Chad know 5 out of every 50 students has blue eyes there are 660 students in the school how many students have blue eyes

Ashley is riding her bike to train for a triathlon and so far has traveled 96 miles.

Elina [12.6K]

Answer:

6.4

Step-by-step explanation:

she has been riding her bike for 6.4 hours.

7 0

2 years ago

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

Samantha and Mia each left Julia’s house at the same time. Mia walked north at 7 kilometers per hour. Samantha ran west at 11 ki

Lena [83]

Mia walked 7km/h so after 1 hour, she is 7 km north of the house of Julia

Samantha walked 11km/h so after 1 hour, she is 11 km west of the house of Julia.

The points where Mia and Samantha are after 1 hour , and the house of Julia form a right triangle with sides 7 and 11 km. The distance between the girls, is the hypotenuse of his triangle.

by the pythagorean theorem:

$MS= \sqrt{ 7^{2} + 11^{2} }= \sqrt{49+121}= \sqrt{170}= 13 (km)$

Answer: 13 km