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lubasha [3.4K]
3 years ago
6

Can someone please help me :(

Mathematics
1 answer:
Slav-nsk [51]3 years ago
4 0

Answer:

41/3 - 14 - Square root of 200

Step-by-step explanation:

41/3 is between 13 and 14

14 is 14

Square root of 200 is between 14 and 15

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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
trapecia [35]

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

  • T(2,1) = (2,1)
  • T(-1,2) = (1,-2)

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]

3 0
3 years ago
Given the point (2,3) and the slope of 4, find y when x =22
Lisa [10]
<span>y = mx + b
3 = 8 + b
3 - 8 = b
-5 = b
m = 4 and b = -5
y = 4x - 5
x = 22:
y = (4 x 22) - 5
y = 88 - 5
y = 83
</span>
Hope This Helps You!
Good Luck Studying :)
7 0
3 years ago
Read 2 more answers
At the beginning of the year, Zachary had $40 in savings and saved an additional $20 each week thereafter. Isaac started the yea
guajiro [1.7K]

Zachary function:

Z(t) = 40 + 20t

Isaac function:

I(t) = 85 + 11t

Graph each function to see the interval of time when one person has more money than the other.

8 0
3 years ago
Please help! whats 15 divided by 12
katrin2010 [14]

Answer:

1.25

Step-by-step explanation:

4 0
3 years ago
What is 5+2? Ive been totally stuck on this for the longest time. I really need help
eduard

that's a tricky one!

but it is 7 i believe

5 0
3 years ago
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