Answer:
The distance is minimized 22 minutes after 3:00 pm.
Step-by-step explanation:
Let t is the time for the 2 boats after 3:00 pm, we have the distance of:
- Boat 1: 20t
- Boat 2: 15t and its distance to the dock is given by (15-15t)
The paths of the boats form a right triangle, in which the hypotenuse (also the distance between the two boats) is:
D = (20t)² + (15 - 15t)²
<=> dD/dt = -2(15² )( 1-t ) +2 × 20² × t
<=> dD/dt = 2 (15² + 20²) × t -2 ( 15 )² = 0
<=> t = 2 ( 15 )² : 2 (15² + 20²)
<=> t = 0.36 hours = 0.36 × 60 = 21.6 minutes ≈ 22 minutes
Therefore, the distance is minimized 22 minutes after 3:00 pm.
Answer:
W+253
Step-by-step explanation:
The word sum means the answer to an addition problem, + represents addition.
There are two acceptable ways of solving this. I'll show both (just in case one of them doesn't align with the information from your textbook).
Option 1 (fast and easy):The following is the equation for the area of a regular pentagon with side length s.

Plug s=12 into the equation.


The third choice should be your answer.
Option 2 (much more complicated):The area of a regular polygon can be solved with the following formula.

Let's solve for the apothem.
A pentagon can be divided into 5 congruent isosceles triangles. The vertex angle will be 360/5, or 72 degrees.
An isosceles triangle can be divided into two right triangles. One of the angles of the right triangle will be 72/2, or 36 degrees.
The leg opposite of the 36 degree angle will be 12/2, or 6 inches long.


The apothem is about 8.26 inches.
The perimeter is 12*5, or 60 inches.



(it seems that we're off by 0.1 due to rounding errors)
The answer is the third choice. Hope this helps! :)
Answer:
When a matrix is multiplied by its inverse the result will be the identity matrix. If we multiply two matrix with the same size, the resulting matrix will have the same dimension.
Therefore, if we multiply the matrices X and Y we will get a 2x2 identity matrix, as follows:
![\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%5C%5C0%261%5C%5C%5Cend%7Barray%7D%5Cright%5D)