Answer:

General Formulas and Concepts:
<u>Calculus</u>
Integration
Integration Rule [Reverse Power Rule]:                                                           
Integration Rule [Fundamental Theorem of Calculus 1]:                                 
Integration Property [Multiplied Constant]:                                                     
Integration Property [Addition/Subtraction]:                                                   ![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Cpm%20%5Cint%20%7Bg%28x%29%7D%20%5C%2C%20dx)
Area of a Region Formula:                                                                               ![\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5Eb_a%20%7B%5Bf%28x%29%20-%20g%28x%29%5D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
y = 2x + 3
<em>x</em>-interval [3, 4]
<em>x</em>-axis
<em>See attachment for graph.</em>
<u>Step 2: Find Area</u>
- Substitute in variables [Area of a Region Formula]:                                
- [Integral] Rewrite [Integration Property - Addition/Subtraction]:            
- [Integrals] Rewrite [Integration Property - Multiplied Constant]:            
- [Integrals] Integrate [Integration Rule - Reverse Power Rule]:                
- [Integrals] Integrate [Integration Rule - FTC 1]:                                        
- Simplify:                                                                                                      
∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
 
        
             
        
        
        
There will be 72 flowers in total in the large arrangement.
Step-by-step explanation:
No. of red flowers in vase = 4
No. of white flowers in vase = 5
Ratio of red flowers to white flowers = 4:5
No. of red flowers in large arrangement = 32
No. of white flowers in large arrangement = w
Ratio of red flowers to white flowers = 32:w
Using proportion; 
Ratio of red flowers to white flowers :: Ratio of red flowers to white flowers

Product of extreme = Product of mean

Dividing both sides by 4

Total flowers in large arrangement = Red flowers + white flowers 
Total flowers in large arrangement = 32 + 40 =72
There will be 72 flowers in total in the large arrangement.
Keywords: ratio, proportion
Learn more about ratios at:
#LearnwithBrainly
 
        
             
        
        
        
Answer:
π radians
Step-by-step explanation:
The arc cos(- 1) in degrees is 180° and 180° = π radians
 
        
             
        
        
        
Answer:
C AND D
Step-by-step explanation:
it is a rational and real number
 
        
                    
             
        
        
        
Answer:
2204.62
Step-by-step explanation: