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Serhud [2]
4 years ago
15

The thickness of a quarter is approximately 2 millimeters. How many quarters would you need to make a two kilometer high pile? a

. 100,000 c. 1,000,000 b. 2,000,000 d. 4,000,000
Mathematics
1 answer:
Romashka-Z-Leto [24]4 years ago
4 0

We need 1,000,000 quaters to make a two kilometer pile

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

The thickness of a quarter is approximately 2 millimeters

We need to find the quarters needed to make two kilometer high pile

Let us first convert 2 km to millimeters

<em><u>Use the conversion factor</u></em>

1 kilometer = 1000000 millimeters

Therefore,

2 kilometer = 2 x 1000000 = 2000000 millimeters

We need 2,000,000 mm to make a 2 km pile

Given that, Each quarter is 2 millimeters thick

thickness of quarter = 2 millimeters

<em><u>Divide the total milimetres by the thickness of a quarter</u></em>

\rightarrow \frac{2000000}{2} = 1000000

Thus we need 1,000,000 quaters to make a two kilometer pile

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A conveyor belt carries supplies from the first floor to the second floor, which is 39 feet higher.
Murljashka [212]

The supplies travelled 45ft and it took 0.6min to get to the next floor.

<h3>What is trigonometry?</h3>

Trigonometry is the branch of mathematics dealing with the relationship between the sides of a triangle and the angles.

Analysis:

The supplies distance travelled, distance of first floor from second floor and the ground form a right angled triangle.

so that sin 60 = 39/distance travelled by supplies

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In conclusion, the distance and time time taken for the supplies to get to the next floor is 45feet and 0.6 min respectively.

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2 years ago
Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
Jobisdone [24]
This question is in reverse (in two ways): 

<span>1. The definition of an additive inverse of a number is precisely that which, when added to the number, will give a sum of zero. </span>

<span>The real problem, in certain fields, is usually to show that for all numbers in that field, there exists an additive inverse. </span>

<span>Therefore, if you tell me that you have a number, and its additive inverse, and you plan to add them together, then I can tell you in advance that the sum MUST be zero. </span>

<span>2. In your question, you use the word "difference", which does not work (unless the number is zero - 0 is an integer AND a rational number, and its additive inverse is -0 which is the same as 0 - the difference would be 0 - -0 = 0). </span>

<span>For example, given the number 3, and its additive inverse -3, if you add them, you get zero: </span>
<span>3 + (-3) = 0 </span>

<span>However, their "difference" will be 6 (or -6, depending which way you do the difference): </span>

<span>3 - (-3) = 6 </span>
<span>-3 - 3 = -6 </span>

<span>(because -3 is a number in the integers, then it has an additive inverse, also in the integers, of +3). </span>

<span>--- </span>

<span>A rational number is simply a number that can be expressed as the "ratio" of two integers. For example, the number 4/7 is the ratio of "four to seven". </span>

<span>It can be written as an endless decimal expansion </span>
<span>0.571428571428571428....(forever), but that does not change its nature, because it CAN be written as a ratio, it is "rational". </span>

<span>Integers are rational numbers as well (because you can always write 3/1, the ratio of 3 to 1, to express the integer we call "3") </span>

<span>The additive inverse of a rational number, written as a ratio, is found by simply flipping the sign of the numerator (top) </span>

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<span>(4/7) + (-4/7) = 0/7 = 0 </span>

<span>If you need to "prove" it, you begin by the existence of additive inverses in the integers. </span>
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<span>For example, the additive inverse of 4 is -4 </span>

<span>Next, show that this (in the integers) can be applied to the rationals in this manner: </span>

<span>(4/7) + (-4/7) = ? </span>
<span>common denominator, therefore you can factor out the denominator: </span>

<span>(4 + -4)/7 = ? </span>
<span>Inside the bracket is the sum of an integer with its additive inverse, therefore the sum is zero </span>
<span>(0)/7 = 0/7 = 0 </span>

<span>Since this is true for ALL integers, then it must also be true for ALL rational numbers.</span>
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Step-by-step explanation: Hope this help :D

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