B. 1.08mL
1 lb = 2.2 kg
5 lb = 2.27 kg
2.27kg × 12mg = 27.24 mg
Divide 27.42 mg by 2.5 = 10.896mg
Now change the mg to mL
10.896 ÷ 10 = 1.0896
The <u>correct answer</u> is:
The last graph.
Explanation:
The leaf starts at 12 feet above the ground. This eliminates the <u>first and third</u> graph, leaving the second and last.
The leaf falls at 0.25 ft/sec. This means it would take 4 seconds for the leaf to fall 1 foot.
On the <u>second graph</u>, when we go over to 4 seconds and then up, the line is at 10 feet; this means it fell 2 feet in 4 seconds. This is <u>too fast</u>.
On the <u>last graph</u>, going over to 4 seconds and then up, the line is at 11 feet; this means it fell 1 foot in 4 seconds. <u>This is correct</u>.
<span>center of mass = (0, 0, 96/13) exactly (0, 0, 7.3846) approximately.
The object described is a spherical cap for a sphere with a radius of 10. Since the sphere is centered at the origin, the center of mass will have X and Y coordinates of 0 and we only need to find the Z coordinate. The formula for the geometric centroid of a spherical cap is:
z = 3(2R - h)^2 / 4(3R - h)
where
z = distance from the center of the sphere
R = radius of sphere
h = distance from base of spherical cap to top of spherical cap
And for a spherical cap of uniform density, the geometric centroid is also known as the center of mass.
Since the sphere has a radius of 10 and is cut by the plane z=6, the value h will be 10-6 = 4. So substitute the known values into the formula:
z = 3(2R - h)^2 / 4(3R - h)
z = 3(2*10 - 4)^2 / 4(3*10 - 4)
z = 3(20 - 4)^2 / 4(30 - 4)
z = 3(16)^2 / 4(26)
z = 3(256) / 104
z = 768/104
z = 96/13
z ~= 7.384615385</span>