Answer:
Dimensions: 
Perimiter: 
Minimum perimeter: [16,16]
Step-by-step explanation:
This is a problem of optimization with constraints.
We can define the rectangle with two sides of size "a" and two sides of size "b".
The area of the rectangle can be defined then as:
This is the constraint.
To simplify and as we have only one constraint and two variables, we can express a in function of b as:
The function we want to optimize is the diameter.
We can express the diameter as:
To optimize we can derive the function and equal to zero.
The minimum perimiter happens when both sides are of size 16 (a square).
Answer:
2 · 7 · 4 + 2 · 10 · 7 + 2 · 4 · 10
2(10 · 4 + 10 · 7 + 4 · 7)
Step-by-step explanation:
Given dimensions of the square prism:
- length = 7 units
- width = 4 units
- height = 10 units
In order to find the surface area, we must find the area of each face.
Area of a rectangle = width x length
The square prism has 3 pairs of faces:
SA of bases = 7 x 4
SA of side 1 = 4 x 10
SA of side 2 = 7 x 10
So the total surface area is
2(7 x 4) + 2(4 x 10) + 2(7 x 10) = 276 units squared
<u>Solutions</u>
2 · 7 · 4 + 2 · 10 · 7 + 2 · 4 · 10
2(10 · 4 + 10 · 7 + 4 · 7)
What you do to solve this is:
1- 498 - 52 = 446.
2- 446 adult tickets were sold.
Answer:
12
Step-by-step explanation:
write it out:
3/7 x x/28
cross-multiply and solve:
3*28 and 7x
3 x 28 = 84
make an expression:
84 = 7x
solve the expression:
7x/7 = 1
84/7 = 12
x =12
