Answer:
1. I have simplified the first question:
2. I have found the parabola properties:
The first thing you should do for this case is to use the following table to perform the equation of a line:
y x
41,431 1995
48,729 2005
We have then that the line that best fits this data is
y = 729.8x - 1E + 06
Then, to know in what year the number of shopping centers reaches 80,000 we must replace this number in the equation of the line and clear x:
80000 = 729.8x - 1E + 06
Clearing x
x = (80000 + 1E + 06) / (729.8) = 1479.857495
nearest whole number
1480
This means that after 1480 years, 80000 shopping centers are reached.
Equivalently, this amount is reached in the year:
1480 + 1995 = 3475
In the year 3475
answer
(a) y = 729.8x - 1E + 06
(b) In the year 3475
Answer:
33/16
Step-by-step explanation:
x = y⁴/8 + 1/(4y²), 1 ≤ y ≤ 2
dx/dy = y³/2 − 1/(2y³)
Arc length is:
s = ∫ ds
s = ∫ √(1 + (dx/dy)²) dy
s = ∫₁² √(1 + (y³/2 − 1/(2y³))²) dy
s = ∫₁² √(1 + y⁶/4 − ½ + 1/(4y⁶)) dy
s = ∫₁² √(½ + y⁶/4 + 1/(4y⁶)) dy
s = ∫₁² ½ √(2 + y⁶ + 1/y⁶) dy
s = ∫₁² ½ √(y³ + 1/y³)² dy
s = ∫₁² ½ (y³ + 1/y³) dy
s = ½ (y⁴/4 − 1/(2y²)) |₁²
s = ½ (16/4 − 1/8) − ½ (1/4 − 1/2)
s = 33/16
Answer:
11 ounces
Step-by-step explanation:
- Find out how many ounces are in 4 pounds 2 ounces. There are 16 ounces in a pound, so that would be 66 ounces.
- Divide 66 by 6.
