Answer:
b)0, yes
Step-by-step explanation:
Given:
Vectors (4,8) . (6,-3)
Finding inner product of vectors:
= 4x6 + 8x-3
=24-24
=0
Now to check the angle between them using formula a.b=|a|.|b|cosθ
|a|=
=8.9
|b|=
=6.7
Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,
0= 8.9(6.7)cosθ
cosθ =0
θ=90 degrees
Hence the two vectors are perpendicular !
Answer:
56 regular 37 tropical Maximum profit $204.75
Step-by-step explanation:
Constraints are:
r ≥ 0
t ≥ 0
2r+ 3t ≤ 125
2r + 1t ≤ 150
I will multiply the second by -3 to cancel t variable and see what is the maximum amount for the regular
2r + 3t ≤ 225
-6r - 3t ≤ -450
ADD BOTH
-4r ≤ -225
r≤ 56.5
Since we need to pick whole bottles ,not a fraction of a bottle we need ro round down.It should be less than 65.5.So we need 56 bottles of regular
2*56 +3t ≤ 225
112+3t ≤ 225
3t ≤ 113
t≤ 37.6666
37 bottles of tropical
2*56 + 3*37 = 112+111 =223 223<225
2*56 +37 = 112 +37 =149 149<150
$2.5*56 = $140
$1.75*37 = $64.65
Total profit $204.75
Answer:
:) The Inverse of the Function f(x) = 2x + 1 is f-1(x) = x/2 - 1/2.
Step-by-step explanation:
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