|21. If a ball is projected upward from the ground with initial velocity vo and resistance proportional to v2, deduce from Eq. (14) that the maximum height it attains is Утах — In (1+ 2p

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Q: Supose z is implicitly dofimed by the equation qy+ 3x + XyZ + 32=9 in an onvanment of the point…

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

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: The altitude of a helicopter at three different instants is listed as below: 1, sec | 0.2 h, m |…

A: Given the altitude of a helicopter at three different times  t,sec0.20.30.45h,m445.98471.85503.46 we…

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Q: What value of a makes ƒ(x) = x2 + (a/x) have a. a local minimum at x = 2? b. a point of inflection…

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A: The function is Qx, y=6x2+3ex36y+3y2. The marginal rate of substitution is given by dydx=-QxQy…

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A: For a function fx,y to have minimum value at a,b, which of the given condition is true? 1)…

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A: Given that: displacement, s(t)=2t3-12t2+16t+2

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A: To find the time at which the speed of the partial is minimum. Note that, the velocity is the time…

Q: Find the absolute maximum and minimum of f(x, y) = 3z +y within the domain z² +y? < 4.

A: Use lagrange multiplier.

Q: 1.20 * Prove that the flight-path angle is equal to 45° when v = 90° on all parabolic trajectories.

A: Solution

Q: s(t)%3D512 +t3 :-

A: Given information: st=5t2+t3 Find the velocity at -2.

Q: Findthe absolute minimum on ico, ae) fon f (x) =x+l6,

A: Critical points of the given function can be found if dfdx=0 fx=x+16x Differentiating the function…

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Let f(x) = S* A et dt. At what value of x, f(x) has a minimum? Select one: 4 -2 no value of x

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Q: Find the set on which the curve 8 dt t2 + 8t + 22 y = e downward. n interval notation):

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Q: 2. A rock thrown upward has a height given by s(1) = 49t-9.81 where s is in meters and / is in…

A: Use derivative to solve

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured…

A: c Volume of cube =8m×1.5m×3m=36m3 volume of water =12×3×3×8=36m3 Volume of water is equal to volume…

Q: For function f(x,y) to have maximum value at (a,B) IS 1) rt – s>0 and r0 and r>0 3) rt – s?0 and r>0

A: for function f(x,y) to have maximum value at (a,b) is rt-s2&gt;0,r&lt;0

Q: 2. The altitude of a helicopter at three different instants is listed as below: 0.3 1, sec 0.2 h, m…

A: We will solve this using 2 point forward and 2 point backward difference formula

Q: 4. Find the orthogonal trajectories of the family of curves y=Ce*™ +10

A: We have to find the orthogonal trajectories of the family of curves

Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

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Q: Find A and B so that f(x, y) = x2 + Ax + y² + B has a local minimum at the point (4, 0), with…

A: Given function of two variables is f(x,y)=x2+Ax+y2+B it has local minimum point at (4,0) and minima…

Q: Q1: Use ewton- Raphson method to estimate the Yoot of fcx) = x -x -1 , emp loying an initial %3D…

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Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: s of 0 would be a minimum value on the graph of y = sin 0 over the interval [-27,0)?

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Q: Show that for motion in a straight line with constant acceleration a, initial velocity v0, and…

A: Let the acceleration a(t) = a, constant.Take integral on both sides to get velocity equation,

Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2  Circle x2 + y2 = 1   To find : Minimum values of the given…

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A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

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Q: 8. Suppose that a particle moves along a straight line with velocity defined by v(t) = t2+3t – 18,…

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Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

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Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: Suppose that f(x, y) = x² – ry + y² – 5x + 5y with x² + y? < 52. 1. Absolute minimum of f(x, y) is…

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Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

A: Maxima or minima: For any function f(x), 1) Evaluate f'(x)=0 for critical point. 2) Evaluate f''(x)…

Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Find the minimum and maximum values of y = V120 - V6 sec e on the interval [0, ] fmin fmax

A: Solve

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A: Given that f(x) = ax3 +bx2 + cx + d has a local maximum at the point (0,0) and a local minimum at…

Q: Q 10 Show that for motion in a straight line with constant acceleration a, initial velocity vo , and…

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Q: 1.) If the ball 1s Thrown vertically upward with a Veloorty of 15 m/s then ts heioht aifter t…

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Q: Q3- Choose the correct answer: 1-If velocity of a particle is given 4 points by v = 10 + 2t2 m/s,…

A: If velocity of a particle is given by v=10+2t^2 m/s. the average acceleration between 2 and 5s is…