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den301095 [7]
3 years ago
9

Experts/ace/geniuses helpp

Mathematics
1 answer:
Alex Ar [27]3 years ago
8 0
Square root 144 =  12 so this is the rational number
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Given that cosΘ = -square root 2/2 and that Θ lies in quadrant III, determine the value of sinΘ.
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Answer:

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Step-by-step explanation:

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?
irga5000 [103]
The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

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for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


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n=12k+5=12*415+5=4985

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The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

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