Answer:
BC ≈ 14.5 cm
Step-by-step explanation:
Using the sine ratio in the right triangle
sin65° = =
=
( multiply both sides by 16 )
16 × sin65° = BC , then
BC ≈ 14.5 cm ( to the nearest tenth )
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2018 is the 70th term of the progression.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.
Explanation
We start out finding the common difference of the progression:
46-17 = 29
Now we write the explicit formula for the sequence. It is of the form
We set this equal to 2018 to see if the answer is a whole number. If it is, it will be the term number that gives us 2018:
2018=17+29(n-1)
Using the distributive property,
2018=17+29*n-29*1
2018=17+29n-29
Combine like terms:
2018=29n-12
Add 12 to both sides:
2018+12=29n-12+12
2030=29n
Divide both sides by 29:
2030/29=29n/29
70=n
Since n=70, this means 2018 is the 70th term of the sequence.