Let 7 (t) = < Vt* + 2, cos (t'), te¯+ > Find 7'(t) F'(t) -

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Q: Find the general solution 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D2 – 5D) + 4y = 0 4. (D² – 9)y…

A: 1. D2-D-2y=02. D2+3Dy=03. D2-5D+4y=0 Note:    Multiple sub parts are given, we are answer only three…

Q: its magnitude and direction angle. 14. ļu| = 8, 0 = 225°

A: Topic:- vector algebra

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A: On solving this we will get

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Q: x+dx 1.

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t= 3 T() N(G) .3

A: To find the vectors T(t) and N(t)  for the given r(t) at point t=pi/3.

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Q: How many arbitrary constants will be there n the general solution of a second order differential…

A: The number of arbitrary constants in the general solution of a differential equation is equal to the…

Q: 1- x, x 2 - Which of the following is TRUE? O The function is continuous everywhere. O The function…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

A: Because the parabola is symmetric to the y-axis, the rectangle must also be symmetric to the…

Q: n2 1. Determine whether the series En=1 is convergent and explain why 2n++1 (In n)

A: We will use Ratio-Test to determine converge.

Q: Find curl (8z i + 9x j+ 6y k). curl (8z i+ 9x j+ 6y k) = ( )i + ( i j + ( i )k

A: Find curl

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: The given curves area; y=x3, x=0, y=27   So, the bounded region is as shown below. Apply the…

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Q: dy Find for dx 3) y = In(vx2 + 1+x) sin¯1x X.

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Q: A population of 200 kangaroo is released into the forest. During the first three years, the…

A: Given,initial kangaroo number, n(0) = 200number of kangaroo after 3 years, n(3) =500carrying…

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Q: So 32 (z + 4)° da = 5120 %3D Select one: O True O False S sin4a da = 4 7/3 7/12 %3D Select one: O…

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Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c)…

A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

Q: y" + 9y = 9 sec² 3t, 0<t < T/6

A: To solve the following differential equation

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Q: Evaluate the line integral -ydx + xdy along the curve C: y? = Зх from (3,3) to (0,0). NOTE: Enter…

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Q: Ty csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соfу+ coty dy D) None E у…

A: Integrate by parts.

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Q: Find the partial derivative. z = (x2 + 4x – 2y)° -

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Q: x = -3x1 – 2x2 x2 = 9x1 + 3x2 %3D

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

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Q: A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long…

A: see below the answer and explanation

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Q: dt, if we let V Vt+1-2, then dt is equal to A (4x³+2)dx B None © 2(x²+2)dx D 4x³dx E 4x(x²+2)dx

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A: we have the parallel line equation y=-5x+4 comparing with y=mx+c m=-5 is the slope point slope form…

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: Need

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Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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Q: 3.5n 7n+1 n=1

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Q: 1. Find the equation of the normal line at a given point. y = - @ (5,1)

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Q: if a 2. Then, lim f(x) =

A: To find, limx→2-f(x)

Q: In 2. Determine whether the series E=1 is convergent explain why. 100

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A: To find the area of the shaded region.

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A: topic - application of derivatives

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Q: 2. Use the definition of integral to evaluate the integral (x³ + 1)dx. (hint: [ S(x)dx = lim Ës(x,…

A: A detailed solution is given below

Q: -32 ft/sec?. Assume that the in n object's downward acceleration is given by y"(t) = elocity is y'…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…