Answer:
1. When y = 40,000 x = 27th week.
2. When y = 35,000 x = 18th week.
3. When y = 25,000 x = 10th week.
Step-by-step explanation:
Given:
y = 30 + 10sin[x/26(π-14)]
Required:
Find the value of x when
1. y = 40,000
2. y = 35,000
3. y = 25,000
To solve this we have to equate the expression with the value of y
1. y = 30 + 10sin[π/26 (x-14)]
When y = 40,(000)
We'll take y as 40.
So, we have
40 = 30 + 10sin[π/26 (x - 14)]
Collect like terms
40 - 30 = 10sin[π/26 (x - 14)]
10 = 10sin[π/26 (x - 14)]
Divide both sides by 10
10/10 = 10sin[π/26 (x-14)] ÷ 10
1 = sin[π/26 (x-14)]
Take sin inverse (arcsin) of both sides in radians
sin-¹(1) = [π/26 (x - 14)]
sin-¹(1) = ½π.. So, we have
½π = π/26 (x - 14)
Multiply both sides by 26/π
26/π * ½π = 26/π * π/26 (x - 14)
13 = x - 14
Make x the subject of formula
x = 13 + 14
x = 27.
Hence, when y = 40,000 x = 27th week.
2. y = 30 + 10sin[π/26 (x-14)]
When y = 35,(000)
We have
35 = 30 + 10sin[π/26 (x - 14)]
Collect like terms
35 - 30 = 10sin[π/26 (x - 14)]
5 = 10sin[π/26 (x - 14)]
Divide both sides by 10
5/10 = 10sin[π/26 (x-14)] ÷ 10
½ = sin[π/26 (x-14)]
Take sin inverse (arcsin) of both sides in radians
sin-¹(½) = [π/26 (x - 14)]
sin-¹(1) = π/6.. So, we have
π/6 = π/26 (x - 14)
Multiply both sides by 26/π
26/π * π/6 = 26/π * π/26 (x - 14)
26/6 = x - 14
4.3 = x - 14
Make x the subject of formula
x = 4.3 + 14
x = 18.3
x = 18 --- Approximated
Hence, when y = 35,000 x = 18th week.
3. y = 30 + 10sin[π/26 (x-14)]
When y = 25,(000)
So, we have
25 = 30 + 10sin[π/26 (x - 14)]
Collect like terms
25 - 30 = 10sin[π/26 (x - 14)]
-5 = 10sin[π/26 (x - 14)]
Divide both sides by 10
-5/10 = 10sin[π/26 (x-14)] ÷ 10
-½ = sin[π/26 (x-14)]
Take sin inverse (arcsin) of both sides in radians
sin-¹(-½) = [π/26 (x - 14)]
sin-¹(-½) = -π/6.. So, we have
-π/6 = π/26 (x - 14)
Multiply both sides by 26/π
-26/π * π/6= 26/π * π/26 (x - 14)
26/6 = x - 14
-4.3 = x - 14
Make x the subject of formula
x = -4.3 + 14
x = 9.7
x = 10 --- Approximated
Hence, when y = 25,000 x = 10th week.
