The system shown has the unique solution (2, y, z). Solve the system and select the values that complete the solution. y = 0 y =
2 answers:
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Answer:
Step-by-step explanation:
We can do this the easy way and just set up an inequality and let the factoring do the work for us. The inequality will look like this:
We will move the constant over and get
and when you factor this you get that
3 < t < 4
Between 3 and 4 seconds is where the projectile reaches a height higher than 192 feet. With a little more work and some calculus you can find the max height to be 196 feet.
Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
- Not all items fit
- No matter the order
- Elements are not repeated
That is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:
It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
- n: 3
- m: 11
Replacing:
Solving:
being:
- 3!=3*2*1=6
- 8!=8*7*6*5*4*3*2*1=40,320
- 11!=39,916,800
So:
C= 165
<u><em>165 different teams of 3 students can be formed for competitions</em></u>