Answer:
X-intercepts:
Y-intercepts:(0,3)
Step-by-step explanation:
Hello!
given expression
x-intercept is the point on the graph where y=0
solve
Thus, x-intercept
y-intercept is the point on the graph where x=0
solve
Thus, y-intercept (0,3)
Hope it helps!
Rolle's Theorem states that:
If f is a continuous function in [a,b] and is differentiable in (a,b)
such that f(a)=f(b)
Then there exist a constant c in between a and b i.e. c∈[a,b]
such that: f'(c)=0
Here we have the function f(x) as:
where x∈[-1,3]
Also,
f(-1)=15
(Since,
)
and f(3)=15
( Since,
)
Hence, there will exist a c∈[-1,3] such that f'(c)=0
Hence, the c that satisfy the conclusion is: c=1
(a) The explicit rule to model the sequence formed by the number of seats in each row is
(b) The 35th row has 120 seats
Step-by-step explanation:
The rule of the nth term of an arithmetic sequence is
, where
∵ There are 18 seats in the 1st row
∵ There are 21 seats in the 2nd row
∵ 21 - 18 = 3
∵ The number of seats is increased by 3 with each additional row
- The number of seats in each row represents an arithmetic
sequence because there is a common difference between
each two consecutive rows
∴ The number of seats in each row formed an arithmetic sequence
∵ The number of seats in the first row = 18 seats
∴ a = 18
∵ The number of seats in a row continues to increase by 3 with each
additional row
∴ d = 3
- Substitute the values of a and d in the rule of nth term
∴
- Simplify the right hand side
∴
- Add like terms
∴
(a) The explicit rule to model the sequence formed by the number of seats in each row is
∵ There are 120 seat in a row
- Substitute by 120 in the rule above
∴ 120 = 15 + 3n
- Subtract 15 from both sides
∴ 105 = 3n
- Divide both sides by 3
∴ n = 35
∴ The number of the row is 35
(b) The 35th row has 120 seats
Learn more:
You can learn more about the sequences in brainly.com/question/7221312
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