For positive constants A and B, the force between two atoms in a molecule is given f(r) = 1 + 2/3, where r> 0 is the distance between the atoms. Note: A and B are upper case letters

Q: Obtain the general solution of the following differential equations 6. xdy - ydx - √√x² - y² dx = 0…

A:

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

A:

Q: Use Ay f'(x)Ax to find a decimal approximation of the radical expression. √84 What is the value…

A:

Q: Evaluate the iterated integral. 5 2x x-2 S S S dz dy dx -2 0 y

A:

Q: Let a = (5, 1, 0) and b = (2, – 4, − 1).

A:

Q: The graph of a twice-differentiable function is shown in Which one of the following sets of…

A: Please see the below picture for detailed solution.

Q: f(x) = 2x³ 3x² - 36x +14 use f'(x), find maximum point. - O (-2, 58) (3, -67) (0, 0) O none of the…

A: The given function is  f(x) = 2x3 - 3x2 - 36x + 14 To find minimum point

Q: Question 5. The rate of change in revenue from a recently-installed machine is 60,000t + 45,000…

A: The rate of change in revenue from a recently-installed machine is  60,000t+45,000 dollars per year…

Q: A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No…

A: Given that , Fencing cost = $14 per foot find the dimension for the plot that would enclose the most…

Q: Ĉ the given curve is rotated around the y-axis Find the area of the resulting surface y = I 9 2 "² I…

A: The given curve is:y=14x2-12ln x ;           4≤x≤5

Q: Use the washer method to determine the volume of the solid formed when the region bounded by y =…

A:

Q: metal Bar at a temperature of 120°F is placed in room temperature 10F, If after 20 mins, the…

A: Given: T1=temperature of the metal bar, 120°FT2=room temperature, 10°FT=temperature of the metal bar…

Q: To get the best view of the Statue of Liberty, you should be at the position where is a maximum.…

A:

Q: increasing two hours later? mi/h

A:

Q: 3. For f(x) = x³ - 5x² - 8x + 4,find the followings.

A:

Q: Find the volume of the solid generated by rotating about the x-axis the region bounded by y = 2.3*,…

A:

Q: Prove: There exist functions f, g, h in F such that g o f = h o f, but g is not equal to h.

A: The objective is to prove there exist functions f, g, h in F such that g o f = h o f, but g is not…

Q: h(x)=5.5x-3.42

A: We have given a polynomial  hx=5.5x-3.42 Leading term =5.5x

Q: In Exercises 29-34 use the ratio test to analyze whether the given series converges or diverges. If…

A:

Q: The gradient of f(x, y) = zy at (x, y) = (-1,1) is

A: The gradient of function f(x,y) is represented by ∇f(x,y) where:∇f(x,y)=∂f∂x,∂f∂y          Equation…

Q: Find the centroid (x, y) of the region bounded by: y = e³¹, y = 0, x = 0, and x = 2.

A:

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

A:

Q: Write an iterated integral for and x = 243 using a. vertical cross-sections, b. horizontal…

A:

Q: Suppose the number of phone subscribers between 1995 and 2006 can be modeled by S9x) = 18.33x +…

A: We need to find year when subscribers were 244,340,000.

Q: Learning Target INTI: I can correctly antidifferentiate basic functions and identify…

A: To find the general antiderivative of the given functions . The general antiderivative, also known…

Q: cos xdx sin³ 3 X S

A:

Q: K 400 (p+8)³ a) Find the equation for elasticity. E(p) = For the demand function q = D(p) = a) The…

A:

Q: Which of the following is the implicit solution to the initial value problem (e* sin y - 2y sin x −…

A:

Q: Solve the given differential equation. 5ydx-5xdy + xdx=9dx

A: 5ydx-5xdy+x7dx=9dxwe know  d(yx)=xdy-ydxx2∫xndx=xn+1n+1+c

Q: Obtain the general solution of the following differential equations 5. xydx - (x² + 3y²)dy = 0

A: Solution given below

Q: A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 90 ft high. a) How…

A:

Q: Form a partial differential equation by eliminating the arbitrary functions from the relation z =…

A:

Q: Let a = (4, -2, -1) and b = (2, -2, 5). Find the projection of b onto a. proja b =<

A:

Q: The safe load, Z, of a wooden beam supported at both ends varies jointly as the width, w, and the…

A: Terminology Load = L width = w length = l depth = d

Q: ver Find the slope of the tangent to the curve f(x) = X- - () at x = 0.

A:

Q: 19. What is the general-term equation, an, for the arithmetic sequence below and what is the 27th…

A:

Q: Show that the equationy/= -9y is satisfied for y = cos 30.

A: We are required to check that y=cos3θ satisfies the equation y''=-9y.

Q: [1-R] [CLO 12] What is the slope of the line f⊥, where f⊥ is a line perpendicular to the line f,…

A: The given line is: 4y-3x=5

Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: If 3 A = -4 -4 8 1 x 4 1 1 Is a singular matrix, then x is 1

A:

Q: A cable runs along the wall from C to P at a cost of ​$4 per​ meter, and straight from P to M at a…

A:

Q: at is the general solution to the equation? 10 = 2 cos 0 tan 0 g solutions to the box to correctly…

A: Please see the below picture for detailed solution.

Q: Question 3 of 10, Step 1 of 1 Suppose that y varies inversely as the 4th power of .t, and that y = 4…

A: Given y varies inversely as 4th power of x  let proportionality constant = k

Q: Let f (x)  =  { 8x x  ≤  12 −4x + 144 x  >  12 Evalute  36 ∫ 0f (x) dx.

A:

Q: A rectangular beam is cut from a cylindrical log of radius 15 cm. A cross-section of the log is…

A: The given figure is:   Radius r=15 cm Let the dimeter is d  ∴d=2r=215=30cm

Q: Ten and one-half foot-pounds of work is required to compress a spring 2 inches from its natural…

A:

Q: Find the area of the surface obtained by rotating the curvey = 4x³ from x = 0 to x = 1 about the…

A:

Q: If y = 2x³ + 5x and dy = dt 5 dx dt dy dt = 4, find when x = 3.

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: please see the below picture for detailed solution.

Q: Show that the lines L₁ : x = 5 – t, y = 2t, z = 1+t and L₂: x = 1+2t, y = 3-4t, z = 5 - 2t are…

A: