Denver, Colorado is called "The Mile High City" because its elevation is 5280 feet above sea level. The elevation of Death Valle
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Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a = a + (n - 1)d
- a is the first term
- d is the common difference between each 2 consecutive terms
- n is the position of the term
The formula of the sum of nth terms is S =
[2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S = 185
→ Substitute the value of S and d in the 2nd rule above
∵ 185 = [ 2a + (n - 1)3]
∴ 185 = [2a + 3(n) - 3(1)]
∴ 185 = [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10
We want to find a linear equation that models the given situation.
The solution is p = $0.0001*q - $23
The general linear equation is:
p = m*q + c
Where m is the slope and c is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
Here we have the two points:
price = $9, boxes = 320,000
price = $8.50, boxes = 270,000
We can rewrite these as:
(320,000 , $9)
(270,000 , $8.50)
Then the slope of the line will be:
Then the line is something like:
p = $0.0001*q + c
To find the value of c we can use one of the two given points, I will use the first one, (320,000 , $9).
Replacing that in our equation we get:
$9 = $0.0001*320,000 + c
$9 - $0.0001*320,000 = c = -$23
Then the linear equation is:
p = $0.0001*q - $23
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