Answer:
(a) Orthogonal, (b) Neither, (c) Parallel, d( Orthogonal
Step-by-step explanation:
a and b are parallel is a=kb
a and b if a dot b = 0
(a) a dot b = (9)(-4)+6(6)=-36+36=0
a and b are orthogonal
(b) a dot b = 40-7-21=12
a=kb -> there is no k value satisfying the equation
a and b are neither parallel or orthogonal
(c) a dot b = -12-108-48=-168
a=kb -> k=-3/4 satisfies the equation
a and b are parallel
(d) a dot b= 9-3-6=0
a and b are orthogonal
Answer:
( 1.5, 0)
Step-by-step explanation:
1. Find the coordinates ; in this case (7,-2) and (-4, 2)
2. Plug it into the formula (x1 + x2 ÷ 2 ) , (y1 + y2 ÷ 2)
3. ( 7 + -4 ÷2) = 1.5 And ( -2 + 2 ÷ 2) = 0
4. Therefore, the midpoint is ( 1.5, 0 )
Answer:
3003 units^3.
Step-by-step explanation:
Just multiply the dimensions :
11 * 13 * 21
= 143 * 21
= 3003 units^3.
Perimeter (P) = 2 · Length(L) + 2 · Width (W) → P = 2L + 2W
Solve for either L or W (I am solving for L).
200 - 2W = 2L
(200 - 2W)/2 = L
100 - W = L
Area (A) = Length (L) · Width (W)
= (100 - W) · W
= 100W - W²
Find the derivative, set it equal to 0, and solve:
dA/dW = 100 - 2W
0 = 100 - 2W
W = 50
refer to the equation above for L:
100 - W = L
100 - 50 = L
50 = L
Dimensions for the maximum Area are 50 ft x 50 ft
