The weekly number of tourists visiting an island is approximated by the equation given below y equals 30 plus 10 sine left bracket startfraction pi over 26 endfraction left parenthesis x minus 14 right parenthesis right bracket where y is the number of visitors (in thousands) in the xth week of the year, starting with x equals 1 for the first week in january. find the week in which the number of tourists to the island is a. 40 comma 000, b. 35 comma 000, and c. 25 comma 000

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.

the answer is two. hope this !

answer: 80,000

step-by-step explanation:

the population doubles every day.

10,000*2=20,000 day 4

20,000*2=40,000 day 5

40,000*2=80,000 day 6