Answer:
π − 12
Step-by-step explanation:
lim(x→2) (sin(πx) + 8 − x³) / (x − 2)
If we substitute x = u + 2:
lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)
lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u
Distribute the cube:
lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u
lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u
lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u
Using angle sum formula:
lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u
lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u
Divide:
lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]
lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)
lim(u→0) (sin(πu) / u) − 12
Multiply and divide by π.
lim(u→0) (π sin(πu) / (πu)) − 12
π lim(u→0) (sin(πu) / (πu)) − 12
Use special identity, lim(x→0) ((sin x) / x ) = 1.
π (1) − 12
π − 12
The value of 2 in 2783 (2000) is 10 times the value of two in 7283 (200).
Hope this helped!
Nate
Answer:
1. 68%
2. 50%
3. 15/100
Step-by-step explanation:
Here, we want to use the empirical rule
1. % waiting between 15 and 25 minutes
From what we have in the question;
15 is 1 SD below the mean
25 is 1 SD above the mean
So practically, we want to calculate the percentage between;
1 SD below and above the mean
According to the empirical rule;
1 SD above the mean we have 34%
1 SD below, we have 34%
So between 1 SD below and above, we have
34 + 34 = 68%
2. Percentage above the mean
Mathematically, the percentage above the mean according to the empirical rule for the normal distribution is 50%
3. Probability that someone waits less than 5 minutes
Less than 5 minutes is 3 SD below the mean
That is 0.15% according to the empirical rule and the probability is 15/100
Answer:
D. 18.9 ÷ 9
Step-by-step explanation:
we need to divide
1.89 ÷ 0.9 but write it in different form
so ,we need to eliminate decimal from 0.9
as 0.9*10 = 9
thus,we multiply both 1.89 and 0.9 with 10, then we will have
(1.89*10) ÷ (0.9*10)
=> 18.9 ÷ 9
Thus, based on above calculation new look would be D. 18.9 ÷ 9
Answer:
$1.25 per pound
Step-by-step explanation:
$3.75/3 = 1 pound price
