Find the volume of the sphere. Use 3.14 or- 5) Use 3.14 for л. A) 14.13 yd3 6) Use 3.14 for 7. d = 3 yd for π as indicated. B) 9.42 yd3 C) 113.04 yd3 D) 7.948 yd3
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- Use Lagrange multipliers to find the dimensions of the box with volume 216 cm3 that has minimal surface area. (Enter the dimensions (in centimeters) as a comma separated list.) ? Thank youIntegrate ?(?, ?) = ?^2 + ? ?? + ?^2 over the region: ? = {(?, ?): (?^2 + +?^2) ≤ 2}The minimum vertical dimension (B) for the junction box shown in the Figure is _______
- Use Lagrange multipliers to find the dimensions of the box with volume 125 cm3 that has minimal surface area. (Enter the dimensions (in centimeters) as a comma separated list.)Find the area of the shaded area using the trapezoidal rule with a step size of 2 and 1 and the Romberg technique with a step size of twoan isosceles triangle has a baseline between (0,0) and (x,0), while the third corner is placed in y= 32-x2/6. Find the largest area the triangle can have if y>0
- The city of Squaresburg is in the shape of a rectangle, whose border is shown in the graph below. A highway running along the x-axis borders one side of the town, and the grid is shown in miles along each axis.The population density of Squaresburg is a(y)=2000-500y, where a(y) is measured in peoplemile2 and y is measured in miles from the highway.Consider a thin, rectangular slice of the town, cut parallel to the x-axis with thickness Δy. Write an expression that approximates the population living in this region.Population in this region ≈ ΔyUse an integral to calculate the population in the whole town of Squaresburg. Round your answer to the nearest whole number (if appropriate).Population in the whole town ≈ people3. A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 12 km of fence available, find the dimen- sion of the rectangle to maximize the area of the sanctuary.Define the term given nonrejection region