A bucket is filled with sand so that the total mass (sand and bucket) is 20 kgs. The bucket is to be lifted to the top of a 10 meter tall building by a rope of negligible weight. However, the bucket has a hole in it, and leaks 0.2 kgs of sand each meter it is lifted. Find the work done lifting the bucket to the top of the building. Joules

Q: Use the equations to find дz дх дz ду || || дz дх дz дх OF дх ƏF дz and and əz ду дz ду x2 - y2 + z²…

A: Given: ∂z∂x=-∂F∂x∂F∂z and ∂z∂y=-∂F∂y∂F∂zx2-y2+z2-8z=9 We are required to find: ∂z∂x and ∂z∂y

Q: A company manufactures a units of one item and y units of another. The total cost in dollars, C, of…

A: We have to find the minimum cost and additional cost or saving.

Q: Use the chain rule to find dw dt = dw dt w = In (√x² + y² + z²), x = 8 sin(t), y = 7 cos(t), z = 2…

A:

Q: Find the vectors T, N, and B at the given point. T = N = B || r(t) = (6 cos(t), 6 sin(t), 6…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The integral J W 6 3t 1 + 9t² 1 By substitution we have 3 18 1 + 9t² dt can be rewritten as In(1 +…

A: Given:

Q: If f (x) = √x² - 6x +10, then what is the derivative of f at x=3 ? Round to the nearest tenth.

A: If fx=x4-6x+10, then to find the derivative of fx at x=3.

Q: Evaluate the triple integrals ſſy dV, W = {(x,y,z):0≤x≤3,0≤y≤x,x=y≤z≤x+y}. W

A: Given data

Q: Second derivative of f(x) =2^x/x

A: To find the second derivative of the following function. fx=2xx

Q: The total U.S. personal income I (in billions of dollars) can be approximated by I=535.6(1.054)t  ,…

A:

Q: ƒ(x) = x + 1 X

A: fx=x+1x

Q: horizontal asymptote (c) Describe the end behavior of the function. End behavior: y y → as x → ∞ as…

A:

Q: I have a problem that I really need help with:  Find f(g(4)) if f(x)=x^3/2 and g(x)=1-3x^2 I know…

A: f(x)=x3/2 , g(x)=1-3x2 We have to find f(g(4))

Q: The revenue, in dollars, derived from the sale of a units of device model SDP732 is given by…

A:

Q: that the indicated family of functions is a solution of the given differential equation. Assume an…

A: The given differential equation is;  d2y/dx2 - 6dy/dx + 9y=0

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…

Q: 1. Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)…

A: Given data 2+5i2-4i

Q: 2. Find the anti-derivative of the function f(x) = e* sin (^te^)

A:

Q: A dynamite blast blows a heavy rock straight up from the ground." Height = 0 when time=0" The…

A: Vt=160-32t

Q: Compute the definite integral fa xe9x dx. ←

A:

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: given radius of a right circular cone is increasing at a rate of 1.2ins and height is decreasing at…

Q: The equation for the price of a television, based on the demand, is P(x)=175-0.4e0.001x What should…

A: The equation for the price of television based on demand is P(x) = 175 -0.4e0.001x. Our task is to…

Q: Evaluate the following integral S 4x cos (5x) dx=

A:

Q: Quadratic equations are not nol in the form f(x) = ax²+bx+c to find (h, k). Begin by completing the…

A:

Q: 14x^2-13x-12 using box method

A:

Q: Find the area of the parallelogram whose vertices are given below. A(0,0,0) B(4.2.6) C(8,0,6)…

A: Vertices of a parallelogram, to find its area.

Q: Find the maximum and minimum values of the function f(x, y) = xy subject to g(x, y) = x² + xy + y² =…

A: Objective function fx,y=xyConstraint function gx,y=x2+xy+y2-108

Q: Determine the slope and the equation of the tangent to the curve f(x) = sin(x) + sin(x) at x=

A: f(x)=sin2x+sinx at x=π

Q: 104) 12 (1) 2 - sina da

A: For a function f(x), we know the definite integral property as follows:…

Q: əz дz Use implicit differentiation to find and Әх ду дz Әх дz ду = = II x2 - y2 + z² - 42 = 3

A:

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)¹e-x dy…

A: We need to solve (e^y+1)^2 e^(-y)dx+(e^x+1)^4 e^(-x) dy=0.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L-1100 feet apart. As the…

A: The given image of the problem is: L=1100  feetA=50°B=35°

Q: Find a parametrization of the line in which the planes x+y+z=4 and y + z = 8 intersect. Find the…

A:

Q: The equation below follows from the integration by parts formula by replacing u by f(x) and v by a…

A: given ∫f(x)exdx=f(x)ex-∫exf'(x)dx

Q: In this question, you will solve a definite integral using the method of substitution. 3 Ső (4 x −…

A:

Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

A: The rate at which water drains from a tank is recorded at half minute intervals ∆t=0.5

Q: Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve the given differential equation by separation of variables. xy + 7x -y - 7 xy - 2x + 8y - 16…

A:

Q: Find the distance from the point S(-2,-1,6) to the line x=2t, y = 10t, and z = -1t. The distance is…

A: point s-2,-1,6line x=2t, y=10t, z=-1t

Q: A bucket begins holding 15 kgs of sand. The bucket is to be lifted to the top of a 20 meter tall…

A: Initially sand present in bucket = 15 kg,Bucket leaks 0.2 kg/m sand when it is lifted.

Q: Find the scalar equation of the plane that contains a(7,1,3), b(-3,4,0) and c(1,-1,2).

A: We have, Points:- A(7, 1, 3) B(-3, 4, 0) C(1, -1, 2)

Q: swer the following ston based -2 f f(x) d -2 -1 of's 0 f's 2 214 f(x) dx = [a] -1 -2 f(x) dx = [b]…

A: a)∫-20fxdx

Q: The growth of a colony of bacteria can be described by exponential growth. If the colony initially…

A: Pt=P0ert⇒P0=initial population⇒r=Growth rate⇒Pt=Population at time t⇒t=time in hours

Q: 3. Compute the area bounded by the three leaf rose curve given by r(0)=5sin30. Compute the area…

A:

Q: 3. Use the Intermediate Value Theorem to show that there is some c in the interval (-1,0) at which…

A: f(-1) = (-1)³ - 3(-1) + 1 = -1 + 3 + 1 = 3.  f(0) = (0)³ - 3(0) + 1 = 0 + 0 + 1 = 1.

Q: The equation of the line that goes through (3, 2) and (-7, 10) can be written in the form y = mx +…

A:

Q: Evaluate the double integral circles x² + y² = 9 and x² = 9 and x² Answer: SSR y² -dA, where R is…

A: To evaluate the given double integral use the following substitution. x=rcosθ y=rsinθ x2+y2=r2

Q: .1/3 Let ƒ(x) = x¹/³, and let T₁(x) be the nth Taylor polynomial of f centered at a =

A:

Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)

Q: Given u = a. 27 + 47 b. u c. u x d. lul V V [-4,4, 4] and = - [-5,6, 2] find

A: Addition of two vector formula and product rules

Q: Suppose parametric equations for the line segment between (5, 1) and (6, −3) have the form: a + bt c…

A: Here we have given the parametric equations as follows: x=a+bt y=c+dt Now, here it is given that at…