The x-coordinate of the center of the sphere is the midpoint of x=2 and x=16, that is (2+16)/2=18/2=9.
The y-coordinate of the center of the sphere is the midpoint of y=4 and y=18, that is (4+18)/2=22/2=11.
The z-coordinate of the center of the sphere is the midpoint of z=7 and z=21, that is (7+21)/2=28/2=14.
We also notice that the side lengths of the cube are:16-2 = 18-4 = 21-7 = 14
Thus, we have a sphere centered at (9, 11, 14) and radius R=14/2=7 units.
The equation of the sphere with radius R and center

is given by:

Thus the equation of the largest sphere contained in the box is:
Since these pools are similar, they have a scale factor that determines the ratio between each of the sides.
VR = 12
BF = 4
12 / 4 = 3
The scale factor = 3
WZ and TM are similar sides so,
7 * 3 = 21
a = 21
Answer:
4i.
Step-by-step explanation:
To find the flux through the square, we use the divergence theorem for the flux. So Flux of F(x,y) = ∫∫divF(x,y).dA
F(x,y) = hxy,x - yi
div(F(x,y)) = dF(x,y)/dx + dF(x,y)dy = dhxy/dx + d(x - yi)/dy = hy - i
So, ∫∫divF(x,y).dA = ∫∫(hy - i).dA
= ∫∫(hy - i).dxdy
= ∫∫hydxdy - ∫∫idxdy
Since we are integrating along the boundary of the square given by −1 ≤ x ≤ 1, −1 ≤ y ≤ 1, then
∫∫divF(x,y).dA = ∫₋₁¹∫₋₁¹hydxdy - ∫₋₁¹∫₋₁¹idxdy
= h∫₋₁¹{y²/2}¹₋₁dx - i∫₋₁¹[y]₋₁¹dx
= h∫₋₁¹{1²/2 - (-1)/2²}dx - i∫₋₁¹[1 - (-1)]dx
= h∫₋₁¹{1/2 - 1)/2}dx - i∫₋₁¹[1 + 1)]dx
= 0 - i∫₋₁¹2dx
= - 2i[x]₋₁¹
= 2i[1 - (-1)]
= 2i[1 + 1]
= 2i(2)
= 4i
Answer: Also 57
Step-by-step explanation: You have to round up cause you can't type in decimals.
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