At this point in time, you can use a technique called cross-mutiplication, where you say that
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At this point in time, you can use a technique called cross-mutiplication, where you say that
Take the cross product, then normalize the result.
This has norm
and so a unit vector orthogonal to both given vectors is
An equally correct answer would be the negative of this vector, since
.
This has norm
and so a unit vector orthogonal to both given vectors is
An equally correct answer would be the negative of this vector, since
A equation to represent this situation is:
Now we have to find x.
Step 1: Subtract 0.5x from both sides.
<span><span><span><span>0.75x</span>+7.5</span>−<span>0.5x</span></span>=<span><span><span>0.5x</span>+10</span>−<span>0.5x</span></span></span><span><span><span>0.25x</span>+7.5</span>=10
</span>Step 2: Subtract 7.5 from both sides.
0.25x+7.5−7.5=10−7.50.25x=2.5
Step 3: Divide both sides by 0.25.
<span><span><span>0.25x/</span>0.25</span>=<span>2.5/<span>0.25
</span></span></span>Answer:
<span>x=<span>10</span></span>
They will cost the same after 10 rides.
Now we have to find x.
Step 1: Subtract 0.5x from both sides.
<span><span><span><span>0.75x</span>+7.5</span>−<span>0.5x</span></span>=<span><span><span>0.5x</span>+10</span>−<span>0.5x</span></span></span><span><span><span>0.25x</span>+7.5</span>=10
</span>Step 2: Subtract 7.5 from both sides.
0.25x+7.5−7.5=10−7.50.25x=2.5
Step 3: Divide both sides by 0.25.
<span><span><span>0.25x/</span>0.25</span>=<span>2.5/<span>0.25
</span></span></span>Answer:
<span>x=<span>10</span></span>
They will cost the same after 10 rides.