Answer:

Step-by-step explanation:
we know that
Using proportion

Answer:
The maximum volume is: 11.52 *10.52*2.74 = 332.06 
Step-by-step explanation:
Let x is the side of the square in inches.(x >0)
The volume of the resulting box when the flaps are folded up can be expressed as:
V = x (17 -2x)(16-2x)
= (17x -2
)(16-2x)
=
- 66
+ 272x
To find the value of x which yields the maximum of volume (V), take the first derivative of this equation and set it equal to zero.
= 12
- 66x + 272
Solve 12
- 132x + 272 = 0
<=> x = 2.74
The dimensions of the box are:
Length: (17 -2x) = (17 -2*2.74) = 11.52
Width: (16-2x) = (16-2*2.74) = 10.52
High: x = 2.74
So the maximum volume is: 11.52 *10.52*2.74 = 332.06 
answer
11.46m²
Area = π·(d
2
)2 = 3.14·(3.82
2
)2 = 3.14·(1.91)2 = 11.46
Given the integral on the picture, we can use integration by parts to find the antiderivative.
First, let u = t² an dv = cos3t dt. If we find the derivative of u and the integral of v, we get:

then, using the formula for integration by parts, we have the following:

notice that the resulting integral on the right side also can be solved by parts. The solution of this integral is the following:

then, combining both results, we get: