<span><span>SPOTLIGHT DEMYSTIFIED QUIZZES GALLERIES LISTS ON THIS DAY BIOGRAPHIES</span>SEARCH BRITANNICAWhat are you looking for?SearchBROWSE POPULAR TOPICS:<span>Pearl Harbor attack American Revolution Reign of Terror Photosynthesis Las Posadas</span></span><span>You have reached Britannica's public website.<span>For ad-free access to your Britannica School or Library account CLICK HERE</span></span><span>Chemical compound<span>WRITTEN BY: </span><span>Melvyn C. UsselmanRichard O.C. NormanSteven S. ZumdahlCarl R. Noller</span>See Article History<span><span>Chemical compound, any substance composed of identical moleculesconsisting of atoms of two or more chemical elements.<span><span>Methane, in which four hydrogen atoms are bound to a single carbon atom, is an example of a basic chemical compound. The structures of chemical compounds are influenced by complex factors, such as bond angles and bond length.Encyclopædia Britannica, Inc.</span></span>All the matter in the universe is composed of the atoms of more than 100 different chemical elements, which are found both in pure form and combined in chemical compounds. A sample of any given pure element is composed only of the atoms characteristic of that element, and the atoms of each element are unique. For example, the atoms that constitute carbon are different from those that make up iron, which are in turn different from those of gold. Every element is designated by a unique symbol consisting of one, two, or three letters arising from either the current element name or its original (often Latin) name. For example, the symbols for carbon, hydrogen, and oxygen are simply C, H, and O, respectively. The symbol for iron is Fe, from its original Latin name ferrum. The fundamental principle of the science of chemistry is that the atoms of different elements can combine with one another to form chemical compounds. Methane, for example, which is formed from the elements carbon and hydrogen in the ratio four hydrogen atoms for each carbon atom, is known to contain distinct CH4 molecules. The formula of a compound—such as CH4—indicates the types of atoms present, with subscripts representing the relative numbers of atoms (although the numeral 1 is never written).<span /></span></span><span><span>
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Answer:
what si the questions
Step-by-step explanation:
We are given the dimensions of the box:
l = 50 cm
w = 20 cm
We know that the volume of a box is:
V = l w h
where h = x
However since x cuts is made on both all sides of the box,
therefore the new dimensions would be:
V = (l – 2x) (w – 2x) x
V = (50 – 2x) (20 – 2x) x
V = 1000x – 100x^2 – 40x^2 + 4x^3
V = 4x^3 – 140x^2 + 1000x
<span>To get the maxima value, we get the 1st
derivative of the function then set dV/dx = 0 to solve for x:</span>
dV / dx = 12x^2 – 280x + 1000
12x^2 – 280x + 1000 = 0
Transpose 1000 to the right side and divide everything by
12:
x^2 – (280/12)x = -(1000/12)
Completing the square:
x^2 – (280/12)x + (78400/576) = -(1000/12) + (78400/576)
[x – (280/24)]^2 = 52.78
x – (280/24) = ±7.26
<span>x = (280/24) ± 7.26</span>
x = 4.40, 18.93
x cannot be 18.93 since this would result in a negative
value of 20 – 2x, therefore:
x = 4.40 cm
Calculating for the volume:
V = (50 – 2*4.4) (20 – 2*4.4) (4.4)
<span>V = 2030.34 cm^3</span>
