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Vera_Pavlovna [14]
3 years ago
6

Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10

) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.
Mathematics
1 answer:
Vladimir [108]3 years ago
5 0

Answer:

0011100000

1010010001

0111001110

Step-by-step explanation:

As the question is not complete, Here is the complete question.

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

So, we need to express a) b) and c) into bit strings.

Firstly, number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal set as well as in sub set.

0 = No, element is not present in sub set but present in universal set.

Hence, we have:

a) Sub set {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Sub set {1, 3, 6, 10} = 1010010001

c) Sub set {2, 3, 4, 7, 8, 9} = 0111001110

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viktelen [127]

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

x_{2}=3x_{1} -2

substitute in equation (2), we get

9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k

we cannot find the value of x_{1} and x_{2}.

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

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3 years ago
A barrel was 2/3 full of water. After 60 liters were used from the barrel, it was 5/12 full. how much water does the barrel hold
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Answer: 240 liters

Step-by-step explanation: This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.

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<h3><u>Explanation</u></h3>
  • Method 1 (Formula)

\begin{cases}h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{2a}  \end{cases}

The vertex of Parabola is the maximum/minimum point depending on the value of a.

  • Find Vertex

<u>h-value</u>

h =  -  \frac{5}{2(1)}  \\ h =  -  \frac{5}{2}

<u>k-value</u>

k =  \frac{4(1)( - 6) -  {(5)}^{2} }{4(1)}  \\ k =  \frac{ - 24 - 25}{4}  \\ k =  \frac{ - 49}{4}  \\ k =  -  \frac{49}{4}

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

  • Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

  • Differentiate Function

f'(x) = 2 {x}^{2 - 1}  +  {5x}^{1 - 1}  - 0 \\ f'(x) = 2x + 5

Substitute f'(x) = 0

0 = 2x + 5 \\  - 5 = 2x \\   -  \frac{5}{2}  = x

Substitute x = -5/2 in the original equation.

f(x) =  {( -  \frac{5}{2} )}^{2}  + 5( -   \frac{5}{2} ) - 6 \\ f(x) =  \frac{25}{4}  -  \frac{25}{2}  - 6 \\ f(x) =  \frac{25}{4}  -  \frac{50}{4}  -  \frac{24}{4}  \\ f(x) =  \frac{25}{4}  -  \frac{74}{4}  \\ f(x) = -   \frac{49}{4}

<h3><u>Answer</u><u /></h3>

<u>\sf{the  \:  \: minimum  \:  \: value \:  \:  is   \:  \: -  \frac{49}{4}  \:  \: at \:  \:  x =  -  \frac{5}{2} }</u>

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