X + 7x = 56 + 8
Simplifying x + 7x = 56 + 8 Combine like terms: x + 7x = 8x 8x = 56 + 8 Combine like terms: 56 + 8 = 64 8x = 64 Solving 8x = 64 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '8'. x = 8 Simplifying x = 8
C . bc its the right answer :)
Answer:
f(7) = 13.7
f(8) = 18.7
Recursive Function Is: f(1) = -16.3; (fn) = f(n - 1) + 5
Step-by-step explanation:
The recursive function of the arithmetic sequence is
f(1) = first term; f(n) = f(n-1) + d, where
- d is the common difference between each two consecutive terms
∵ f(5) = 3.7 and f(6) = 8.7
∵ d = f(6) - f(5)
∴ d = 8.7 - 3.7
∴ d = 5
∵ f(7) = f(6) + 5
∴ f(7) = 8.7 + 5
∴ f(7) = 13.7
∵ f(8) = f(7) + 5
∴ f(8) = 13.7 + 5
∴ f(8) = 18.7
→ To find f(1) subtract from each term the value of d
∵ f(5) = f(4) + d
∴ f(4) = f(5) - d
∴ f(4) = 3.7 - 5
∴ f(4) = -1.3
∵ f(3) = f(4) - 5
∴ f(3) = -1.3 - 5
∴ f(3) = -6.3
∵ f(2) = f(3) - 5
∴ f(2) = -6.3 - 5
∴ f(2) = -11.3
∵ f(1) = f(2) - 5
∴ f(1) = -11.3 - 5
∴ f(1) = -16.3
∴ Recursive Function Is: f(1) = -16.3; (fn) = f(n - 1) + 5
Notice that
(1 - <em>x</em>)⁵ (1 + 1/<em>x</em>)⁵ = ((1 - <em>x</em>) (1 + 1/<em>x</em>))⁵ = (1 - <em>x</em> + 1/<em>x</em> - 1)⁵ = (1/<em>x</em> - <em>x</em>)⁵
Recall the binomial theorem:
Let <em>a</em> = 1/<em>x</em>, <em>b</em> = -<em>x</em>, and <em>n</em> = 5. Then
We get an <em>x</em> ³ term for
2<em>k</em> - 5 = 3 ==> 2<em>k</em> = 8 ==> <em>k</em> = 4
so that the coefficient would be
