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Nookie1986 [14]
3 years ago
8

How do you construct a line segment perpendicular to the segment given through the point given?

Mathematics
1 answer:
maw [93]3 years ago
8 0
Use the opposite reciprocal of the slope of the known line segment, then plug the point given as well as the opposite reciprocal of the slope into y = mx + b
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2 years ago
Using the bijection rule to count binary strings with even parity.
AleksandrR [38]

Answer:

Lets denote c the concatenation of strings. For a binary string <em>a</em> in B9, we define the element f(a) in E10 this way:

  • f(a) = a c {1} if a has an odd number of 1's
  • f(a) = a c {0} if a has an even number of 1's

Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

f   is well defined:

To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

f is injective (or one on one):

If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

f is surjective:

Let y be an element of E10, Let x be the first 9 elements of y, then f(x) = y:

  • If x has an even number of 1's, then the last digit of y has to be 0, and f(x) = x c {0} = y
  • If x has an odd number of 1's, then the last digit of y has to be a 1, otherwise it wont be an element of E10, and f(x) = x c {1} = y

This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

3 0
3 years ago
a wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a
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Answer:

  • 5 km/h or 6 km/h

Step-by-step explanation:

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  • 6/(x - 2)

<u>Time in the lake:</u>

  • 15/x

<u>The difference:</u>

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Solve for x to find the speed of the boat

<u>Multiply both sides by x(x - 2) to clear the fraction:</u>

  • 6x = 15(x - 2) - x(x - 2)
  • 6x = 15x - 30 - x² + 2x
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  • (x - 5)(x - 6) =0
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3 years ago
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Pablo runs 1.5 miles on his first day of training for a road race the next day he increases his distance run by 0.5 miles the da
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