Answer:
Exact form: ![\sin{(6x)} = \frac{8}{9}](https://tex.z-dn.net/?f=%5Csin%7B%286x%29%7D%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
Decimal form: ![\sin{(6x)} = 0.8889](https://tex.z-dn.net/?f=%5Csin%7B%286x%29%7D%20%3D%200.8889)
The solution for x is: The solution for x is of 10.455º
Step-by-step explanation:
We are given the following equation:
![8 = 9\sin{(6x)}](https://tex.z-dn.net/?f=8%20%3D%209%5Csin%7B%286x%29%7D)
Placing into the desired format, the exact format is:
![\sin{(6x)} = \frac{8}{9}](https://tex.z-dn.net/?f=%5Csin%7B%286x%29%7D%20%3D%20%5Cfrac%7B8%7D%7B9%7D)
In the decimal part, we divide 8 by 9. So
![\sin{(6x)} = 0.8889](https://tex.z-dn.net/?f=%5Csin%7B%286x%29%7D%20%3D%200.8889)
Solving for x:
We apply the inverse sine. So
![\sin^{-1}{\sin{(6x)}} = \sin^{-1}{0.8889}](https://tex.z-dn.net/?f=%5Csin%5E%7B-1%7D%7B%5Csin%7B%286x%29%7D%7D%20%3D%20%5Csin%5E%7B-1%7D%7B0.8889%7D)
![6x = 62.73](https://tex.z-dn.net/?f=6x%20%3D%2062.73)
![x = \frac{62.73}{6}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B62.73%7D%7B6%7D)
![x = 10.455](https://tex.z-dn.net/?f=x%20%3D%2010.455)
The solution for x is of 10.455º
The first term of the sequence is -3.
According to the formula each next term will be obtained by multiplying the previous term by 2.
So, next terms will be:
Second term = 2 x First Term = 2 x (-3) = - 6
Third term = 2 x (-6) = -12
Fourth term = -24
Fifth term = -48
Sixth term = -96
So, the sequence will be:
-3, -6, -12, -24, -48, -96 ...
The solution to this similar triangles is; XY = 11.25
<h3>What is the ratio of the similar triangles?</h3>
In triangle ABC, we see that;
AB = 5, BC = 12, CA = 8.
In triangle XYZ;
XY = N, YZ = 27 ZX = 18
To find:
The length of XY
If two triangles are similar, then their corresponding sides are proportional.
Since ΔABC is similar to ΔXYZ, then we say that;
AB/XY = BC/YZ = CA/ZX
5/N = 12/27 = 8/18
Cross multiply to get;
8N = 18 * 5
N = 90/8
N = 11.25
Thus, the solution is XY = 11.25
Read more about Ratio of Similar Triangles at; brainly.com/question/18473666
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Answer:
Let total non-fiction books = 3x
And total fiction books = 5x
After reading 6 non-fiction books, remaining non-fiction books = 3x-6
After reading 13 fiction books, total fiction books remaining fiction books = 5x-13
(3x-6)/(5x-13) = 3/4
Solving for x, we get x = 5
So total non-fiction books = 15 and fiction books=25
So total number of books bought = 40
Answer:
Step-by-step explanation:
Here you go mate
Use PEMDAS
Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction
Step 1
4n-9=2(5+2n) Equation/Question
Step 2
4n-9=2(5+2n) Remove parenthesis
4n-9=4n+10
Step 3
4n-9=4n+10 Subtract 4n to sides
-9=10
Step 4
-9=10 Add 9
0=19
Answer
No solutions
Hope this helps