7. A spring is stretched 200 mm by a 15-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 0.75 m/s, determine the equation which describes the motion, Assume that positive displacement is downward. O y = 0.107 sin (7.00t) + 0.100 cos(7.00t) y = 0.100 sin(7.00t) + 0.107 cos(7.00t)

Q: = X ¹0 = 1 8 = = 0 ay!!

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Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: The objective of the question is determine the area bounded by the given curves.

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A: Given: 6x186=0

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

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A: Topic = Geometry As per guidelines , At a time only one question can be answered. please repost for…

Q: Find dz/dt where z = 2xy - x² y² and x = 2t, y = t².

A: Given: Now,        z=2xy-x2y2  =22tt2-2t2t22  =4t3-4t6

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A: We will solve the given question using simple Integration rules.

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Q: 34five X 2five

A: Follow the procedure given below.

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Q: 33. " +9y sin 2x; y(0) = 1, y' (0) = 0 34. y" + y = cos x; y (0) = 1, y'(0) = -1 35. y" - 2y + 2y =…

A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

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A: To find out the domain of the functions.

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Q: Q2: Fill the blank: 1) lim (1+)52 x48 4x 2) lim x.e-3x = X-80 3) (csch¯¹x³) = . dx 5x =...

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Q: 4. If x - 2y = -1 and x + 2y = 3, then a +y is equal to O 1 O ♡

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A: 1 f(x) = -4x df(x)/dx = -4  answer C is right    2 cos(x) dcosx/dx = -sinx  answer B is right

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A: To find out the relative growth rate.

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Q: Determine whether each equation is true or false. 1. f sin x dx = cos x + C 2. fcos x dx = sin x + C…

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A: Given problem:- Evaluate the integral ∫√(x2+6x) dx

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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A: Solution

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A: For a function of form w=f(z)=u+iv is said to satisfy Cauchy-Riemann Equation if ux=vy  and uy=-vx…

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A: This question is indeterminate form of 1infinity and solved using L Hospital rule.

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A: Follow the procedure given below.

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Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: Find dy /dx for the following functions: -) y².cotx= [sin(x. y)]-¹ b) y = (lnx+x) tan x

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