Answer:

Step-by-step explanation:
 
        
             
        
        
        
The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is 
(x - x^2)^2 * sqrt(3)/4. 
Integrating from x = 0 to x = 1, we have 
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4 
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144. 
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
 
        
             
        
        
        
Answer:The greatest common factor is 15 to 10.
Step-by-step explanation:
 
        
             
        
        
        
The function of the water balloon is an illustration of a quadratic function.
The balloon will splat on the ground after 2.5 seconds
The function is given as:

When the balloon splats on the ground, the value of h(t) is 0.
So, we have:

Expand the expression

Factorize the above expression

Factor out 2t - 5 in the 2t - 5

Split the equation into 2

Rewrite as:

Solve for t

The value of t cannot be less than 0 i.e. negative.
So, we have

Divide 5 by 2

Hence, the balloon will splat on the ground after 2.5 seconds
Read more about quadratic functions at:
brainly.com/question/11631534