Step-by-step explanation:
y = -3x² + mx + 10
dy/dx = -6x + m.
When dy/dx = 0, -6x + m = 0. => x = m/6.
We have y = -3(m/6)² + m(m/6) + 10 = 37.
=> -m²/12 + m²/6 = 27
=> -m² + 2m² = 324
=> m² = 324
=> m = 18 or m = -18.
1) yes
2) x=-4,y=-7
3) x= -3, y=4
4) x= -1, y=2
5) x= -5, y=-8
Given:
The given sequence is:
To find:
The recursive formula for 
, the nth term of the sequence.
Solution:
We have,
Here, the first term is 5.
The common difference is -7.
The recursive formula for the nth term of the sequence is
Where, 
is the common difference.
Putting 
in the above formula, we get
Therefore, the recursive formula for the nth term of the sequence is .
Answer:
4951 students
Step-by-step explanation:
If there was 99 students from each state, that would make the total to be:
99 * 50 = 4950
We can use the pigeon hole principle to make this the minimum number required.
The pigeon hole principle basically tells us that if you have more "pigeons" than "holes" then there must be one hole with multiple objects in it.
So, using this idea, we see that:
we need at least 1 more to ensure this
So, min number required would be
4950 + 1 = 4951
Answer:
2x+5
Step-by-step explanation:
X represents the number in "2 times a number." You could insert any number into x.
