Create a bucket by rotating around the y axis the curve y=2ln(x−4)y=2ln(x-4) from y = 0 to y = 4. If this bucket contains a liquid with density 820 kg/m3 to a height of 3 meters, find the work required to pump liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity
Create a bucket by rotating around the y axis the curve y=2ln(x−4)y=2ln(x-4) from y = 0...
Create a bucket by rotating around the y-axis the curve y=5ln(x−4) from y = 0 to y = 6. If this bucket contains a liquid with density 720 kg/m3 filled to a height of 2 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity. Work =_____ Joules
Find the volume and the center of gravity of the solid formed by rotating the curve y = x(4 − x) around the x-axis over the interval 0 ≤ x ≤ 4.
The shape of a container is obtained by rotating the curve y = x^2 over the interval 0 ≤ x ≤ 2 about the y-axis. If the tank is full of water, the work required for pumping all water to the top of the tank can be expressed as an integral W = f(b,a) f(y)dy. Use trapezoidal rule on four subintervals of equal length to estimate the work. (Assume that water density is ρ kg/m3, and gravity acceleration g m/s2.)...
4. Find the centroid of the area bounded by the curve x2 (y-4), the x-axis and the y-axis on the first quadrant. A. , 8/5 B. 2, 64/3 C. , 5/4 D. 1/8,5 5. What is the area within the curve r2 16 cos 0? C. 30 A. 26 B. 28 D. 32 6. A uniform chain the weighs 0.50 kg per meter has a leaky 15-liter bucket attached to it. If the bucket is full of liquid when 30...
5 1.) A storage container has the shape obtained by revolving the curve y = 1x4 (shown on the right) from x = 0 to x = 2 about the y-axis, where x and y are measured in meters. 4 4 3 The tank is partially filled with coconut oil, up to a height of 1 meter. 2 1 kg : 900 = and the (The density of coconut oil is p acceleration due to gravity is g m3, т...
5 points WORK LIFT PROBLEM An inverted conical tank at a chemical plant has a base radius of 4 m and height of 3 m and is completely filled with liquid nitrogen, which has a density of 808.4 kg/m3. The Earth's gravitational constant is -9.8 m/s2. How much work is needed to pump all of the liquid nitrogen up through an outflow pipe that empties 3 meters above the top of the tank? (Note that the conical tank is opening...
Find the volume of the solid created by rotating y=x + 4 around the y-axis, O SX54. Give your answer as a decimal rounded to four decimal places.
Let S be the ‘football’ surface formed by rotating the curve y = 0, x = cos z for z ∈ [−π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area. Please answer in full With full instructions. Let S be the 'football, surface formed by rotating the curve y = 0, x-cosz for-E-π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area 3 Let S be the 'football, surface...
Find the parametric equations using sine and cosine for the surface obtained by rotating the curve x = sin(y) about the y-axis over the interval 0 < y < pi.
The portion ofthe graph y = tan−1 x between x = 0 and x = 1 is rotated around the y axis to form a container. The container is filled with water. Use n = 6 subintervals andSimpson's rule to approximate the work required to pump all of the water out over the side of the container. Give your answer in decimal form.(Distance is measured in meters, the density of water is 1000 kg/m3, and use 9.8 m/s2 for g.)I...