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liberstina [14]
2 years ago
9

What is the arithmetic mean of the following numbers? 3,5,6,7,9,6,8

Mathematics
2 answers:
9966 [12]2 years ago
8 0

Answer:

6 3/7

Step-by-step explanation:

Remember, the mean is the average of the number

Meaning that you have to add up all the numbers then divide them by the amount of numbers there are.

3, 5, 6, 7, 9, 6, 8

(3 + 5 + 6 + 7 + 9 + 6 + 8) / 7

44 / 7

6 3/7

zhannawk [14.2K]2 years ago
4 0
Your answer you are going To get is 6 3/7
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Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is reflection over the line y=1/2x
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Answer:

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

Step-by-step explanation:

We have to see how the canonical vectors are transformed throught T. Lets first define T in any basis.

Since T is a reflection, then any element of the line y = x/2 if fixed by T. Therefore T(2,1) = (2,1).

On the other hand, any vector perpendicular to the line direction should be sent to its opposite value. We can take, for example, (-1,2) (note that the scalar product (2,1) * (-1,2) = -2+2 = 0). As a consecuence T(-1,2) = (1,-2). We have

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By summing the first vector with the double of the second one we get, using linearity

T(0,5) = T( (2,1) + 2(-1,2)) = T(2,1) + 2T(-1,2) = (2,1) + 2(1,-2) = (4,-3)

Hence, T(0,1) = (4/5,-3/5)

Now, we take the second vector and substract it the double of the first one (to kill the second variable)

T(-3,0) = T( (-1,2) - 2*(2,1) ) = T(-1,2) -2T(2,1) = (1,-2)-2(2,1) = (-3,-4)

Therefore, T(1,0) = (1,4/3)

The matrix A induced by  T has in its first column T(1,0) and in its second column T(0,1). We conclude that

A = \left[\begin{array}{cc}1&\frac{4}{5}\\\frac{4}{3}&-\frac{3}{5}\end{array}\right]

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Answer:

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Step-by-step explanation:

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a graph - blue

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