a-planner-for-an-electronics-supplier-plots-a-grid-on-a-map-and-finds-that-its-three-biggest-custome

Question

A planner for an electronics supplier plots a grid on a map and finds that its three biggest customers are located at $A(0,0), B(60,0)$ and $C(20,50),$ where units are in $\mathrm{km}$. If the supplier builds a warehouse at the point $W(x, y),$ express the sum $S$ of the distances from $W$ to $A, B,$ and $C$ as a function of $x$ and $y .$ See Fig. $29.5 .$ (Hint: Use the distance formula given in Section $21.1 .)$

Thane Stiles · Accepted Answer

So if we are graphing to three dimensional points you first Sirkin want or why access XX ISS Z axis, the actual order of them doesn&#x27;t matter. You&#x27;ll get the same answers. So our first point of call P will be 50 and 10. We&#x27;ll go over five on the X axis and an up 10 on disease will be room here circle. Probably make that different colors. That&#x27;ll be RP. Next will be Q, which is three negative six and seven, which will be around here three dimensionally Now, if you will find the distance between those points going to use the distance formula and take square root of three minus five squared plus negative six minus zero square waas seven minus 10 squared that will simplify down to negative to negative six and negative three, which will come out to be a little seven.

Thane Stiles · Answer

we&#x27;re going to plot to different three dimensional things with points we can first start out with our XX ISS. Why? Access Z axis? If we have p at 310 then P is going to be at three 10 So your point p beat out right here. Next up will be our Q, which is negative. 12 and then negative five on the C axis. Just gonna be about down here. Okay? Now, if we&#x27;re going to find the distance way, take the root of X two minus x one squared plus y two miles wide, one squared plus C to minus C one&#x27;s way. That&#x27;s gonna come out to the root of minus one minus three. Squared plus to minus one. Squared Los negative five minus zero squared. All that will simplify out to equal to 6.48

Thane Stiles · Answer

we&#x27;re going to plot some three dimensional points were first gonna want our X and y axis. Then we&#x27;re going to want our Z axis clean up the wild. Okay, so if one point is native to negative 10 we can just kind of ignore our see excess for a minute and think about plotting negative to negative one. And that&#x27;s not so hard. Okay? And the next is negative. 12 30 So, really, because both of them have zero as their Z axis, you can just think of it as a two dimensional problem. Said we have negative 12 impulsive three. We don&#x27;t even need RC access. Here we have our PM key, So now we can think about how to get the distance between them. We use the distance from New. We will have negative two minus negative, two squared plus three minus negative. One square. We know both disease or zero, so that would just be plus cereal that comes out to negative. 10 squared positive four squared, which is root of 1 16 which comes out to 10.77

Kara Merfeld · Answer

right, So he drops in coordinates for a 10. So All right, let&#x27;s draw the base of our tent. So we&#x27;re told that, um, one corners of the origin in the next corner there. Sorry. Versi Vertex one. Vertex is at the origin, and the expert Tex is at X equal. Seven. Yours was to find the coordinates of the universities. Um, so we know that the tent is five units wide. So comes out five units. Yes. That&#x27;s a good no good five. Great. So this this point right here, where it touches the Y axis has then got to be zero in the extraction, five in the Y direction and zero losey direction. Right? So then this one here is seven, five and zero, right? And the other two overseas are more tricky. Oh, so the other two mercies air the vertical ones, right? So would be, like up here and up here. So we&#x27;re told that this 10 is six units tall, right? That means equal six up here. We&#x27;re also told that this length is roughly the same as this length. So that means that this length is also roughly the same as this length, so this length here is five. So it has to be 2.5 out and six up. Right? So then the coordinates of this point up here would be seven out of X 2.5 out. And why? And, uh, six up NZ. Right? Okay, so then by the same logic right of this point, we&#x27;re here. It&#x27;d be zero out of X. Um, 2.5 on why? And six up z. Very good. Um, something. The question it is. Yes. Okay.

Foster Wisusik · Answer

Okay, This question wants us to find the shortest distance between this point and a line. So to do that, we&#x27;re just going to find a vector between P and L. That&#x27;s orthogonal to L and then find the magnitude of that. So first, we&#x27;re just going toe convert our point to the tip of a position vector. And then this problem already gave us a vector that describes airline. So now we can start by finding the parallel component of PPI because that&#x27;s what&#x27;s going to be giving us extra distance. So we&#x27;re gonna have to subtract that off for our vector. So a parallel component is the projection of P on the line for Peeta l divided by the magnitude of L squared. Times are vector l. So in our case, the stop product zero plus zero minus 24 divided by the magnitude squared, which is three squared plus four squared or 25 and then l is 30 negative for So now we can just go ahead and distribute giving us are parallel component is just plugging in. Here we get negative 72/25 zero and 96 over 25 so Now we can subtract this vector away from our entire P to get are perpendicular part. So, P, we said was 0 to 6 and then the maker Sorry, p parallel was what we just found. And then we can write our perpendicular component as 72/25 two and then six is 1 50/25 So 1 50 minus 96 which is 54/25. So now our distance is just the magnitude of peeper. And if we do this, the simplifies under the radical too. 2/5 times the square root of 106 and that started

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