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noname [10]
2 years ago
3

How many minutes are in the time interval from 7:09 a.m. to 10:36 a.m.?

Mathematics
1 answer:
Elan Coil [88]2 years ago
7 0
7:09 - 10:09 = 3 hours
10:09 - 10:39 = 30 minutes
10:39 - 10:36 = -3 minutes

3 hours and 27 minutes
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What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real
dem82 [27]
We know the following relationship:

csc(\theta)=\frac{1}{sin(\theta)}

The domain of a function are the inputs of the function, that is, a function f is a relation that assigns to each element x in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function csc(\theta) we can write its domain as follows:

1. D<span>omain of validity for csc(\theta):
</span>
D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0 
 
When:

sin(\theta)=0?

when:

\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi

where k is an integer either positive or negative. That is:

sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...

To match this with the choices above, the answer is:

<span>"All real numbers except multiples of \pi"

</span>
2. which identity is not used in the proof of the identity 1+cot^{2}(\theta)=csc^{2}(\theta):

This identity can proved as follows:

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The identity that is not used is as established in the statement above:

<span>"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

</span>\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)<span>


</span>
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