Covert standard form to slope-intercept form
4x + 7y + 3 = 0
7y = -4x - 3
y = (-4/7)x - 3/7 so the slope of this line is -4/7
The slope perpendicular to this is - 1 (-4/7) = 7/4
The required line has equation:-
y - 1 = (7/4)(x - (-2))
y - 1 = (7/4)x + 14/4
y = (7/4)x + 18/4 That is the answer in slope intercept form
Multiply through by 4
4y = 7x + 18
7x - 4y = 18 in Standard form Answer
Answer:
Step-by-step explanation:
slope is -3/2
y intercept is 4. y intercept is where the line crosses the y axis.
Answer:
All of them
Step-by-step explanation:
According to the ratio test, for a series ∑aₙ:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
(I) aₙ = 10 / n!
lim(n→∞) |(10 / (n+1)!) / (10 / n!)|
lim(n→∞) |(10 / (n+1)!) × (n! / 10)|
lim(n→∞) |n! / (n+1)!|
lim(n→∞) |1 / (n+1)|
0 < 1
This series converges.
(II) aₙ = n / 2ⁿ
lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|
lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|
lim(n→∞) |(n+1) / (2n)|
1/2 < 1
This series converges.
(III) aₙ = 1 / (2n)!
lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|
lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|
lim(n→∞) |(2n)! / (2n+2)!|
lim(n→∞) |1 / ((2n+2)(2n+1))|
0 < 1
This series converges.
-3 + -2 = -5
-5 + 5 = 0
0 x 2 = 0
