edwardelric14
contestada

We want to make an open-top box by cutting out corners of a square piece of
cardboard and folding up the sides. The cardboard is a 9 inch by 9 inch square. The
volume V(x) in cubic inches of the open-top box is a function of the side length x in
inches of the square cutouts.
a.
Write an expression for V(x).
b.
What is the volume of the box when x = 1?
C.
What is a reasonable domain for V in this context.

Respuesta :

The required answers are-

a. The expression for V(x) = x(9 - x)²

b. The volume of the box when x = 1 is 64 cubic square.

c. The reasonable domain for V is  x ∈ [0,9].

What is volume?

Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units or by various imperial units.

Now, the given dimension of cupboard square is 9 inch by 9 inch.

and, the cutout side length be x inch.

So, the length of the box is (9 -x) inch

the width of the box is (9 -x)  inch and

the height of the box is x inch

a. Expression for V(x).

∴The volume of the box, V(x) = (length)*(width)*(height).

⇒The volume of the box, V(x) = x*(9 -x)*(9 -x)

⇒The volume of the box, V(x) = x(9 -x)²

b. volume of the box when x = 1

Put x = 1 in V(x)

V(1) = 1(9 -1)²

V(1) = 8²

V(1) = 64 cubic inches

c. reasonable domain for V

V(x) = x(9 -x)²

y = x(9 -x)²

x(9 -x)² ≥ 0

⇒ x ≥ 0

⇒(9 -x)² ≥ 0

⇒9 -x ≥ 0

⇒ x ≤ 9

⇒ x ∈ [0,9]

So, reasonable domain for V is x ∈ [0,9]

Hence,The required answers are-

a. The expression for V(x) = x(9 - x)²

b. The volume of the box when x = 1 is 64 cubic square.

c. The reasonable domain for V is  x ∈ [0,9].

More about volume :

https://brainly.com/question/23821509

#SPJ2

Otras preguntas