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Ratling [72]
2 years ago
10

PLEASE I NEED HELP WITH THIS

Mathematics
1 answer:
Ber [7]2 years ago
3 0

Given:

The figure of a circle.

To find:

The measure of arc AD and measure of each arc.

Solution:

The measure of arc is equal to the central angle of that arc.

The central angle of arc AD is 105 degrees. So,

m(arc(AD))=105^\circ

The central angle of arc BC is 35 degrees. So,

m(arc(BC))=35^\circ

The central angle of arc CD is 50 degrees. So,

m(arc(CD))=50^\circ

The central angle of a complete circle is 360 degrees. So,

m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ

105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ

190^\circ+m(arc(AB))=360^\circ

m(arc(AB))=360^\circ-190^\circ

m(arc(AB))=170^\circ

Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°

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Could the inverse of a non-function be a function? Explain or give an example.
Kitty [74]

Answer:

The inverse of a non-function mapping is not necessarily a function.

For example, the inverse of the non-function mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! is the same as itself (and thus isn't a function, either.)

Step-by-step explanation:

A mapping is a set of pairs of the form (a,\, b). The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.  

A mapping is a function if and only if for each possible input value x, at most one of the distinct pairs includes x\! as the value of first entry.

For example, the mapping \lbrace (0,\, 0),\, (1,\, 0) \rbrace is a function. However, the mapping \lbrace (0,\, 0),\, (1,\, 0),\, (1,\, 1) \rbrace isn't a function since more than one of the distinct pairs in this mapping include 1 as the value of the first entry.

The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping \lbrace (a_{1},\, b_{1}),\, (a_{2},\, b_{2})\rbrace is the mapping \lbrace (b_{1},\, a_{1}),\, (b_{2},\, a_{2})\rbrace.

Consider mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!. This mapping isn't a function since the input value 0 is the first entry of more than one of the pairs.

Invert \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! as follows:

  • (0,\, 0) becomes (0,\, 0).
  • (0,\, 1) becomes (1,\, 0).
  • (1,\, 0) becomes (0,\, 1).
  • (1,\, 1) becomes (1,\, 1).

In other words, the inverse of the mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! would be \lbrace (0,\, 0),\, (1,\, 0),\, (0,\, 1),\, (1,\, 1) \rbrace\!, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)

Thus, \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! is an example of a non-function mapping that is still not a function.

More generally, the inverse of non-trivial ellipses (a class of continuous non-function \mathbb{R} \to \mathbb{R} mappings, including circles) are also non-function mappings.

3 0
2 years ago
John and Liz are sharing a large pizza. John ate of the pizza, and Liz ate of the pizza. How much of the pizza is left?
Aloiza [94]
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kykrilka [37]

Answer:

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So since the experimental probability is the number of times an event occurs out of the total number of trials...

The answer to "what is the experimental probability that the band's  next show will be sold out?" Is \frac{1}{5}!!!

Hope this helped you!

Have a nice evening!

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