The volume of a box can be found with the function V, where x is the length of the shortest edge of the box: V(x) = x3 + 5x2 – 1
1 answer:
Answer:
The length of the shortest edge of the box is 3 units
Step-by-step explanation:
Since the volume of the box is given by the function
V(x) = x³ + 5x² – 14x
Where V is the volume and x if the length of the shortest edge of the box.
To determine the length of the shortest edge of the box if it has a volume of 30 cubic units, we will put V(x) = 30 and then find the value of x.
30 = x³ + 5x² – 14x
∴ x³ + 5x² – 14x – 30 = 0
The solution to the cubic equation is shown in the attachments below.
x₁ = 3 , x₂ = – 1.55, and x₃ = – 6.45
Since the length cannot be negative, the length of the shortest edge of the box is 3 units.
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Answer:
(a) 12π in
(b) 53.5 in
(c) 96 grams
Step-by-step explanation:
In the figure attached, the ornament is shown
(a) four three-quarter circles is equivalent to 4*3/4 = 3 circles. The perimeter of a circle is the total length of the circular portions.
Perimeter of each circle: 2*π*r
The radius is 2 in long, then for 3 circles:
Perimeter = 3*2*π*2 = 12π in
(b) Perimeter of square: 4*side length
The side length of the square is 4 in, then:
Total length of wire needed = 4*4 + 12π = 53.5 in
(c) The wire weighs 1.8 grams per inch, then:
total weight of the ornament = 1.8 grams/in * 53.5 in = 96 grams
