<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>
Answer: They can order 78 shirts.
Step-by-step explanation:
9x + 8 = 710
9x = 702
x = 78
**Since the shipping fee is $8 for ANY amount ordered, the price of shipping doesn’t change with the number of shirts — the shipping price is a constant.
Answer:
at t = 5.4485 units (maybe seconds, but it is not given)
Step-by-step explanation:
In the equation, h is the height above/below the rest position and t is the time.
Since we want to know WHEN (t) will it be 3 INCHES ABOVE (h = +3), we can simply plug in 3 into h and solve for t. Shown below:
Hence,
At t = 5.4485 seconds (no unit of time is given, i am assuming seconds), the height of the weight will be 3 inches above the rest position.
Answer:
, explanation for how to get there
Step-by-step explanation:
If we have the equation 
, we want to isolate c on one side and find it's value.
Let's first divide both sides by 4.
Now let's solve for the absolute value. We know that:
or
Possibility 1:
Subtract 3c from both sides:
Possibility 2:
Add 4c to both sides:
Subtract 5 from both sides:
Divide both sides by 7:
Plugging both of these values into the equation, we can see that only 5 works.
Hope this helped!
Answer:
He used the commutative property incorrectly as he had no such addition of the property of any function to be done in sequence.
