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.
Note the order of the letters:
A C E G
M N P R
You read it like this:
A ≅ M
C ≅ N
CE ≅ NP
AG ≅ MR
... and so on
In the following choices:
CE ≅ NP is the true statement
Answer:
15, 8, 25 The teacher payed 0.40 per book.
Step-by-step explanation:
4/10 = 2/5 Simplify the 4/10 to find the unit rate.
15: 2/5 = 6/x Set up your proportion.
2x =30 Cross multiply
/2 /2 Divide both sides by 2 to isolate x
x =15
8: 2/5 = x/20 Set up proportion
40 =5x Cross multiply
/5 /5 Divide both sides by 5 to isolate x
8 =x
25: 2/5 = 10/x Set up proportion
2x =50 Cross multiply
/2 /2 Divide both sides by 2 to isolate x
x =25
Graph: y=mx+b To graph, you will need to use y=mx+b format
y= 2/5 x+2 2/5 is your unit rate. Your rate changes every 2 books bought. To graph, start at (0,2) and go up 2 and to the right 5, plot. Continue moving up 2 and to the right 5 to graph.
The teacher payed 0.40 per book because 2/5 simplifies to 0.40.
Answer:
x=291/76
Step-by-step explanation:
Convert:
1/2x(6x+ 1/2)=-0.8x+16-1.2
Remove parenthesis and move terms:
3x+1/4=-0.8x+14.8
Collect the like terms and convert:
3x+0.8x=14.8-1/4
Subtract the fractions:
3.8x=74/5-1/4
Divide both sides by 3.8:
3.8x=291/20
x=291/76
3y=8x
Explanation:
If y varies directly with x then
y=c⋅x for some constant of variation c
If (x,y)=(14,23) is a solution to this equation, then
23=c⋅14
→c=23⋅41=83
So
y=83x
or (clearing the fraction)
3y=8x