The items below show the complete steps as to how this is being answered.
1. 3x - 4 = 14 >>>> Given
2. 3x - 4 + 4 = 14 + 4 >>>
Step number 2 above is an addition property of equality. Both sides of the equation are added with 4.
3. Simplifying >>>
3x = 18
4. 3x/3 = 18/3 >>>> Division property of equality
5. >>>> Simplifying,
x = 6
Hence, the order of the choices as answers is C, E, B, A, D.
Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
Selection C is appropriate.
_____
A. The population is constant at 8.
B. The population is constant at 24.
C. Matches the problem description.
D. The initial population is 24 and after 1 hour is 72.
[ (12 - n)/7 ] = -1
12- n = -7
-n = -19
n = 19
Answer:
736.05
Step-by-step explanation:699.00 x 5.3%=37.047
699.00 + 37.05 = 736.05
