Answer:
1. x=10,-10
2. x = 5
x = -5
3. x=-5
4. x ∈ {4,- 3/2}
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Given:
First term of an arithmetic sequence is 2.
Sum of first 15 terms = 292.5
To find:
The common difference.
Solution:
We have,
First term: 
Sum of first 15 terms: 
The formula of sum of first n terms of an AP is
![S_n=\dfrac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Where, a is first term and d is common difference.
Putting
, n=15 and a=2 in the above formula, we get
![292.5=\dfrac{15}{2}[2(2)+(15-1)d]](https://tex.z-dn.net/?f=292.5%3D%5Cdfrac%7B15%7D%7B2%7D%5B2%282%29%2B%2815-1%29d%5D)
![292.5=\dfrac{15}{2}[4+14d]](https://tex.z-dn.net/?f=292.5%3D%5Cdfrac%7B15%7D%7B2%7D%5B4%2B14d%5D)
![292.5=15[2+7d]](https://tex.z-dn.net/?f=292.5%3D15%5B2%2B7d%5D)
Divide both sides by 15.




Dividing both sides by 7, we get


Therefore, the common difference is 2.5.
Answer:
All except one interval [-2,8]
Step-by-step explanation:
Notice that the function, wich an hyperbola, has a vertical asymptote in both -2 and 8 and there is nothing between this two values.
So we will exclude what's between them out of the domain.
ANSWER
The turning point is

EXPLANATION
The function given to us is

At turning point,

So we need to differentiate the given function and equate it to zero.
We using the chain rule of differentiation, we obtain,

We equate this to zero to obtain,

We divide through by 3.

We solve for x to get,


We substitute this x-value in to the function to obtain the corresponding y-value of the turning point.



Therefore the turning point is

C is the correct answer.