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Alchen [17]
2 years ago
13

nickel has an approximate diameter of 20 mm and an approximate thickness of 2 mm what is the approximate volume of a stack of 40

nickels?
Mathematics
1 answer:
ziro4ka [17]2 years ago
8 0

Answer:

The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.

Step-by-step explanation:

A nickel can be modelled by the formula of a right cylinder, the approximate volume of the stack of nickels (V_{net}), measured in cubic milimeters, is the product of the number of elements (n), no unit, and the volume of each element (V), measured in cubic milimeters. That is:

V_{net} = n\cdot V (1)

By volume equation of right cylinder, we have the following formula:

V_{net} = \frac{\pi}{4}\cdot n \cdot D^{2}\cdot h (2)

Where:

n - Amount of nickels, no unit.

D - Diameter of nickel, measured in milimeters.

h - Thickness of nickel, measured in milimeters.

If we know that n = 40, D = 20\,mm and h = 2\,mm, then the net volume of the stack of nickels is:

V_{net} = \frac{\pi}{4}\cdot (40)\cdot (20\,mm)^{2}\cdot (2\,mm)

V_{net} \approx 25132.741\,mm^{3}

The approximate volume of a stack of 40 nickels is 25132.741 cubic milimeters.

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The discount amount would be $1470.00

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For given question,

A car dealer gave a 7% discount to the first 50 people through the door.

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this means, to find the discount amount, we need to find the 7 percent of $21,000.00

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White raven [17]

<em><u>Statement:</u></em>

The hypotenuse of a right angled triangle is 2√13 cm. If the smaller side is increased by 2 cm and the larger side is increased by 3 cm, the new hypotenuse will be √117 cm.

<em><u>To find out:</u></em>

The length of the larger side of the right angled triangle.

<em><u>Solution:</u></em>

Let us consider x as the smaller side and y as the larger side.

Then, in the right angled triangle,

x² + y² = (2√13)² ...(I) [By Pythagoras Theorem]

Now, if the smaller side is increased by 2 cm, then the smaller side will be (x + 2).

And if the larger side is increased by 3 cm, then the larger side will be (y + 3).

Then, in the new right angled triangle,

(x + 2)² + (y + 3)² = (√117)² [By Pythagoras Theorem]

or, x² + 2 × 2 × x + 2² + y² + 2 × 3 × y + 3² = (√117)²

or, x² + 4x + 4 + y² + 6y + 9 = (√117)²

or, x² + y² + 4x + 6y + 13 = (√117)²

Now, put the value of x² + y² from equation (I),

or, (2√13)² + 4x + 6y + 13 = (√117)²

or, (2 × 2 × √13 × √13) + 4x + 6y + 13 = (√117 × √117)

or, 52 + 4x + 6y + 13 = 117

or, 4x + 6y = 117 - 52 - 13

or, 4x + 6y = 52

or, 4x = 52 - 6y

or, x = \frac {(52 - 6y)}{4} ...(II)

Now, put the value of x of equation (II) in (I),

x² + y² = (2√13)²

or, \frac {(2704-624y +36y²)}{16} + y² = 52

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or, y²-12y +36 = 0 ÷ 52

or, y²-12y +36 = 0

or, (y)² - 2 × 6 × y + (6)² = 0

or, (y - 6)² = 0

or, y - 6=0

or, y = 6

We have taken y as the length of the larger side of the right angled triangle.

So, the length of the larger side is 6 cm.

<em><u>Answer:</u></em>

6 cm

Hope you could understand.

If you have any query, feel free to ask.

6 0
2 years ago
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