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3 years ago

Estimate the sum or difference of 1 3/8 subtract 8/9

Mathematics

2 answers:

deff fn [24]3 years ago

7 0

Answer: https://www.calculatorsoup.com/calculators/math/fractionsestimating.php

use this website it will help

sasho [114]3 years ago

4 0

0.48611111111 = 0.486
Just turn it into a fraction

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A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

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

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

If a 2 centimeter cube is placed inside a box that is 9 cm by 5 cm by 8cm ,

Bumek [7]

Answer:

360 cm3

Step-by-step explanation:

Option d is the right answer

8 0

3 years ago

Order the numbers from least to greatest<br><br>-3,9,0,-11,7,-6

igor_vitrenko [27]

-11 ,-3, -6, 0, 7, 9 I hope im right

7 0

3 years ago

Write an e explicit formula for an, the nth term of the sequence 22, 19, 16, ...<br>

alexira [117]

Answer:

$a_{n} = 22 + (-3)(n - 1)$

Step-by-step explanation:

The first term is 22. It looks like each term after that is the term before, plus a negative 3.

a-sub-one = 22

common difference = d= -3

Formula for $a_{n}$ :

$a_{n} = 22 + (-3)(n - 1)$ = 25 - 3n

4 0

3 years ago

I need to know how to fill in the chart Ik how to plug it in it just isn't working out when I'm doing it any help?

Vanyuwa [196]

Okay so -2 would be where you plot your first point because it is B in the equation. Then you would go up 3 units (Bc it's positive) and to the right one unit (BC it's positive) The three is the same as 3/1 and it is M in the equation which is your slope so that is where I got that number from. So you just continue the pattern of up 3 over to the right 1 until you reach the end of the graph. The slope would be 3 and the y intercept will be the number that is plotted on the y axis

5 0

3 years ago

Estimate the sum or difference of 1 3/8 subtract 8/9​

Estimate the sum or difference of 1 3/8 subtract 8/9