A pendulum consists of a 3.5 kg stone swinging on a 4.1 m string of negligible mass. The stone has a speed of 8.0 m/s when it passes its lowest point. (a) What is the speed when the string is at 60° to the vertical? (b) What is the greatest angle with the vertical that the string will reach during the stone's motion? (c) If the potential energy of the pendulum-Earth system is taken to be zero at the stone's lowest point, what is the total mechanical energy of the system? (a) Number i Unit (b) Number i Unit (c) Number i Unit

Q: Which of the following is an improper integral?

A:

Q: Evaluate * cos (e + a?) dx 24 +1

A: To find: The integral ∫44cose3x+x2x4+1dx Concept used: ∫aaf(x)dx=0

Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

A:

Q: 10. Two numbers sum to 100. How small can the sum of one number and the other number be? square of t...

A:

Q: Evaluate P(n, k – 1)P(n – 1,n – k). - k=1

A: We have to evaluate ∑k=1nPn,k-1Pn-1,n-k

Q: Differentiate y = 4sin (x) + 11x and evaluate y (0). Enter the value y (0) in the box and upload you...

A: topic - derivative of a function

Q: 5. y = xArctanx - In VI+x

A:

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

A: Given problem:- Show that the vector field A = (3x²z+ y²)ax + 2xyay + x³az is conservative. =

Q: What is the integrable form of sin-cos-sin0 do? 2 2 (A) 1- u² du B - 2 sinu du u² – 1 du 2 cosu du

A:

Q: dx For -= In(F (x))+C. What is F (/3) if C=0? (x+x³) (xtan-1(x) + 1)

A: Let's find. 

Q: 1. y= x - x'cosx + 2xsinx + 2cosx

A: solution:-(1)y=x3-x2cosx+2xsinx+2cosxy'=ddxx3-x2ddxcosx+cosxddxx2+2xddxsinx+sinxddxx+2ddxcosx=3x2-x2...

Q: Given revenue and cost functions R(q)=80q−0.3q2 and C(q)=14q+550​, find the quantity when profit is ...

A:

Q: cos2x - sin2x cos2x -dx =-F(x)+C• For What is F(x)? cosx – sinx 2 sinx + -cosx+ cosx + -sinx 3 3 2 s...

A: Using cos(2x) =cos2 (x) - sin2 (x) 

Q: 8. W ( 10л 3 9. W W (–317) 22л 10. W 3

A: Since there are multiple questions the first question is answered as per our guidelines. kindly repo...

Q: Estimating an Angle In Exercises 7-10, estimate the angle to the nearest one-half radian. 7. 8. 9. 1...

A: Find your answer below 

Q: Find the center of the circle 4x? + 4y?+ 24y – 4x – 35 = 0. O (3, 1/2.) O (3/2, -3) NONE OF THESE O ...

A: Given the equation of circle  4x2 + 4y2 + 24y + 4x - 35 = 0 We need to find centre of circle. As we ...

Q: 10* -dx may be written as Aln secB*+ tanB*| +C. where A, B, and C are constants not equal to zero. E...

A: ∫10xcos 10xdx Substitute 10x=u⇒10xln 10 dx=du⇒10xdx=1ln 10du =∫1ln 10ducos u=1ln 10∫sec u du=1ln 10l...

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the direc...

A:

Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

A:

Q: sinx sinx +x cosx - e +e The integral / dx may be written as me"sinx + px + qe* + C. where m, n, p, ...

A:

Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x) ...

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per B...

Q: A particle moves in a straight line according to a law of motion s = f (t), t>0, v %3D in seconds an...

A:

Q: 2xyy'=1+y; whent = 2, y = 3 Ans. y = 5x-1

A:

Q: Find the area of the triangle with vertices P(1, 4, –3), Q(0,0,0) and R(3, 5, 1). NOTE: Enter the ex...

A:

Q: dy (16) 2xy = x² + 2y² dx

A:

Q: Use the First Derivative Test to find relative (local) maxi points, if any, of the given functions. ...

A:

Q: 4. Determine where V(z) = z*(2z – 8)³ is increasing and decreasing.

A:

Q: 1. Consider the curve of the function f (x) = 2x² a. Find an expression for the slope of the curve a...

A:

Q: What are the radius and center of the circle that passes through the points (2,0), (18,0), and is ta...

A: From the equation of the tangent line we can deduce that the slope of the radical line would be -1/4

Q: Show that the equation x – 18x + c = 0 has at most one root in the interval [-2, 2].

A:

Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 713 f(2) dz 7/3 f(2) dz -2...

A:

Q: 3. The diagram shows a cuboid that is formed by bending a long wire of length 336 cm?. 3x (c) Find t...

A:

Q: dx - = In[F(x)]+C•What is F(/3) if C = 0? For (x+x³) (x Tan-lx+1) -1 + - -1

A: Solved below

Q: What is partial fraction decomposition

A:

Q: 3. Solve for x: (3)*+1 = V3

A:

Q: 2+ x², ={ 1 2* +2, 4 -2 <x<0 f(x)dx; f(x) 0<x<4

A:

Q: I Find the second derivatively") of the following functions and simplity the final results. 1. y=x-x...

A:

Q: The slope of the tangent line at any point (x, y) on a curve is 2vx. If the point (9, 3) is on the c...

A:

Q: Find the indefinite integrals: 15/2 + 4x + 1 a) rp- b) 6t" + + xe' ) dt

A:

Q: sinx dx cos³x (1 – sec*x)3 A)를 (1-sectx)-4 +C B)를 In(1 sec*x)3 + C c)금 (1-sec+x)-2 + C D)름 (1-sec*x)...

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: xtra questions: Find the Derivative of 8 1. y = 10 vx ++ x2 2. y = ta n(si n x) 3. у %3D cot?3x

A:

Q: Find d of the function given implicitly and evaluate the derivative at the given point. y = sin ( 6x...

A:

Q: 53х dx (53x + 1)2 A) 3 V5x + 1 + C B) – 3 V5x + 1 + C In5 3 C) 3ln5 (V5x + 1) + C D) V5x + 1 + C 3 E...

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve...

Q: I Find the second derivative (y") of the following functions and simplify the final results. 2sin x-...

A: topic - double derivative of a function

Q: +00 e-*dx

A: Topic = Integration

Q: dx For - = In[F(x)]+C•What is F(/3) if C = 0? (1+x;_u®_L x)(;x+x) 6. + + -15

A:

Q: 3 8. f (t) = (10t)z %3D 9. f(t) = tg'(t)

A: Given  f(t)=10t32 To find Laplace transform: 

Q: Let f(x)=4x^2lnx f'(e^3)=

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: Here we have to find the unit vectors.