Answer:
The correct answer is 25
Step-by-step explanation:
It is given a quadratic equation,
x² – 8x = 9
<u>To find the number to be added</u>
The given equation be x² – 8x = 9
here we have to add (b/2)² - the square of half the coefficient of x,
Here b = -8
(b/2)² = (-8/2)² = -4² = 16
Add both side with 16
x² – 8x + 16 = 9 + 16
(x - 4)² = 25
(x - 4)² = 5²
Answer:
[4, 6]
Step-by-step explanation:
∑ₙ₌₁°° (x − 5)ⁿ / n²
Use ratio test.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(x − 5)ⁿ⁺¹ / (n+1)²] / [(x − 5)ⁿ / n²]│< 1
lim(n→∞)│[(x − 5) n² / (n+1)²│< 1
│x − 5│< 1
-1 < x − 5 < 1
4 < x < 6
If x = 4, ∑ₙ₌₁°° (4 − 5)ⁿ / n² = ∑ₙ₌₁°° (-1)ⁿ / n², which converges.
If x = 6, ∑ₙ₌₁°° (6 − 5)ⁿ / n² = ∑ₙ₌₁°° 1 / n², which converges.
So the interval of convergence is [4, 6].
D. (d-9)(d-5)
Since they are both negative, they will multiply to a positive number (45) and add to a negative number (-14)
If it takes an hour to fill 1 tank in 1 hour 1 tank will be full
