What is the length of a diagonal of a cube with a side length of 1 cm?
1 answer:
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Answer:
√3 cm
Step-by-step explanation:
The square of a face diagonal is given by the Pythagorean theorem:
(face diagonal)² = 1² + 1² = 2
Then the square of the space diagonal is ...
(space diagonal)² = 1² +2 = 3
So, the length of the space diagonal is ...
space diagonal = √3 cm
_____
In the attached diagram, AB and BC are edges of a face of the cube. AC is the diagonal of that face, a "face diagonal." That makes a right triangle with edge CD of the cube. The hypotenuse of that triangle is AD, the "space diagonal". As we have shown, the length of the space diagonal is ...
AD² = CD² +AC² = 1² +(√2)² = 3
AD = √3
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Answer:
<em>1680 is the answer.</em>
Step-by-step explanation:
Here, we have 11 letters in the word <em>MISSISSIPPI.</em>
Repetition of letters:
M - 1 time
I - 4 times
S - 4 times
P - 2 times
As per question statement, we need a substring MISS in the resultant strings.
So, we need to treat MISS as one unit so that <em>MISS always comes together in all the strings</em>.
The resultant strings will look like:
<em>xxxxMISSxxx</em>
<em>xxMISSxxxxx</em>
<em>and so on.</em>
After we treat <em>MISS </em>as one unit, total letters = 8
Repetition of letters:
MISS - 1 time
I - 3 times
S - 2 times
P - 2 times
The formula for combination of letters with total of <em>n </em>letters:
where <em>p, q</em> and <em>r</em> are the number of times other letters are getting repeated.
<em>p = 3</em>
<em>q = 2</em>
<em>r = 2</em>
<em></em>
So, required number of strings that contain MISS as substring:
So, <em>1680 is the answer.</em>