Answer:
Height of flagpole = 571 ft
Step-by-step explanation:
Given:
Angle of elevation to the top of the flagpole is 55° .
Distance from the eyes to the base of flagpole = 400 ft.
To find the height of the flagpole.
Solution:
We can draw the situation as a right triangle as shown below.
In triangle ABC.
∠C= 55°
To find the length AB (height of the flagpole).
Applying trigonometric ratio :
Plugging in values.
Multiplying both sides by 400.
∴
Height of flagpole = 571 ft
Answer:
The integral diverges
Step-by-step explanation:
Consider the integral from 0 to infinity of
We can do this in parts
When we substitute limits infinity we find that the values become infinity
Hence the integral diverges
The given improper integral diverges
Answer: Karen picked 1200 pounds.
Bob picked 600 pounds.
Gina picked 400 pounds.
Step-by-step explanation:
Let x represent the number of pounds of oranges that Karen picked.
Let y represent the number of pounds of oranges that Bob picked.
Let z represent the number of pounds of oranges that Gina picked.
Karen picked twice as many pounds as Bob. It means that
x = 2y
y = x/2
Karen picked 3 times as many as Gina picked. It means that
x = 3z
z = x/3
The total weight of the oranges they picked was 2,200 pounds. This means that
x + y + z = 2200- - - - - - - - - -1
Substituting y = x/2 and z = x/3 into equation 1, it becomes
x + x/2 + x/3 = 2200
Cross multiplying by 6, it becomes
6x + 3x + 2x = 13200
11x = 13200
x = 13200/11
x = 1200
y = 1200/2 = 600
z = 1200/3 = 400
A central angle : π / 6 = 30 °
30 ° = 360 ° / 12
The area of the sector is 1/12 of the area of a circle.
Therefore area of the sector is:
A = 36 π / 12 = 3 π
Answer: A ) 3 π in²