Answer:
Tim gets £10 and sam gets £30
Step-by-step explanation:
Answer:
Step-by-step explanation:
The first differences of the sequence are ...
- 5-2 = 3
- 10-5 = 5
- 17-10 = 7
- 26-17 = 9
- 37-26 = 11
Second differences are ...
- 5 -3 = 2
- 7 -5 = 2
- 9 -7 = 2
- 11 -9 = 2
The second differences are constant, so the sequence can be described by a second-degree polynomial.
We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...
f(n) = an^2 + bn + c
Then the first three terms of the sequence are ...
- f(1) = 2 = a·1^2 + b·1 + c
- f(2) = 5 = a·2^2 +b·2 + c
- f(3) = 10 = a·3^2 +b·3 +c
Subtracting the first equation from the other two gives ...
3a +b = 3
8a +2b = 8
Subtracting the first of these from half the second gives ...
(4a +b) -(3a +b) = (4) -(3)
a = 1 . . . . . simplify
Substituting into the first of the 2-term equations, we get ...
3·1 +b = 3
b = 0
And substituting the values for a and b into the equation for f(1), we have ...
1·1 + 0 + c = 2
c = 1
So, the formula for the sequence is ...
f(n) = n^2 + 1
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The 20th term is f(20):
f(20) = 20^2 +1 = 401
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<em>Comment on the solution</em>
It looks like this matches the solution of the "worked example" on your problem page.
Answer:
2
Step-by-step explanation:
Step 1: Write out equation g(f(a))
1/√a
Step 2: Plug in 0.25 for <em>a</em>
1/√0.25
You answer should be 2
Answer:
How to tell the difference: A proportional graph is a straight line that always goes through the origin. A non-proportional graph is a straight line that does not go through the origin.
Step-by-step explanation:
Answer:
x = 5
Step-by-step explanation:
vertical angles are congruent , so
∠ A = ∠ B , that is
5x - 1 = 4x + 4 ( subtract 4x from both sides )
x - 1 = 4 ( add 1 to both sides )
x = 5
