Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).

The formula for a rectangular box = L × B × W

= (23 -2y)(13-2y) (y)

= (299 - 46y - 26y + 4y²)y

= 299y - 72y² + 4y³

Now for the maximum volume:

dV/dy = 0

This implies that:

299y - 72y² + 4y³ = 299 - 144y + 12y² = 0

By using the quadratic formula; we have :

$= \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}$

where;

a = 12; b = -144 and c = 299

$= \dfrac{-(-144) \pm \sqrt{(-144)^2 -4(12)(299)}}{2(12)}$

$= \dfrac{144 \pm \sqrt{20736 -14352}}{24}$

$= \dfrac{144 \pm \sqrt{6384}}{24}$

$= \dfrac{144 \pm79.90}{24}$

$= \dfrac{144 + 79.90}{24} \ \ OR \ \ \dfrac{144 - 79.90}{24}$

$= 9.33 \ \ OR \ \ 2.67$

Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33

Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.

3 0

3 years ago

The radius of a spherical balloon is 1/2 foot. the radius of a second one is 3/4 foot. how do the volumes of the balloons compar

nika2105 [10]

V=(4/3)r^3
first one
V=(4/3)(1/2)^3
V=4/24
V=1/6

V=(4/3)(3/4)^3
V=108/192
V=9/16

compare

1/6 to 9/16

16/96 compared to 54/96
well, the bigger ballon is 19/8 ft^3 bigger than smaller oe

8 0

3 years ago

1. Which of the following is a solution to 2+2 6? O - 4 -2 0 0 2 4

xz_007 [3.2K]

Answer:

Step-by-step explanation:

In general, a solution of a system in two variables is an ordered pair that makes BOTH equations true. In other words, it is where the two graphs intersect, what they have in common. So if an ordered pair is a solution to one equation, but not the other, then it is NOT a solution to the system.

5 0

3 years ago

Read 2 more answers

What is the equation of the line that passes through the point (−0.5,8) and has a slope of −5?

natima [27]

Answer:

Slope=-1.8, X=-0.5, y=1.9

Equation is y^2-y^1=m(x^2-x^1).

Y-1.9=-1.8(X-(-0.5))

Y-1.9=-1.8x+0.90

Add 1.9 on both sides.

Y= -1.8x+1.

I hope this helps you.

Step-by-step explanation:

7 0

3 years ago