

A: Given function is ft=sint cost To find: f'π Solution: Product rule of differentiation is:…

Q: To calculate the surface area of a sphere of radius R we can use the formula b. S= 27 f(x)\/1+…

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Q: The velocity v (in m/s) of a rocket measured at half second intervals is shown in the image below.…

A: Introduction: Suppose, n+1 data points x0,y0,x1,y1,...,xn,yn are given. Then, we can approximate the…

Q: Use Figure to estimate dT /dh at h = 30 and 70, where Tis atmospheric temperature (in degrees…

A: Function is a unique mapping between two variables, where each value in independent variable set has…

Q: find the specific function values.ƒ(x, y) = sin (xy) a. ƒ(2, pai/6)  b. ƒ(pai, 1/ 4 )

A: a) Plug x=2 and y=pi/6 and then simplify

Q: Use the linear approximation of the following. (Answers are to be expressed in 4 decimal places, no…

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Q: r(t) = ti – 4i j+ t² k.Ca unit ator

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) 3t 8…

A: Given:

Q: Q#1 dA-(t) sint). cost dA(t) and dt for A(t) : dt Find -sint cost.

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Q: Find the radius of the osculating circle for 7(t) = (cost+t sin t)i +(sint – t cost)j +3k when t=1.

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Q: a. If Kimberly's velocity in miles per hour during the race is v(t) = 2.3' sin(;), calculate her…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Recall that the volume V of a circular cylinder with a base of radius r and height h can be…

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Q: The velocity of an object in meters per second is given by v(t) 25-, 0sts5. Find: %3D a) The…

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Q: Q4) find at t= from the following functions, x= cost. y= 1+sint

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Q: Speedometer readings for a vehicle (in motion) at 4-second intervals are given in the table. t (sec)…

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Q: The function g(t) = (8t)t – cosh? t + sinh? t satisfies gʻ(c) = 0 for which value of c?

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Q: 20. For the function z = f(x,y) = x? – y + 2, write a formula to calculate approximately the change…

A: Given z=f(x,y)=x^2 -y+2 We have to find a formula which gives the approximate change in z ,…

Q: Jse the information to find and compare Ay and dy. y = x4 + 2 x = -1 Ax = dx = 0.01

A: Here we have,

Q: Determine the rate of chenge in the ar direction of the scaler function U- sin e and calealate it at…

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Q: r(t) = m(-cost + 3)i – m(sint + 3)j+ 3mtk, 0 st <TV10.

A: Given :

Q: . The velocity, v, of an object in a medium at -80 dv time t seconds is given by: t = 20 v(2v – 1) -…

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Q: Use the linear approximation of the following. (Answers are to be expressed in 4 decimal places, no…

A: Given, f(x)=1+x at a=0 to estimate 0.95

Q: The velocity (in ft/s) of an object moving along a straight line is given by v(t) = –28t + 90 Find…

A: Displacement is the speed of the object over in a straight line between two points. Let s(t) be the…

Q: Find for the following function x = a(cost +t sin t),y= a dy dx (sint – t cost)

A: Given problem is  :

Q: (3) ds V3s2 + 1 (4) / sec?(3/t) dt VE

A: Note: As per companys guidelines we are supposed to solve only 1 question ∫s33s2+1dsSubstitute…

Q: 5/155) e'sint, e*cost

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.