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vladimir1956 [14]

2 years ago

7

A wheel has a diameter of 3.5 ft. Approximately how far does it travel if it makes 20 complete revolutions?use 22/7 for pie. Ple

ase help!!

1 answer:

neonofarm [45]2 years ago

6 0

220 ft. 22/7 times 3.5ft times 20

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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

2 years ago

HElP aND tHEy Are all DiffERent ???/questions

guapka [62]

Answer:

Step-by-step explanation:

840 red stripes

720 white stripes

6 0

2 years ago

Read 2 more answers

ANSWER AS MANY THROUGH 1 and 9 FOR 15 POINTS

Tamiku [17]

Number 9 is 1.52 because you divide 15.3 by 10 it will be 1 .52

7 0

3 years ago

Which expression is equivalent to r^m ÷ r^n? a. r^m − ^n b. r^m ^n c. r^m ⋅ ^n d. r^m ÷ ^n

Murljashka [212]

$r^m \div r^n= r^{m-n}$

4 0

3 years ago

-129 = -48 - n <br> Thank you

Flauer [41]

−129=−48−n

Simplify:

−129=−48+−n

Flip the equation.

−n−48=−129

Add 48 to both sides.

−n−48+48=−129+48

−n=−81

Divide both sides by -1.

−n/−1 = −81/−1

n=81

3 0

3 years ago