Answer:
converges
Step-by-step explanation:
well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)
0 < 7 the series converges
Answer:
x = -3/13
Step-by-step explanation:
cross multiply
4x + 6 = 30x + 12
combine like terms
-6 = 26x
x = -6/26 = -3/13
Answer:
Height = 21.78 ft
Step-by-step explanation:
Tan θ = opposite / Adjacent
tan 40 = opposite / 20
where opposite is the part of the traffic light
0.839 × 20 = opposite
opposite = 16.78 ft
Now the total height of traffic light = 16.78 ft +5 ft
Total Height = 21.78 ft
The first step in graphing a linear inequality is to graph the linear equality. The equation -x + 4y = -8 is equivalent to 4y = x - 8, which is equivalent to 
. This is the equation for the line in slope-intercept form, so the line will have a slope of 1/4 and a y-intercept of -2 (see the first image). Notice that the line is solid, rather than dotted. This represents that points on the line are included in the solution, because the inequality sign is ≥, which is not a strict equality (< or >).
Next, we need to figure out which side to shade. To do so, simply pick any point (I like to use the point (0,0) because it makes the calculations easy) and see whether it satisfies the inequality. If it does, shade the side with that point, and if not, shade the opposite side of the graph.
Here we see that the point (0,0) does satisfy the inequality, since -(0) + 4(0) is 0, and 0 ≥ -8, so the top half of the graph should be shaded (see the second image).
3x + 1y = ¹/₃ ⇒ 9x + 3y = 1
2x - 3y = 2²/₃ ⇒ 2x - 3y = 2²/₃
11x = 3²/₃
11 11
x = ¹/₃
3x + y = ¹/₃
3(¹/₃) + y = ¹/₃
1 + y = ¹/₃
- 1 - 1
y = ⁻²/₃
(x, y) = (¹/₃, ⁻²/₃)
