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Naily [24]
3 years ago
10

Write 224% as a fraction in Lowest term

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
3 0
You should Google it because I forgot but others might know
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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
What is the area of the triangle
ehidna [41]

Answer:

45.1 km^2

hope this helps

have a good day :)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
mrs long drive from nashville tennessee to atlanta georgia at an average rate of 50 miles per hour. The following equation can b
Scrat [10]

50t = 250 \\ t =  \dfrac{250}{50}  \\ t = 5

Answer is C. 5

Hope this helps. - M
5 0
3 years ago
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How much fence is needed to surround a garden with side lengths of 2.1 meters, 3.5 meters, 1.9 meters, and 2.25 meters?
ikadub [295]

Answer: 9.75m

Step-by-step explanation:

3.5 + 2.1 + 1.9 + 2.25 = 5.75 + 4 = 9.75 m

8 0
3 years ago
Given the equation 5 + x -12 = 2x - 7. Part A. Solve the equation 5 + x - 12 = 2x - 7. In your final answer, be sure to state th
Nitella [24]

Answer:

srry guys i dont know this

Step-by-step explanation:

5 0
3 years ago
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