Let u = , v = . Find -3u + 2v.

Question

Let u = <-6, -2>, v = <-2, 3>. Find -3u + 2v.

anonymous · Answer

@phi @KingGeorge please I'm slowly dying

kinggeorge · Answer

So first, we just have to multiply the vectors by the scalars -3 and 2. First we have$$-3u=-3<-6,-2>=<-3(-6),-3(-2)>=<18,6>.$$Can you tell me what 2v is?

anonymous · Answer

I figured out the answer it is (14,12) right?

kinggeorge · Answer

That looks correct to me.

anonymous · Answer

YES thank you! Can you help me with one more please? (: @KingGeorge

kinggeorge · Answer

Sure.

anonymous · Answer

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base as shown below.

What is the vertical clearance 7 m from the edge of the tunnel?

anonymous · Answer

attachment

kinggeorge · Answer

Since it's a parabola, a quadratic equation will model that line very well. From the way it's drawn, we know the vertex is at (0,0), and it has a point at (16,-16). So can use the form$$y=a(x-h)^2+k$$where (h,k) is the vertex. So $h=0$ and $k=0$. Then we have that $$-16=a(16-0)^2+0=a16^2\implies a=-\frac{1}{16}$$So your quadratic equation will be $$-\frac{1}{16}x^2$$Make sense so far?

anonymous · Answer

yes!

kinggeorge · Answer

Now, when we're 7m from the edge, this corresponds to an x-value of 16-7=9. So plug in 9 for x to get$$-\frac{1}{16}9^2=-\frac{81}{16}$$But we want the distance of this from the base of the parabola, which is at -16. So we look at$$-\frac{81}{16}-(-16)=\frac{175}{16}=10.9375$$So this would be the vertical clearance they're looking for. 

Still make sense?