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polyanskiymichael
19.03.2020 •
Mathematics
For what values of b are the vectors [−18, b, 9] and [b, b2, b] orthogonal? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) b =
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Ответ:
Therefore the given vectors are orthogonal for b = 0,±3.
Step-by-step explanation:
If
and
are two vectors orthogonal, then the dot product of
and
will be zero.
i.e![\vec a. \vec b =0](/tpl/images/0554/5519/f4206.png)
If
and ![\vec b = x_2\hat i+y_2\hat j +z_2\hat k](/tpl/images/0554/5519/805d5.png)
Given two vectors are (-18,b,9) and (b,b²,b)
Let
and
Therefore,
=(-18).b+b.b²+9.b
= -18b+b³+9b
= b³-9b
Since
and
are orthogonal. Then
= 0.
Therefore,
b³-9b= 0
⇒b(b²-9)=0
⇒b =0 or b²=9
⇒b=0 or b =±3
Therefore the given vectors are orthogonal for b = 0,±3.
Ответ:
1875-(175*3)=1350
1350/(2.5*3)=180
The Band Travelled 180 Miles
Step-by-step explanation:
Take the flat fee and multiply for the 3 buses.
Then (based on the info given) take the cost of the miles per hour and multiply by 3
Take that number and divide 1350 by the cost per miles to determine the miles the band traveled