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FromTheMoon [43]
3 years ago
15

Find the parametric equation of the line r(t), 0 ≤ t ≤ 1, between P = (2, − 3, 1) and Q = (− 2, 1, 7).

Mathematics
1 answer:
alisha [4.7K]3 years ago
7 0

Answer:

x=-2+3t , y=-9-10t

Step-by-step explanation:

I'm going to start by solving the first equation for t....which will give (x-x1)/(x2-x1) =t.

You can now substitute this in the second equation to get....y=y1 + (y2-y1)(x-x1)/(x2-x1)

Rearranging, you get y-y1 = (y2-y1) / (x2-x1) * (x-x1) which is equivalent to y-y1= m(x-x1) which is the point-slope formula for a line.

So since t was varying between 0 and 1,

plugging in t=0 you get x=x1 and y = y1 givin you the coordinate (x1,y1)

similarly, plugging in t=1 leads to (x2,y2)

So this is a representation of a segment connecting these 2 points.

B) just plug in the points into your given formula from part a to get...

x=-2 +(1--2)t and y = 9 +(-1-9)t

or x=-2+3t , y=-9-10t

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A survey of 1,107 tourists visiting Orlando was taken. Of those surveyed:
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Answer:

602 tourists visited only the LEGOLAND.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of this set.

I am going to say that:

-The set A represents the tourists that visited LEGOLAND

-The set B represents the tourists that visited Universal Studios

-The set C represents the tourists that visited Magic Kingdown.

-The value d is the number of tourists that did not visit any of these parks, so: d = 58

We have that:

A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)

In which a is the number of tourists that only visited LEGOLAND, A \cap B is the number of tourists that visited both LEGOLAND and Universal Studies, A \cap C is the number of tourists that visited both LEGOLAND and the Magic Kingdom. and A \cap B \cap C is the number of students that visited all these parks.

By the same logic, we have:

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)

This diagram has the following subsets:

a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)

There were 1,107 tourists suveyed. This means that:

a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107

We start finding the values from the intersection of three sets.

The problem states that:

36 tourists had visited all three theme parks. So:

(A \cap B \cap C) = 36

72 tourists had visited both LEGOLAND and Universal Studios. So:

(A \cap B) + (A \cap B \cap C) = 72

(A \cap B) = 72 - 36

(A \cap B) = 36

79 tourists had visited both the Magic Kingdom and Universal Studios

(B \cap C) + (A \cap B \cap C) = 79

(B \cap C) = 79 - 36

(B \cap C) = 43

68 tourists had visited both the Magic Kingdom and LEGOLAND

(A \cap C) + (A \cap B \cap C) = 68

(A \cap C) = 68 - 36

(A \cap C) = 32

258 tourists had visited Universal Studios:

B = 258

B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)

258 = b + 43 + 36 + 36

b = 143

268 tourists had visited the Magic Kingdom:

C = 268

C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)

268 = c + 32 + 43 + 36

c = 157

How many tourists only visited the LEGOLAND (of these three)?

We have to find the value of a, and we can do this by the following equation:

a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 1,107

a + 143 + 157 + 58 + 36 + 32 + 43 + 36 = 1,107

a = 602

602 tourists visited only the LEGOLAND.

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3 years ago
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