Find four consecutive integers whose sum is 114.
1 answer:
27, 28, 29 and 30
consecutive integers have a difference of 1 between each one
let n be the first integer then the next three are
n + 1, n + 2 and n + 3
hence n + n + 1 + n + 2 + n + 3 = 114
4n + 6 = 114
subtract 6 from both sides of the equation
4n = 114 - 6 = 108
divide both sides by 4
n = = 27
n = 27, n+ 1 = 28, n + 2 = 29, n + 3 = 30
the consecutive integers are 27, 28, 29 and 30
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Answer:
C = 64.145º
Step-by-step explanation:
The Law of Sines is as follows:
=
=
The problem can be draw as the picture attached.
Now, the values of the sides and angles can be substituted into the Law of Sines, and because all parts are equal, only two are needed:
=
Next, cross-multiply:
7sin40º = 5sinC
Then, divide both sides by 5:
= sinC
Finally, take the inverse sin of the left side and convert into a decimal:
C = (
)
C = 64.145
