11th term is 10240
Step-by-step explanation:
- Step 1: Given the sequence 10,20,40. So a(1) = 10, common ration, r = 20/10 = 2 Find the 11th term using the nth term formula, a(n) = ar^n-1
⇒ a(11) = 10 × 2^10 = 10 × 1024 = 10240
Explanation:
In order to prove that affirmation, we define the function g over the interval [0, 1/2] with the formula 
If we evaluate g at the endpoints we have
g(0) = f(1/2)-f(0) = f(1/2) - f(1) (because f(0) = f(1))
g(1/2) = f(1) - f(1/2) = -g(0)
Since g(1/2) = -g(0), we have one chance out of three
- g(0) > 0 and g(1/2) < 0
- g(0) < 0 and g(1/2) > 0
- g(0) = g(1/2) = 0
We will prove that g has a zero on [0,1/2]. If g(0) = 0, then it is trivial. If g(0) ≠ 0, then we are in one of the first two cases, and therefore g(0) * g(1/2) < 0. Since f is continuous, so is g. Bolzano's Theorem assures that there exists c in (0,1/2) such that g(c) = 0. This proves that g has at least one zero on [0,1/2].
Let c be a 0 of g, then we have

Hence, f(c+1/2) = f(c) as we wanted.
Answer:
spents on housing for each year for the state.
Step-by-step explanation:
Given:
Population of State = 2000000
Average Citizen spends on housing = 6000
We need to find total spent on housing for the state.
For finding total spent on housing for state we need to multiply Population of state with average citizen spends on housing.
Total spent on housing for state = Population of State
Average Citizen spends on housing = 
Now expressing the above in scientific notation we get;
Total spent on housing for state = 
The answer would be B 21/4