We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.

The side of box will be $8-x-x=8-2x$ and $10-x-x=10-2x$ .

The height of the box will be $x$ .

The volume of box will be area of base times height.

$\text{Volume of box}=(8-2x)(10-2x)\cdot x$

Now we will use FOIL to simplify our expression.

$\text{Volume of box}=(80-16x-20x+4x^2)\cdot x$

$\text{Volume of box}=(80-36x+4x^2)\cdot x$

Now we will distribute x.

$\text{Volume of box}=80x-36x^2+4x^3$

$V(x)=80x-36x^2+4x^3$

Therefore, the volume of the box would be $V(x)=80x-36x^2+4x^3$ .

6 0

3 years ago

Help me find answer to this

Debora [2.8K]

Answer:

$\angle B=41.81^\circ$

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

The sine ratio relates the opposite side of an angle of the triangle with the hypotenuse:

$\displaystyle \sin B=\frac{\text{opposite leg}}{\text{hypotenuse}}$

Here, the opposite leg to angle B is the side CA=2, and the hypotenuse is the side AB=3, thus:

$\displaystyle \sin \angle B=\frac{2}{3}=0.667$

Calculating the inverse sine function:

$\angle B=\arcsin (0.667)$

$\boxed{\angle B=41.81^\circ}$

5 0

3 years ago