A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral triangles with sides 2 m long and with vertex at the bottom. Setup the integral for the force on one end of the trough. (Hint: Put the bottom of the trough along the x-axis.) A 3000√/3³ (√3-y)ydy ℗ 6000√/35 (√3y-y²) dy B) 9000 (√3y-y²) dy of (√3-y)ydy 4500

Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

A:

Q: convert the cylindrical (5, pi/3, 2) to rectangular

A:

Q: Given the periodic function defined in one period by the function: (bt, f(t) = a, (0, 0 0.

A: The following formulae are used to find the Fourier coefficients of the function fx on the interval…

Q: A forest has a population of cougars and a population of squirrels. Let xx represent the number of…

A: We can solve this using given information

Q: Q.2. The side of a cube is measured with a possible percentage error of ±2%. Use differentials to…

A: Using differential

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: x² So (1+x6) ³ dx

A:

Q: Find the area bounded by the curve 4 square units 8 square units 16 square units 10 square units =…

A:

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

A:

Q: 20102211 is in base 3 convert it in base 10

A:

Q: A spring with a 2-kg mass and a damping constant 8 can be held stretched 1 meters beyond its natural…

A: To find the position of the mass after t seconds.

Q: Find the power series representation for f(x): = 2x (1-x²)² and then find its radius of convergence.

A:

Q: 34) True or False: The transformation shown below is a rotation.

A: Introduction: Symmetricity is very important in geometry. When a line divides a geometrical pattern…

Q: prove that (z(square root 2,+,×)) is integral domain.

A: We have , ℤ2   =  a + b2 / a , b ∈ ℤ We need to show that  , ℤ2 is integral domain. We know that , a…

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

A:

Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: Consider the given curves, x2=4y and y2=4x Draw the diagram of the region revolving,

Q: Consider the surface S given by 22² +2y² = a + 1 = 0. (a) Find the equations of the traces of S on…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional space…

Q: Suppose a,b,n are integers and n>0 s.t. 63a^5b^4=3575n^3, what is the smallest possible n. Explain…

A: Solution : -

Q: Ex: If w = f(x, y, z), x = x(r, 0), y = y(r,0), z = z(r, 0), find wr, we? aw ax aw ay 1 aw

A: Chain rule for total derivative

Q: 2 Classify the point (0, 0) for f(x, y) = xye 2 by using Second derivative test if POSSIBLE. Lütfen…

A:

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by…

A: Solution

Q: 3) Find the derivative f(z) = 100 a) f(z) = 400z(z²-1) (2²+1) 100 99 b) f(z)= c) f(z) = d) f(z) = e)…

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: 18. Figure F is graphed. Transform figure F using the rule (x,y) → (x-8,-y). YA 10 8

A: Introduction: Graph transformation is the process of modifying an existing graph or graphed equation…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

Q: (a) Let V be an inner product space with inner product (,), and let ~1,...Xn,J EV. Use proof by…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find the 4-point discrete Fourier transform (DFT) of the sequence x(n) = {1, 5, 3, 1}.

A:

Q: Find the intercepts and the symmetry for the polar equation r = 1+ sine.

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 9.W.1 The Gram matrix of an inner product on R2 with respect to the standard basis is G = 1 2 -1…

A:

Q: Assume that the Taylor series centred at x = 0 of a function f(x) is Σo anx" Let g(x) = f(x³).…

A: The expansion f(x) is f(x)=∑n=0∞anxn Here a0=1, a2=2, a2=3, a4=4 Since  a0=1⇒f(0)=1…

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A:

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A:

Q: Define R as the region bounded by the graphs of the function f(x) = x3 , the x-axis, x = 0, and x =…

A:

Q: Let S be the quadric with equation 4x² − (y − 3)² + 4z² = 4. What type of quadric is S? Find an…

A:

Q: Question 12 Calculate the area of the smaller region (to the left of the parabola) bounded by…

A:

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Introduction: The definite integration of a real valued function over an interval is the area that…

Q: 5. ) Write an equation for the graph of the rational function shown. Explain your reasoning. 5. 4 -8…

A: Given the graph is

Q: Inz) = Inr ei ) = Inr) + In ( e°0 )=ln r+iᎾ z = reie

A: A complex number is expressed in various ways. Apart from rectangular representation, a complex…

Q: E = 213 31 10 11 0210 0 1 2 3 3]

A:

Q: Consider the initial value problem u" + p(t)u' + q(t)u = g(t), u(0) = uo, u'(0) = u Transform this…

A:

Q: Using the data in the table below and the best combination of trapezoidal and Simpson's rules,…

A: Solution: Solution using Trapezoidal rule, The value of table for x and y x 1 2 3.25 4.5 6 7 8 9…

Q: Please draw cashflow diagram) What amount of money invested today at 15% interest rate compounded…

A: Cash flow diagram for the given data:

Q: Question 17 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

A: To find the inner radius of the circular ring.

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A:

Q: 2. Show that if the orthogonal dimension of a Hilbert space H is finite, it equals the dimension of…

A: Given: Finite dimension To find: Former finite

Q: A = {]-[²]} and A'= "={[_¹₁]-[i]}. If B=[32] is the matrix representation of linear operator Z: R² →…

A: We have to find the transition matrix and matrix representation of linear operator w.r.t. basis.

Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

A:

Q: Determine the value of integral of f(x) = from 1 to 7 by Simpson's X 1/3 rule. Find the relative…

A:

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A:

Q: A forest has a population of lynx and a population of rabbits. Let a represent the number of lynx…

A: Solution: x'=dxdt=-0.25x+y  .....1y'=dydt=-x+4y  .....2B.C.S: x0=0 and  y0=1From equation 1  and 2…

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: