<u>Answer</u>:
<em>I'm bad at explaining this but after this, go to sleepppp</em>
<u>Step-by-step explanation:</u>
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Answer:
Step-by-step explanation:
How to write numbers in standard form:
Write the first number 8.
Add a decimal point after it: 8.
Now count the number of digits after 8. There are 13 digits.
So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³
If Kyle has invested $20,000 of the total $160,000 invested, that means the other give investors invested $140,000. Divide the about they invested by the total amount invested, and you will get .875. That is equal to 87.5%. The five investors own 87.5% of the business.
Using the given formula T = LS
And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:
180 = L x 4-1/2
Solve for L by dividing both sides by 4-1/2:
L = 180 / 4-1/2
L = 40
The length should be 40 inches.
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Sum to Product:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-\sin 2C](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cqquad%202%5Csin%5Cbigg%28%5Cdfrac%7B2A%2B2B%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A%20-%202B%7D%7B2%7D%5Cbigg%29-%5Csin%202C)
![\text{Double Angle:}\qquad 2\sin\bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A - 2B}{2}\bigg)-2\sin C\cdot \cos C](https://tex.z-dn.net/?f=%5Ctext%7BDouble%20Angle%3A%7D%5Cqquad%202%5Csin%5Cbigg%28%5Cdfrac%7B2A%2B2B%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A%20-%202B%7D%7B2%7D%5Cbigg%29-2%5Csin%20C%5Ccdot%20%5Ccos%20C)
![\text{Simplify:}\qquad \qquad 2\sin (A + B)\cdot \cos (A - B)-2\sin C\cdot \cos C](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%202%5Csin%20%28A%20%2B%20B%29%5Ccdot%20%5Ccos%20%28A%20-%20B%29-2%5Csin%20C%5Ccdot%20%5Ccos%20C)
![\text{Given:}\qquad \qquad \quad 2\sin C\cdot \cos (A - B)+2\sin C\cdot \cos (A+B)](https://tex.z-dn.net/?f=%5Ctext%7BGiven%3A%7D%5Cqquad%20%5Cqquad%20%5Cquad%202%5Csin%20C%5Ccdot%20%5Ccos%20%28A%20-%20B%29%2B2%5Csin%20C%5Ccdot%20%5Ccos%20%28A%2BB%29)
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
![\text{Sum to Product:}\qquad 2\sin C\cdot 2\cos A\cdot \cos B](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cqquad%202%5Csin%20C%5Ccdot%202%5Ccos%20A%5Ccdot%20%5Ccos%20B)
![\text{Simplify:}\qquad \qquad 4\cos A\cdot \cos B \cdot \sin C](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%204%5Ccos%20A%5Ccdot%20%5Ccos%20B%20%5Ccdot%20%5Csin%20C)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C ![\checkmark](https://tex.z-dn.net/?f=%5Ccheckmark)