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Convert the point (−7,73,14)  from rectangular coordinates to spherical ( - 7,7 \sqrt { 3 } , 14 ) \text { from rectangular coordinates to spherical } coordinates.


A) (142,π4,2π3) \left( 14 \sqrt { 2 } , \frac { \pi } { 4 } , \frac { 2 \pi } { 3 } \right)
B) (282,2π3,π4) \left( 28 \sqrt { 2 } , \frac { 2 \pi } { 3 } , \frac { \pi } { 4 } \right)
C) (142,2π3,π4) \left( 14 \sqrt { 2 } , \frac { 2 \pi } { 3 } , \frac { \pi } { 4 } \right)
D) (282,π4,2π3) \left( 28 \sqrt { 2 } , \frac { \pi } { 4 } , \frac { 2 \pi } { 3 } \right)
E) (142,π3,π4) \left( 14 \sqrt { 2 } , \frac { \pi } { 3 } , \frac { \pi } { 4 } \right)

F) C) and D)
G) B) and E)

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 Suppose the vector u=(3242,1455,2235} gives the numbers of hamburgers, chicken \text { Suppose the vector } \mathbf { u } = ( 3242,1455,2235 \} \text { gives the numbers of hamburgers, chicken } sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector v=⟨1.44,2.49,1.69}\mathbf { v } = \langle 1.44,2.49,1.69 \} gives the prices (in dollars) per unit for the three food items. Determine the total revenue that the restaurant earned on its three products for that week. Round your answer to two decimal places.


A) $12,079.58\$ 12,079.58
B) $12,118.58\$ 12,118.58
C) $24,138.16\$ 24,138.16
D) $12,068.58\$ 12,068.58
E) $24,136.16\$ 24,136.16

F) B) and E)
G) C) and D)

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Complete the square to write the following equation in the standard form for a sphere. x2+y2+z2−4x+4y+2z+16=0x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 4 x + 4 y + 2 z + 16 = 0


A) (x+2) 2+(y+2) 2+(z+1) 2=25( x + 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } + ( z + 1 ) ^ { 2 } = 25
B) (x−2) 2+(y+2) 2+(z+1) 2=25( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } + ( z + 1 ) ^ { 2 } = 25
C) (x−2) 2+(y−2) 2+(z+1) 2=25( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + ( z + 1 ) ^ { 2 } = 25
D) (x−2) 2+(y+2) 2+(z+1) 2=5( x - 2 ) ^ { 2 } + ( y + 2 ) ^ { 2 } + ( z + 1 ) ^ { 2 } = 5
E) (x−2) 2+(y−2) 2+(z−1) 2=25( x - 2 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + ( z - 1 ) ^ { 2 } = 25

F) A) and B)
G) C) and D)

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Find the component form of the vector u with the given initial and terminal points. Initial point: (5, 7, 8 ) Terminal point: (-2 , 10 , 10 )


A) u=7i−3j−2k\mathbf { u } = 7 \mathbf { i } - 3 \mathbf { j } - 2 \mathbf { k }
B) u=3i+17j+18k\mathbf { u } = 3 \mathbf { i } + 17 \mathbf { j } + 18 \mathbf { k }
C) u=−7i+3j−2k\mathbf { u } = - 7 \mathbf { i } + 3 \mathbf { j } - 2 \mathbf { k }
D) u=−7i+3j+2k\mathbf { u } = - 7 \mathbf { i } + 3 \mathbf { j } + 2 \mathbf { k }
E) u=7i+3j+2k\mathbf { u } = 7 \mathbf { i } + 3 \mathbf { j } + 2 \mathbf { k }

F) B) and D)
G) A) and B)

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Find the distance between the planes given below. 4x−4y+5z−104=020x−20y+25z−100=0\begin{array} { l } 4 x - 4 y + 5 z - 104 = 0 \\20 x - 20 y + 25 z - 100 = 0\end{array}


A) −8457\frac { - 84 } { \sqrt { 57 } }
B) 8457\frac { 84 } { \sqrt { 57 } }
C) 8957\frac { 89 } { \sqrt { 57 } }
D) −16857\frac { - 168 } { \sqrt { 57 } }
E) 16857\frac { 168 } { \sqrt { 57 } }

F) D) and E)
G) A) and C)

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