Answer:
8 inches
Step-by-step explanation:
ROCK is a kite. The area of a kite is denoted by:
A = (1/2) * d1 * d2, where d1 and d2 are the diagonals
Here, the two diagonals are x and 15, and we know the area is 60, so plug these into the equation:
A = (1/2) * d1 * d2
A = (1/2) * 15 * x
60 = (1/2) * 15 * x
x = 120 / 15 = 8
Thus, x = 8 inches.
Answer:
4π
Step-by-step explanation:
We are asked to calculate the area of a circle whose diameter is equal to 4, we know that the area of the circle is given by the following equation:
A = π * (r ^ 2)
where r is the radius of the circle, we know that the radius of the circle is half the diameter, therefore:
r = d / 2 = 4/2
r = 2
replacing, we are left with:
A = π * (2 ^ 2)
A = 4π
Which means that the area of the circle is 4π
Answer:
The maximum volume of the open box is 24.26 cm³
Step-by-step explanation:
The volume of the box is given as 
, where 
and 
.
Expand the function to obtain:
Differentiate wrt x to obtain:
To find the point where the maximum value occurs, we solve
Discard x=3.54 because it is not within the given domain.
Apply the second derivative test to confirm the maximum critical point.
, 
This means the maximum volume occurs at 
.
Substitute into to get the maximum volume.
The maximum volume of the open box is 24.26 cm³
See attachment for graph.
4.5(8 - x) + 36 = 102 - 2.5(3x + 24)
36 - 4.5x + 36 = 102 - 7.5x - 60
72 - 4.5x = 42 - 7.5x
-4.5x + 7.5x = 42 - 72
3x = - 30
x = -30/3
x = -10 <===
Hope this helps!
