A circular plate of radius 5 cm is immersed in a liquid of specific weight w such that its horizontal diameter is 8 cm below the surface. With the x-axis coinciding with the horizontal diameter, the integral expression for the force acting on one side due to liquid pressure is

Q: What is the volume of a rotational body formed by rotating the area bounded the = 4-x ² function…

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Q: calculate (by integration, showing all working) the distance from the nose of the jar to the centre…

A: Given figure: Given, z2=14yz=12y

Q: A certain spring has a natural length of 4 meters. If it stretched so that it is 6 meters long, it…

A: A force of 30N is required to stretch the spring 6m−4m=2m from its natural length. Using Hooke's law…

Q: Why is integration used to find the total force on the face of a dam?

A: Given: Important of integration to find the total force on the face of the dam

Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: A hose feeds into a small screen box of volume 10 cm3 that is suspended in a swimming pool. Water…

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Q: How can you use line integrals to find the centers of mass of springs or wires? Explain

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Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: 4. A cannon ball is shot From the position (0,0,100) with initial velocity (100,120,40) when and…

A: Initial sped of the ball u=(0,0,100) x0=(100, 120, 40) Acceleration due to gravity g=(0,0,-32)…

Q: The vertical cross section of an irrigation canal is modeled by f(x) = 5x2/(x2 + 4) where x is…

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Q: A box is pulled to a horizontal distance of 100m by a force of 500N applied at an angle 30° to the…

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Q: Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y2 = 4 and…

A: Solution is given as below:

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Find the approximate surface area of a sphere of radius 3.02 in. (Use differentials)

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Q: A tank that has a shape of an inverted circular cone with height 15 meters and base radius 6 meters…

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Q: If a force of 128 lbs is required to stretch a 10-ft spring by 4 ft. How much work is done by…

A: Here we have to use the concept of integral calculus

Q: Suppose that a semicircular wire has the equation y= V25- x and that its mass density is 8 = b- y.…

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Q: 20. V9 – x² dx

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Q: Why is integration used to find the work done by a variable force?

A: Explain the reason behind that the integration used to find the work done by a variable force.…

Q: A water tank has the shape of an upright cylinder with a base radius r = 2 meters and a height h = 5…

A: Work done bringing up a mass m to height h is mgh Volume of a cylinder is pir^2h

Q: A body of mass 6 kg moves in a (counterclockwise) circular path of radius 6 meters, making one…

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Q: Find the moment of inertia of the area bounded by the curve x^2=8y, the line x=4 and the x-axis on…

A: Use moment of inertia concept

Q: The plane tangent to the surface z+1= ze" cos z at (1,0,0) can be represented by the equation Z= 1.…

A: As per our guidelines, we are allowed to answer only one question. Since you have posted multiple…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Why is integration needed to compute the work performed in stretching a spring?

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Q: A water tank has the shape of an upright cylinder with a base radius r = 2 meters and a height h = 5…

A: Given:for cylinder radius of baser=2 meters.              heighth=5 meterswater level filled in…

Q: Prove that the homogeneous integral equation

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Q: If v is the velocity field of a fluid, the flux of v across C is equal to the flow rate ( amount of…

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Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: Suppose a cylindrical tank with a height 8 m and radius 4m is half-full of water. Assume the density…

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Q: For rigid-body motion, the strains will vanish. Under these conditions, integrate the strain…

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Q: Find the moment of inertia of the area in the first quadrant bounded by the curves y = 9 – x² and y…

A: Moment of inertia bounded by the curves y2 and y1 about y-axis is  Iy=∫abx2(y2-y1)dx Consider the…

Q: A 570-g squirrel with a surface area of 865 cm2 falls from a 4.0-m tree to the ground. Estimate its…

A: Consider the given question,The formula of terminal velocity is given by,

Q: Find volume y=3x^2, x=1, and y=0 about x axis

A: y=3x^2, x=1, and y=0 about x axis

Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: A cylindrical barrel of oil has a diameter of 1 meter and its sides are 2 meters high. Given that…

A: The objective here is to set up the formula to evaluate the work required to pump the oil over the…

Q: A disk of radius 3 cm has density 6 g/cm? at its center, density 0 at its edge, and its density is a…

A: Given radius of disc r = 3 cm Density at center ρc = 6 g/cm2 Density at edge ρe = 0 given density is…

Q: The radius of a circular disk is given as 20 cm with a maximum error in measurement of 0.4 cm. Use…

A: Given: The radius of a circular disk is 20 cm ie., r = 20 cm  error in measurement is 0.4 cm ie., dr…

Q: The dimensions of a closed rectangular box are measured as 89 cm, 61 cm, and 35 cm, respectively,…

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Q: What is the differential form for the total surface area of a frustum of a cone with l as the slant…

A: The curved surface area of a frustum of a cone is:

Q: 3. Use differentials to approximate the volume of a spherical shell whose inner radius is 5 cm and…

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Q: Find the total population within a 4-km radius of the city center (located at the origin) assuming a…

A: Given that, σx, y=2000x2+y2-0.2        ...(1)

Q: Find the limits of integration with respect to u and v

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Q: A rectangular plate 0.6 m wide and 1.2 m deep lies within a water body such that its plane is…

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Q: A firefighter is standing on top of a building 19 m high, holding a firehose 1 m above the top of…

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Q: The linear density of a rod at a point a centimeters from the left end is, where the left 2 grams…

A: Here, the objective is to find the mass and center of mass of the rod.

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: From the given graph, The function y = k x13  limits from x = a  to  x = b

Q: Use Stokes's Theorem to evaluate

A: Given,          F(x, y, z)=x2i+z2j-xyzkS:z=4-x2-y2