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tangare [24]
3 years ago
7

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form a

n open box. The volume of the box is 420 in.3.
The equation 4x3 – 72x2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.

What is the side length of the square that is cut from each corner, to the nearest inch?

Mathematics
2 answers:
beks73 [17]3 years ago
4 0

Answer:

The length of the side is 3 inches.

Step-by-step explanation:

Given : The volume of the box is 420 inches cube. The equation 4x^3-72x^2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.

To find : The side length of the square that is cut from each corner, to the nearest inch.

Solution :

To solve the equation we solve it using graph.

We plot the graph of the equation y=4x^3-72x^2 + 320x and y=420

The intersection of these points would be the side of the length.

The intersection points are (2.89,420) ,(3,420) and (12.11,420)

We see that the roots of the equation is (0,0) , (8,0), (10,0)

There the factored form is

y=4x^3-72x^2 + 320x=x(10-x)(8-x)

4x^3-72x^2 + 320x = 420

4x(10-x)(8-x)=420

x(10-x)(8-x)=105

x(10-x)(8-x)=3(7)(5)

Thus comparing we get x=3

Therefore, The length of the side is 3 inches.

Reika [66]3 years ago
3 0

The <em><u>correct answer</u></em> is:

3 inches.

Explanation:

We will use the Rational Roots Theorem to solve this.

First we can divide both sides of the equation by 4 in order to simplify it:

\frac{4x^3-72x^2+320x}{4}=\frac{420}[4} \\ \\x^3-18x^2+80=105

In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:

x^3-18x^2+80x-105=105-105 \\x^3-18x^2+80x-105=0

The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.

Using synthetic division, we try 1 in the box:

<u>1 |</u> 1 -18 80 -105

_______<u> 1</u>__<u> -17</u>___<u>63</u>__

1 -17 63 -42

Since there is a remainder, this is not a root. Trying -1,

<u>-1 |</u> 1 -18 80 -105

_______<u>-1</u>__<u> 19 </u>_<u>-99</u>_

1 -19 99 -204

This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.

Trying 3,

3 | 1 -18 80 -105

________<u>3</u>__<u>-45</u>___<u>105</u>_

1 -15 35 0

Since there is no remainder, 3 is a root, and is the answer we are looking for.

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A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the
dem82 [27]

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

-----------

π × r

= 8 × 180. 8 × 180

-------- or ---------

9/2. 4.5

= 8 × 180 × 2

------------

9

= 8 × 20 × 2

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GarryVolchara [31]

Answer:

Factory A should be operated 6.11 days

Factory B should be operated 6.88 days

The minimum cost for factory A is $6,110

The minimum cost for factory B is $5,504

Step-by-step explanation:

Factory A

Daily production: 16 3-speed and 20 10-speed bikes

Total daily production = 16+20 = 36 speed bikes

Order: 80 3-speed and 140 10-speed bikes

Total order = 80+140 = 220 speed bikes

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Cost per day = $1,000

Minimum cost for 6.11 days = $1000 × 6.11 = $6,110

Factory B

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Total daily production = 12+20 = 32 speed bikes

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Cost per day = $800

Cost for 6.88 days = $800 × 6.88 = $5,504

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