Answer:
![\displaystyle \frac{d}{dx}[3x + 5x] = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%205x%5D%20%3D%208)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Differentiate</u>
- Simplify:
- Derivative Property [Multiplied Constant]:
![\displaystyle y' = 8\frac{d}{dx}[x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%208%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D)
- Basic Power Rule:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
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{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)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
Answer: The required system of equations representing the given situation is
Step-by-step explanation: Given that Sam needs to make a long-distance call from a pay phone.
We are to write a system to represent the situation.
Let x represent the number of minutes Sam talked on the phone and y represents the total amount that he paid for the call.
According to the given information,
with prepaid phone card, Sam will be charged $1.00 to connect and $0.50 per minute.
So, the equation representing this situation is
Also, if Sam places a collect call with the operator he will be charged $3.00 to connect and $0.25 per minute.
So, the equation representing this situation is
Thus, the required system of equations representing the given situation is
if she doesnt have the money ot begin with then the number is going to be negative which means less than ZERO.
9x - 4(x - 2) =x + 20
We move all terms to the left:
- 9x -4(x - 2) - (x + 20) = 0
Multiply
- 9x - 4x -(x + 20) + 8 = 0
We get rid of the parentheses.
We add all the numbers and all the variables.
We move all terms containing x to the left hand side, all other terms to the right hand side
