A ramp is inclined at 12° to the horizontal. A cart is pulled 8 m up the ramp by a force of 120 N, at an angle of 10° to the surface of the ramp. Determine the mechanical work done against gravity.

Q: 6.) Find the local extrema and saddle point(s) of f(x, y) = x²y-6y²-3x².

A:

Q: (b) Prove that the improper integral ]] converges. dr dy (1 + x² + y²)³/2

A: Given problem:-

Q: 0 1 5. Let A = -1 -1 1 a) Find the decomposition PA=LU for the matrix. b) Solve the system Ax=(1 1…

A: Given problem:-

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (7x²2) to…

A: Maclaurin series of sin(x) :              sin(x) = x-x33!+x55!-x77!+...

Q: Assume that f(x) is a function defined by f(x) x²-3x+1 2x1 for 2 ≤ x ≤ 3. Prove that f(x) is bounded…

A:

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

A:

Q: The result of the following dot product (- 2j + 3k) · (−2ī +2j - 2k) is b. -6 c. 0 a. -10 d. 10 e. 6

A:

Q: Which statement is true about the following vector field? O Vectors all point toward the origin O…

A:

Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: 2 OM a) Find the area of the region b) Find the length of the curve c) Find the surface area generat…

A: A detailed solution is given below.

Q: 32) Find the amount of a continuous money flow in which $2000 per year is being invested at 5%,…

A: Given.

Q: 1. Find the interest paid on a loan of $2000 for 1 year at a simple interest rate of 7% per year…

A: "According to the guidelines issued by the company we are supposed to answer only one question.…

Q: he vector, parametric, and scalar equations of the plane for each of g situations: 1961 301 il bari…

A:

Q: How much did Speedy Movers borrow for a debt that accumulated to $51,034.26 in four years? The…

A: Given, Amount(A)= $ 51034.26 t= 4 years r= 3.25%= 0.0325 n= 2(semi-anually)

Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

A:

Q: y = x² and x² = y

A: Area of the bounded region is

Q: to onuabjanip 2+1 (-1) 7-1 Jo to - 두 + 두 Soudbranvol - 1 Prove the

A:

Q: Let the vector v have an initial point at (2, −6) and a terminal point at (6, –4). Determine the…

A: To find out the components of vector v.

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

Q: Find and sketch the domain for f(x, y) = ² 2x-14y²

A:

Q: Suppose F(4)=-4, f(x)cos F(x) dz F(5)= 3, and F'(x) = f(x). 3 cos (3) +4 cos(4)

A: We can evaluate the given integral by using the substitution u= F(x).

Q: Use the binomial theorem to expand the binomial. (5x+2)4

A: Please refer to the image below

Q: b) Calculate (i) the following integrals x² (3x³ + 2)²dx

A:

Q: S₁ √√x² √√√xª dx 4 -2

A:

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

Q: The solution of a certain differential equation is of the form y(t) = aest + bet, where a and b are…

A:

Q: 2. Evaluate r sin rdr using integration by parts.

A:

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and concept we will…

Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: Q4/Find x and y that make the equations equal to zero: 5x+2y-4-0 6x+8y-2-0

A: Simplify both equation for x and y .

Q: 3. Evaluate sin5 xdx

A:

Q: Find the divergence of the following vector field: 0 O 2z O O F = (y, -x + z², 3x)

A:

Q: If ū = and = and ū is orthogonal to , then k is a. -8 b. 8 C. 4.5 d. -4.5 e. 0

A:

Q: Find the particular solution of the following differential equations with the given condition. 3) dy…

A:

Q: Use Lagrange multipliers to find the dimensions of the right circular cylinder with maximum volume…

A: Given that  a right circular cylinder with surface area = 24π square unit.   As volume is to be…

Q: Ju -To uv-s to Explain why the substitutions below are inappropriate. Let = x dx 1. Suppose we apply…

A:

Q: Evaluate the following limits: 2. lim G(x) if G(x) = = x →-00 x+61 x+6 2

A: We have to find the limit

Q: Example 99 Consider the set M = {(x, y) = R²: x,y #0}. Find M. Solution:

A: The orthogonal complement are subspace

Q: (Q3:- prove the Cose =(A.B/AB Q4:- Find the angle between along diagonal and an adjacent face…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Q3. Evaluate the following integrals 1) cothx.csch²x. dx (50-3x - W√x++) de

A:

Q: 1- What are the disadvantages of the Newton method for solving the following nonlinear systems.…

A: answer is in next step . please give a like

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: There are three methods to find the volume of a solid generated by revolving a curve f(x) about a…

Q: Consider the differential equation y" = ef + xy' where y is considered to be a function of . In this…

A:

Q: find differential equation of the following equation 3) dy +xsin(2y) = x cos² (y)

A: Given

Q: T -2 -1 4 3 2 - -3 1 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) =…

A: (a)  limx→-4f(x)=2   (b)  limx→-3f(x)=-2   (c)  limx→-2f(x)=-3   (d)  limx→1f(x)=infinite

Q: 3. What is the height of the right circular cylinder with greatest volume that can be inscribed in a…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 4. Multiply: 7(cos 15° 5. Using your answer 1/4.

A:

Q: Step 4 of 4: Find lim f(x). x-3 Enable Zoom/Pan 10 -5 10 Keypac Keyboard Shortc Selecting a radio…

A:

Q: Solve the following second order differential equation, clearly showing all calculation steps d²y dy…

A: