A raindrop falls with acceleration 9.8 m/sec² , where "v" is its velocity. What is the raindrop's velocity?

Q: For the next six questions, consider the differential equation: y/" + 4y = g(x), g(x) # 0

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Q: S(x+ )´ dx 2 1 X X.

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Q: Find the greatest volume that a right circular cylinder can have if it is inscribed in a sphere of r...

A: Here we have to find the greatest volume that a right circular cylinder can have if it is inscribed ...

Q: Find a number a so that the tangent lines to y= x° + 11x +x + 13 at x = a and at x = a+ 1 are parall...

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -6 and x = -2 x-intercept...

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Q: Given the function: f(x, y) = 3x°y² – 72²y+ 5x – 4y Find the folowing: show complete solution fzy(x,...

A: Given:      fx,y=3x3y2-7x2y+5x-4y   a) fxyx,y:     fxyx,y=∂2∂y∂x=∂∂y∂∂x      fxx,y=∂∂x3x3y2-7x2y+5x-...

Q: Describe the surface of 4z2 – 4x² – y = 4 - |

A: The general equation of a  hyperboloid on two sheets is given by x2a2-y2b2-z2c2=1 notice that there ...

Q: Find the​ curve's unit tangent vector.​ Also, find the length of the indicated portion of the curve.

A: Given that      r(t) = 6t3i + 2t3j + 3t3k  , 1<=t<=2 

Q: -5x + cos (9x) – 1 Evaluate lim 2x Submit an exact answer.

A: To Evaluatelimx→0-5x+cos(9x)-12x  

Q: 3 -dx 4 - x

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Q: Find the points at which the following function is discontinuous. (2r2 + 4 ifx 4 Select the correct...

A: The given function is f(x)=2x2+4if x<-56x2+2if -5≤x<42x+90if x≥4 Since polynomial functions ar...

Q: 2xyy'=1+y^2 solve using separation of variable (diff eq) when y=3 and x=2

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Q: (y)² = 1-y? 1-x? 2

A: First we take variable separable then integrate it.  Then using given conditions y(1) =1/2 Then we g...

Q: Evaluate the following: 1. S(6x² – 4x + 1) dx

A: As we know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫c·fx...

Q: Question 1 Consider the function (x²y² – y³ x2 + y2 if (x, y) # (0,0) f(x, y) = %3D 0, if (x, y) = (...

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Q: Let sk En(0.1)" n=1 Find s9.

A: Given that sk=∑ n=1k n (0.1)n -(i) Our Aim is to find s9=?

Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly i...

Q: x2+1 2²+1 dx = 0 xe"dy +

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Q: Solve the exact differential equation. If the given is not exact, determine the integrating factor t...

A: We have to find complete solution of differenrial equation

Q: Vr csc Vx ,2

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Q: Find 7(t)dt if 7(t) = (2 cos t, sin t, 2t). A. (2-1.) B. (2.0,) c. (2.1) D. (2.2. ) 2, –1, 2,0, E. n...

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Q: For the next four questions, consider the differential equation y" – y = x²e* +5

A: Let's find. 

Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the...

A: A detailed solution is given below.

Q: Find the equations of all tangent lines to the graph of y=x -7 x+ 49 that pass through the origin (0...

A: Equation does not passing through origin.  Hence there are no tangent line whose passing through ori...

Q: Instruction: Solve the following indefinite integrals. Show complete solutions.

A: Question no. 11,Given,            ∫xsec1+x2dx

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral wi...

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Q: +2 7. (i) Show that A(c) !! (-2)* (ii) Given the previous part, find a closed form for >

A: Find your answer below 

Q: Solve the following problem related to function. (Show your solution) 4. What is the equation of the...

A: Given, fx=x+1 We have to write the equation of the graph of a function when fx=x+1 Vertically stret...

Q: (MULTIPLE CHOICE) Which of the following is(are) differential equation (s) with homogeneous coeffici...

A: To determine which of the following is(are) differential equation(s) with homogeneous coefficients.A...

Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t. Dete...

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Q: Problem 1. Draw a direction field for the given differential equation. By hand, sketch an approxi- m...

A: Solutionn is here

Q: PART - B IA. Solve (4xy + 3y? - x)dx + x(x +2y)dy = 0 with y(2)=2. IB. Solve (x²D2 + xD - 1)y =ri

A: Since, you have posted multiple questions. As per guidelines we will solve only first question. If w...

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: Given the: 7(t) = (cos (3t), 4t, sin (3t)) Find the folowing: show complete solution a. unit tangent...

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Q: Find the slope, TL and NL of the function y= 2x2 +2x at the point x=1/2. Graph the function, TL, and...

A: We have to find equation of tangent line and normal line

Q: х — 3 (x+ 2) (x – 1)²

A: The given integral is; (x-3)/[(x+2)(x-1)2].

Q: For the next five questions, consider the following differential equation: ( + ry")dr + (5y - ry+ y'...

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Q: Eliminate c, x'y =1+ cx (2+x3y)dx + xdy = 0 B (1+x?y)dx + x³dy = 0 © (1+x?y)dx + x²dy = 0 D (1+x3y)d...

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Q: 3. Express the quadratic function g(x)=-4x² +4x+5 in the form a(x-h)' +k by completing the square, a...

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Q: In the decomposition a = aTT + aNN, what do aT and aN represent?

A: Solution: Given data, a = aTT + aNN

Q: 1 dx x+/x

A: Given: ∫1x+xdx

Q: Use the given graph of the function to find the z-values for which f is not differentiable. 1.A Answ...

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Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth Taylo...

A: Given :   f(x)=ex x0=6

Q: S (x +) dx 2 X.

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Q: - 1. der the equation In ay Ehow that (r, y) = (1,1) is a solution to this equation. dy Find dz (my)...

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Q: 2- 1- -4 -3 -21 0 2 3 Graph of f The function fis continuous for -4 <x <4. The graph of f shown abov...

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Q: Answer 2 only

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

Q: • f(x) = -1 when r 2 • f(0) = 1. 1 2 ) Define the function f on the interval [-2,2] such that f is ...

A: (i) We can take fx=x+1-2≤x≤0-12x+10≤x≤2. Note it is obtained by connecting the known points via line...

Q: 2 S (x+) dx C cor?(?r)dr

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Evaluate f tan²xsec*xdx using trigonometric integrals

A: Our Aim is to evaluate the integral given below:-∫tan2 (x) sec4 (x) dx -(i)