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Crazy boy [7]
2 years ago
11

Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to

Mathematics
1 answer:
sukhopar [10]2 years ago
7 0
<h3>Answer:  (2, 3)</h3>

===============================================

Explanation:

For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.

Let's find the slope of line NM through use of the slope formula.

m = (y2-y1)/(x2-x1)

m = (3-8)/(7-2)

m = -5/5

m = -1

Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.

Rule: If the slopes multiply to -1, then the lines are perpendicular.

Or you can apply the negative reciprocal rule to go from -1 to 1.

We'll keep this perpendicular slope in mind for later.

----------------

Now let's find the midpoint of points N and M.

Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5

Do the same for the y coordinates:  (y1+y2)/2 = (8+3)/2 = 5.5

The midpoint of N and M is at (4.5, 5.5)

The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.

--------------------

In short, the perpendicular bisector for line segment NM is the equation y = x+1.

If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.

----------------------

At this point, we have the system of equations

\begin{cases}y = x+1\\y = -3x+9\end{cases}

Let's use substitution to solve for x and y

y = x+1

-3x+9 = x+1

-3x-x = 1-9

-4x = -8

x = -8/(-4)

x = 2

y = x+1

y = 2+1

y = 3

So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)

This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.

You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.

I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.

Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.

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Can someone please help with this
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Answer:

   3. 43.96 cm

  4. 81.64 ft

Step-by-step explanation:

3. The formula for the circumference of a circle in terms of radius is ...

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The only answer choice even close to 6.28×(7 cm) is the one shown above.

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<em>Comment on the solution</em>

For questions like these, you only need to be able to estimate the answer to 1 or 2 significant digits. The answer choices are not so close together as to cause any confusion.

6×7 = 42, so the answer will be a few more than 42.

3×26 = 78, so the answer will be within a few numbers larger than that.

In each case, the answer is the largest value on the list. The other choices differ by a factor of 2, so aren't even close.

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Cells B1, C1, and D1 contain the values Seat1Row1, Seat1Row2, and Seat1Row3. If cells B1, C1, and D1 were selected, and autofill
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Answer:

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The autofill feature of Ms Excel works data types such as numbers and alphanumeric among others.

But for autofill to work on alphanumeric in Ms Excel, only the numeric part will be altered.

In this case, the series of text in B1, C1 and D1 are Seat1Row1, Seat1Row2, Seat1Row3

"Seat1Row" will be regarded as string while 1,2,3 will be incremented and the resulting alphanumeric values will be saved in their respective cells.

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