Answer:
8.6
Step-by-step explanation:
Sine is opposite/hypotenuse so you have
Sin20° = a/25.
To get a you have to multiply 25 to both sides of the equation to get
25 Sin20° = a
Find Sin20° on a calculator and you'll get approximately 0.3420
Then you multiply Sin20° by 25 and you'll get approximately 8.5505 which rounds to 8.6 which is a.
Answer:
The first three terms of the series are 8, 10 and 12. The number of terms is 12 to make the sum 228.
Step-by-step explanation:
The series is defined as
![t_n=2(n+3)](https://tex.z-dn.net/?f=t_n%3D2%28n%2B3%29)
Put n=1.
![t_1=2(1+3)=2\times 4=8](https://tex.z-dn.net/?f=t_1%3D2%281%2B3%29%3D2%5Ctimes%204%3D8)
Put n=2.
![t_2=2(2+3)=2\times 5=10](https://tex.z-dn.net/?f=t_2%3D2%282%2B3%29%3D2%5Ctimes%205%3D10)
Put n=3.
![t_3=2(3+3)=2\times 6=12](https://tex.z-dn.net/?f=t_3%3D2%283%2B3%29%3D2%5Ctimes%206%3D12)
The first three terms of the series are 8, 10 and 12.
It is an arithmetic series. The first terms is 8 and the common difference is
![d=a_2-a_1=10-8=2](https://tex.z-dn.net/?f=d%3Da_2-a_1%3D10-8%3D2)
The sum of n terms of an arithmetic series is
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
![288=\frac{n}{2}[2(8)+(n-1)2]](https://tex.z-dn.net/?f=288%3D%5Cfrac%7Bn%7D%7B2%7D%5B2%288%29%2B%28n-1%292%5D)
![288=\frac{2n}{2}[8+n-1]](https://tex.z-dn.net/?f=288%3D%5Cfrac%7B2n%7D%7B2%7D%5B8%2Bn-1%5D)
![288=n[n+7]](https://tex.z-dn.net/?f=288%3Dn%5Bn%2B7%5D)
![0=n^2+7n-288](https://tex.z-dn.net/?f=0%3Dn%5E2%2B7n-288)
![0=n^2+19n-12n-288](https://tex.z-dn.net/?f=0%3Dn%5E2%2B19n-12n-288)
![0=n(n+19)-12(n+19)](https://tex.z-dn.net/?f=0%3Dn%28n%2B19%29-12%28n%2B19%29)
![0=(n+19)(n-12)](https://tex.z-dn.net/?f=0%3D%28n%2B19%29%28n-12%29)
Equate each factor equal to zero.
![n=-19,12](https://tex.z-dn.net/?f=n%3D-19%2C12)
The number of terms can not be negative, therefore the value of n must be 12.
Yes. Rational numbers are numbers that never end. 2.75 ends at the five. Therefore it is rational!
Imagine you're at origin when you saw another trial 45 degrees from your trail
so the correct answer is the answer is arctan(cos(45)tan(10))
Answer:
196.47%
Step-by-step explanation:
move the decimal to the right two times