25974 questions

What are the most important points to consider when carrying out my EPQ?

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Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5

Substitute values of one equation into another.  (1) x+y+2z = -2; (2) 3x-y+14z=6; x+2y=-5 (3). Substitute x in (1) and (2) from (3). We get -y+2z=3 in (1).  We get -7y+14z=21 in (3). Since (3) is (1)*7, we can conclude that the system has infinite solutions.
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When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.

Insert the negative values of the divisors and put them into the polynomial. x-2 -> P(2) = 3*4+2a+b=2   x+1 -> P(-1)=3*(-1)+(-1)a+b=5.  22+2a+b=0 -8-a+b=0, then solve the simultaneous equations and obtain the answer: a=-10, b=-2.
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Name several sort algorithms of an array, their working principles and their efficency.

Bubble sort (compare two elements and switch them if one of them is higher than other, depending on ordering preference), iterate over the whole array of elements. Efficency O(n2). Insert sort, make a separate list, where you insert the elements in an ordered manner, that is start at the smallest element and go until an element that is bigger than the input or end of list and insert it before that. Efficency O(n2). Selection sort, iterate over the whole array and find the smallest element, put it into start, then iterate from smallest +1, then smallest +2. Efficency O(n2). Merge sort, split array into smaller arrays until size 1 is reached, then assume size 1 is sorted, then merge them while sorting, the sub arrays. Efficency O(n logn). Quicksort. Select a pivot point, split all elements that are larger than that to one side, smaller to other, then put the pivot, where it belongs. After do it on smaller arrays, when all is done, the arrays are merged and the final array is sorted. Efficency O(n logn).
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Name the memories in the computer and rate them by the amount of space and their price. When should which be used.

Processor memory (cache), RAM (Random Access Memory), Hard memory (Hard Drive, Magnetic Tapes, Solid State drive).  Processor is fastest, ram is next, hard is slowest. Processor is most expensive, then ram, then hard. In hard memory, magnetic is cheapest, then hard drive, then solid state. Magnetic is slowest, then hard drive, then solid state.  Cheapest memory should be used for data that is used least (backups), more expensive for the one that is more often used.
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Add the binary numbers 100101 and 101001 and convert them to decimal (they are unsigned integers). What are possible issues when adding the numbers?

The result is 1001110, which converted is 78. The problem that can occur is overflow, since original number is 6 digit, but result is 7, which may cause to drop the most significant bit and become 14 instead. The result can be arrived by adding all the numbers together from the right side towards left and carrying over if both of them are 1. Conversion is done from right to left by adding all the numbers starting by 1 multiplying by 2 for every digit count and multiplying by the value itself, so 1*0+1*2*1+ 1*2*2*1+....
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How is frequency density calculated?

Frequency divided by class width
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What is a ligand?

A species with one or more valence electron pairs that forms co-ordinate bonds with a metal ion.
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