Answer:
Verified
Step-by-step explanation:
Let the diagonal matrix D with size 2x2 be in the form of
Then the determinant of matrix D would be
det(D) = a*d - 0*0 = ad
This is the product of the matrix's diagonal numbers
So the theorem is true for 2x2 matrices
Answer:
a. After the first bounce, the ball will be at 85% of 8 ft. After 2 bounces, it'll be at 85% of 85% of 8 feet. After 3 bounces, it'll be at (85% of) (85% of) (85% of 8 feet). You can see where this is going. After n bounces the ball will be at
b. After 8 bounces we can apply the previous formula with n = 8 to get
c. The solution to this point requires using exponential and logarithm equations; a more basic way would be trial and error using the previous increasing the value of n until we find a good value. I recommend using a spreadsheet for that; the condition will lead to the following inequality:
Let's first isolate the fraction by dividing by 72.
Now, to get numbers we can plug in a calculator, let's take the natural logarithm of both sides:
. Now the two quantities are known - or easy to get with any calculator, replacing them and solving for n we get:
Now, since n is an integer - you can't have a fraction of a bounce after all, you pick the integer right after that, or n>27.
