Answer: A. ![\left[\begin{array}{ccc}29&13\\13&10\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D29%2613%5C%5C13%2610%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The question is asking us to find the product of the matrices. The key difference is the second A has a little <em>T</em> in the exponent. This <em>T</em> means transpose. You multiply A by the transpose of A. To find the transpose, you turn the rows into columns.
![A^T=\left[\begin{array}{ccc}5&3\\2&-1\\\end{array}\right]](https://tex.z-dn.net/?f=A%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%263%5C%5C2%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Now that we have our transpose, we can multiply the matrices.
![\left[\begin{array}{ccc}5&2\\3&-1\\\end{array}\right] \left[\begin{array}{ccc}5&3\\2&-1\\\end{array}\right] =\left[\begin{array}{ccc}5*5+2*2&5*3+2(-1)\\3*5+2(-1)&3*3+(-1)(-1)\\\end{array}\right] =\left[\begin{array}{ccc}29&13\\13&10\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%262%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%263%5C%5C2%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%2A5%2B2%2A2%265%2A3%2B2%28-1%29%5C%5C3%2A5%2B2%28-1%29%263%2A3%2B%28-1%29%28-1%29%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D29%2613%5C%5C13%2610%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
Step-by-step explanation:
It can be shown that all four sides of this figure have the same length. This, in turn, is the definition of a rhombus.
Answer:
Positive
Step-by-step explanation:
Answer:
232.820513
Step-by-step explanation:
Let the number you are looking for is x,
equation,
90.8 * x = 39
90.8/39 = 2.32820513
Now we multiply 100 because we are dealing with percentages so,
2.32820513 * 100 = 232.820513
So, the answer is 232.820513
Hope this helps! Good luck to everyone!
If the airport is located at the origin, for units of miles and hours, we can write the equations of position for airplanes "a" and "b" in rectangular coordinates as
a = (-30 +250t, 0)
b = (0, -40 +300t)
The distance between these (moving) points can be computed in the usual way using the Pythagorean theorem.
d = √((-30 +250t - 0)² +(0 - (-40 +300t))²)
d = √(2500 -39000t +152500t²)
Then the rate of change of d is the derivative of this.
d'(t) = (-19500 +152500t)/√(2500 -39000t +152500t²)
At the present time (t=0), the rate of change of distance between the planes is
d'(0) = -19500/√2500 = -390
The distance between the planes is decreasing at 390 mi/h.
