Since the sum of the angles of a triangle = 180°
Then  <span>80º + (2x + 2)º + 5xº  = 180</span>°
                          82° + (7x)° = 180°
                                    (7x)° = 180° - 82°
                                        x   =  98° ÷ 7
                                    ∴  x   = 14
        
             
        
        
        
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

 
        
             
        
        
        
The answer is (9c/5)+32=F
        
                    
             
        
        
        
Answer:
B
Step-by-step explanation:
Since the triangle is right use the sine/ tangent ratios to solve for x and y
note sin60° =  and tan60° =
 and tan60° = 
sin60° =  =
 = 
ysin60° = 3
y ×  = 3
 = 3
multiply both sides by 2 and divide by 
y v= 6 = 6
 = 6
tan60° =  =
 = 
xtan60° = 3
x ×  = 3
 = 3
divide both sides by 
x = 3 = 3
 = 3
 
        
                    
             
        
        
        
Answer:
percentage change in weight ≈ 10%
Step-by-step explanation:
The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as 
decrease in weight = original weight - new weight
original weight  = 48 kg
new weight = 43 kg
decrease in weight = 48 - 43 = 5 kg
Since the weight decrease their will be a percentage decrease in weight.
% decrease = decrease in weight/original weight × 100
% decrease = 5/48 × 100
% decrease = 500/48
% decrease = 10. 42666666667
percentage change in weight ≈ 10%