5. Set up the integral for the total work it takes to pump the water to 10 ft above the semi-spherical tank with radius of 20 ft as shown in the following picture? (water weight = 64.2 lb/ft³) 10 t R-20

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A: Consider the equation of the curve, y=x3+500 for -1≤x≤2. the arc length is defined by the formula,…

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A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

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A: Please refer the attached image for complete solution. THANK YOU.

Q: A closed right circular cylindrical tank made of s inch thick metal has an outer radius of 2 ft and…

A: solution:-(1)outer radius, r=2 ftheight, h=6 ftouter surface area of cylinder= 2πrh+2πr2…

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A: Given that: Volume of cylinder = 1000 cm3

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Q: in. BASE in. 14 in. Lateral Surface Area Total Surface Area (Formula) (Formula) (Solution)…

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A: Given: r=11+0.9 cos(θ) Differentiate with respect to θ drdθ=0.9 sin(θ)(1+0.9 cos(θ))2 drdθ=0.9…

Q: V. A hemispherical basin of radius 4 ft contains liquid to a depth of 3 ft. If the liquid weighs 48…

A: This is a problem related to pumping volume of the spherical basin to the 3 ft above the container.…

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A: Formulas for the volume and the surface area of a cylinder with radius y and height s.

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A: Topic : integration

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A: Given curve, y=4-x2 Portion of given graph rotate around X axis in first quadrant, Therefore Put x=0…

Q: 2) Use the surface area formula: S = 2ny 1+ () dx to find the surface area y = x, where 0 <x <1 of:

A:

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A: Work=Distance*density*volume   Distance=9-ydensity=ρvolume=πx2×dyas it is cylinder , x = r…

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Q: Calculate the work (in Joules) required to pump all of the water in this hemispherical tank to the…

A: We will find work done to empty a horizontal slice of watr and then integrate it to find total work…

Q: The area of the surface obtained by revolving the curve x= Vy+4 for a-4.)

A: We have dxdy=12y+4

Q: 5. Set up the integral for the total work it takes to pump the water to 10 ft above the…

A: Since equation of circle is x2+y2=202                 (1) If we draw a small cylinder with height…

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A: GivenVolume of right circular cone of radius x and height y is given byV=13πx2yAlso    V=3π cm3To…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm³. Suppose R and H are the…

A: We will use derivative to minimize the area.

Q: 5. Consider a hollow spherical bowl with radius r = 18 cm that is filled to the top with water. h(t)…

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A:

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

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Q: 4. Find the work required to pump the water out of the top of a full tank that is shaped like the…

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Q: 2. A tank in the shape of a cone (as shown below) is filled with water. Assuming the density of…

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Q: 1–q² (b) Interpret Vr2 + y? dydx as a volume and calculate the integral without integrating.

A: b)

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