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mars1129 [50]
3 years ago
13

If x2 + y2 = 14 and xy = 5, find the value of (1/2 x + 1/2 y)2.

Mathematics
2 answers:
yaroslaw [1]3 years ago
6 0

( 1/2x +1/2y)²

= { ( x + y )/ 2xy }²

= ( x² + 2xy + y² )/4(xy)² —(1)

As we know that x² + y² = 14 — (2)

and xy = 5 —(3)

So, substitute the value of equation 2 and 3 in equation 1,

= ( x² + 2xy + y²)/4(xy)²

=( 14 + 2*5)/(4*5²)

= 24/(4*25)

= 6/25.

aleksley [76]3 years ago
5 0

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

let me know if I'm wrong.

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Answer:

<u>The correct answer is C. 66.7</u>

Step-by-step explanation:

1. y varies directly with regard to x

y = 9 and x = 24

If y = 25, what is the value of x?

2. For finding that value of x, first of all, we should understand what happened to y.

If y moves from 9 to 25 it means that y has been multiplied by 2.77, using this simple division

25/9 = 2.777

3. And we should use that same number or value to calculate the new value of x

If x was 24, now the new value of x is 24 * 2.777

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<em>1. Sample Mean = 2.50 </em>

<em>2. Sample Variance = 1.35</em>

<em>3. Standard Deviation = 1.16</em>

Step-by-step explanation:

Note: As this question is not complete, similar can be found on internet where following are asked to calculate and here I will calculate these as well.

1. Sample Mean.

2. Sample Variance.

3. Sample Standard Deviation.

So, for sample mean to calculate from the given data points. We need to apply to following formula to calculate sample mean.

Sample Mean = (X1 + X2 + .... + XN) divided by Total number of data points.

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Likewise, from the answer of sample mean we can calculate sample variance by following steps.

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

1.      Subtract the obtained mean from each of the data point given.

       (0.17 - 2.50) = -2.33

       (1.94 - 2.50) = -0.56

       (2.62 - 2.50) = 0.12

       (2.35 - 2.50) = -0.15

       (3.05 - 2.50) = 0.55

       (3.15 - 2.50) = 0.65

       (2.53 - 2.50) = 0.03

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2.      Square each of the differences obtained in step 1.

            -2.33^{2} = 5.43

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            -0.15^{2} = 0.02

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              0.65^{2}  = 0.42

              0.03^{2} = 0.01

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           -0.58^{2} = 0.34    

3.  Sum all of these squares.

(5.43 + 0.31 + 0.01 + 0.02 + 0.30 + 0.42 + 0.01 + 5.34 + 0.34) = 12.18

4. Divide 12.18 by (n-1), where n = 9.

<em>Sample Variance =  12.18/9 = 1.35</em>

Now, by using sample variance, we can calculate standard deviation with easy simple steps.

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<em>Standard Deviation = </em>\sqrt{1.35}<em> = 1.16 </em>

<em>Good Luck!</em>

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